# Archive

Here we archive past talks (abstracts, handouts, links, …).

### 2024

- April 25, Paige North (Utrecht)

**The Univalence Principle**

The Equivalence Principle is an informal principle asserting that equivalent mathematical objects have the same properties. For example, group theory has been developed so that isomorphic groups have the same group-theoretic properties, and category theory has been developed so that equivalent categories have the same category-theoretic properties (though sometimes other, ‘evil’ properties are considered). Vladimir Voevodsky established Univalent Foundations as a foundation of mathematics (based on dependent type theory) in which the Equivalence Principle for types (the basic objects of type theory) is a theorem. Later, versions of the Equivalence Principle for set-based structures such as groups and categories were shown to be theorems in Univalent Foundations.

In this work, we formulate and prove versions of the Equivalence Principle (using the “Univalence Principle”) for a large class of categorical and higher categorical structures in Univalent Foundations. Our work encompasses bicategories, dagger categories, opetopic categories, and more. Many of the notions used in our work were inspired by Makkai’s First-order logic with dependent sorts.

Time: 15.30 – 17.00

Location: Drift 6, room 0.07

- April 4, Davide Grossi (Groningen/Amsterdam)

**Deliberative Consensus**

I will present a model of deliberative processes. The model focuses on a setting in which a community wishes to identify a strongly supported proposal from a large space of alternatives, in order to change a ‘status quo’ alternative. Agents dynamically form coalitions around proposals that they prefer over the status quo. Using this model I will show how the properties of the underlying abstract space of proposals and the ways in which agents can form coalitions affect the success of deliberation in identifying consensus positions. We show that, as the complexity of the proposal space increases, more complex forms of coalition formation are required in order to guarantee success. Intuitively, this seems to suggest that complex deliberative spaces require more sophisticated coalition formation abilities on the side of the agents. The model aims at providing theoretical foundations for the analysis of deliberative processes in platforms for democratic deliberation support.

This is joint work with Edit Elkind (University of Oxford), Ehud Shapiro (Weizmann Institute) and Nimrod Talmon (Ben-Gurion University).

Time: 15.30 – 17.00

Location: Janskerkhof 13, room 0.06 (Stijlkamer)

- March 14, Dragan Doder (Utrecht)

**Interplay between beliefs and intentions in dynamic environments**

This talk is based on joint work with Mehdi Dastani, Marc van Zee, Leon van der Torre, Thomas F. Icard III and Eric Pacuit, published in Artificial Intelligence journal 2020. In my talk I will present some results on the interplay of beliefs and intentions. I will present a formal system for reasoning about actions, time and belief, in which assumptions of actions are represented by their preconditions. Intended actions are coherent with beliefs, as long as these assumptions are not violated, i.e. as long as the actions can be performed, such that their preconditions hold as well. Then, I will formalize what-if scenarios: what happens with actions and beliefs if a new intention is adopted, or if the belief base is updated? The agents are committed to their intended actions as long as their belief-intention databases are coherent. I will present postulates for revision operators of those databases, and a Katsuno-Mendelzon-style representation theorem which characterizes all the revision operators that satisfy the postulates. Finally, I will briefly present some current and future work based on this paper.

Time: 15.30 – 17.00

Location: Janskerkhof 13, room 0.06 (Stijlkamer)

- February 15, Federico Pailos (CONICET/Buenos Aires)

**Suprastructural logics**

Over the last decades, considerable attention has been paid to substructural logics, that is, logical systems that forego at least one of the structural principles sanctioned by classical logic. However, little or no attention has been paid to the dual notion of a suprastructural logic, that is, a system that sanctions at least one structural principle that classical logic foregoes. In the present paper we explore this notion and present different types of systems where at least one classically invalid structural metainference holds. We introduce two families of contrastructural logics: Boolean logics and Strong-Kleene logics. Afterwards, we present some strictly suprastructural logics. We show that LP and K3 are strictly suprastructural from a global perspective. We then introduce some metainferential logics that are strictly suprastructural from a local perspective, and show that some of them are also supraclassical. This leads us to consider two different notions of suprastructurality: one that focuses on metainferences and the other that focuses on closure properties.

Time: 15.30 – 17.00

Location: Janskerkhof 13, room 0.06 (Stijlkamer)

- January 25, Aleksi Anttila (ILLC, Amsterdam)

**Propositional and modal team semantics: the failure of downward closure
**

In team semantics (introduced by Hodges (1997)), formulas are evaluated with respect to sets of evaluation points called teams, as opposed to the single evaluation points of standard Tarski-style semantics. The shift to teams allows for the perspicuous articulation of certain phenomena which are not readily expressible in the standard semantics: Väänänen’s (2007) dependence logic, for instance, introduces team-semantic atoms which denote dependence relations not expressible in first-order logic.

The most prominent team-based logics are downward closed, meaning that if a formula of one of these logics is true in a team T, it is also true in all subteams of T. Expressive completeness theorems with respect to closure properties such as downward closure play an important role in the study of propositional and modal team semantics—a common method for proving the completeness of an axiomatization, for instance, makes use of such theorems. In this talk, I examine a number of propositional and modal team-based logics which fail to be downward closed, present expressive completeness theorems for these logics, and give examples of how such theorems are utilized.

Time: 15.30 – 17.00

Location: Drift 6, room 0.07

### 2023

- December 7, Fan Yang (Utrecht)

**Propositional and modal team semantics: an overview**

Abstract: Team semantics was introduced by Hodges in 1997 primarily to provide a compositional semantics for Hintikka and Sandu’s independence-friendly logic (1989). This framework was further developed by Väänänen in dependence logic (2007), a formalism for reasoning about dependence and independence relations. The fundamental idea of team semantics is that dependency properties manifest themselves in multitudes. Logics based on team semantics thus evaluate formulas on sets of first-order assignments or sets of possible worlds (called teams), instead of single assignments or single possible worlds as in the traditional semantics. This shift provides a versatile perspective, applicable to various fields, with teams representing relational databases, datasets, or information states. Notably, inquisitive semantics (Ciardelli and Roelofsen, 2011), with the goal of characterising questions in natural language, independently also adopts team semantics.

This talk aims to provide a concise overview of the core theory of team semantics and highlight recent research within this framework, focusing particularly on propositional and modal logics.

Time: 15.30 – 17.00

Location: Janskerkhof 13, room 0.06 (Stijlkamer)

- November 16, Wessel Kroon (ILLC, Amsterdam)

**Knowledge as issue-relevant information**

In standard epistemic logic, knowledge is equated with information possession. A growing body of literature, however, posits that knowledge encompasses more than undirected information. Following this line of research, we take inquiry to be fundamental in knowledge acquisition and put forth a notion of knowledge as information that is relevant with respect to an agent’s issues. We argue that a framework based on this notion leaves room for the goal-directed nature of epistemic processes. As a consequence, contentious epistemic principles such as closure under deduction and positive introspection are restricted in a principled manner. We draw on Minica’s issue-epistemic models in order to formally capture knowledge and issue-relevance. Several logics dealing with information, issue-relevance and knowledge are axiomatized and proven to be sound and complete with respect to these models. Finally, we show that the static framework can be enhanced in order to accommodate a dynamic logic that cannot only model information change, but also the process of gaining or losing interest in issues.

Time: 15.30 – 17.00

Location: Janskerkhof 13, room 0.06 (Stijlkamer)

- October 26, Fabio Lampert (Universität Greifswald)

**No-choice closure and the contingent a priori: a new way out of theological fatalism**

There are ancient arguments purporting to show that divine omniscience is incompatible with free will. In recent decades, interesting and strong formulations of such arguments have been presented relying on a closure principle according to which no one has a choice about a truth that is entailed (i.e. strictly implied) by a truth no one has a choice about. I will argue that this principle leads to seemingly paradoxical arguments when paired with truths involving contingent a priori knowledge and widely held assumptions from modal logic and semantics. I will suggest that a rejection of the aforementioned closure principle is the less costly solution to the paradoxes in question, which would therefore disarm, too, some of the best arguments for theological fatalism.

Time: 15.30 – 17.00

Location: Drift 6, room 0.07

- September 28, Albert Visser (Utrecht)

**Clash of the Titans: Markov versus Smullyan**

What is a good Gödel numbering? This question has technical, didactical, and philosophical aspects. In my talk, I zoom in on two concrete initial steps towards Gödel numberings, one due Andrey Markov jr. (in 1954) based on SL|2(**N**) and one due to Raymond Smullyan (in 1961) based on the length-first ordering. I will present these initial steps towards Gödel numberings in some detail and will discuss possible follow-up steps to obtain full Gödel numberings. Then, I use these two examples as illustration of various technical, didactical and philosophical issues.

Time: 15.30 – 17.00

Location: Drift 6, room 0.07

- June 8, Franz Berto (St Andrews)

**‘I Wasn’t Thinking About That!’ – The Logic of Framing Effects**

*Framing effects* concern the having of different attitudes towards logically or necessarily equivalent propositions. Framing is of crucial importance for cognitive science, behavioral economics, decision theory, and the social sciences at large. We need a logic of framing.

We argue that framing is grounded in (i) the structural distinction between beliefs activated in *working memory* and beliefs left inactive in *long term memory*, and (ii) the topic- or subject matter-sensitivity of thought: a feature of propositional attitudes which is attracting growing research attention in the literature.

We introduce a class of models featuring (i) and (ii) to represent, and reason about, agents whose belief states can be subject to framing effects. We axiomatize a logic which we prove to be sound and complete with respect to the class.

Time: 15.30 – 17.00

Location: online only!

- May 11, Hein Duijf (Utrecht)

**Individualism, reductive explanations, and logical regularity**

Methodological individualism is the position that all social phenomena are to be explained in terms of the actions and interactions of individuals. Most prominent theories of explanation require the existence of a logical regularity between the explanandum and explananda. In this talk, we show that methodological individualism can be put to logical scrutiny by making the social and individualistic languages fully explicit and mathematically precise. In particular, we combine game theory with formal logic to argue against methodological individualism: we prove that there are no reductive explanations of the statement that a group maximizes expected utility using statements in an individualistic formal language that can be used to model actions, omissions, abilities, and expected utility maximization of finitely many individual agents. (Joint work with Frederik Van De Putte)

Time: 15.30 – 17.00

Location: Ravensteynzaal (Kromme Nieuwegracht 80, room 1.06)

- April 13, Sebastian Speitel (Bonn)

**Logic, Logicality and Arithmetical Determinacy**

Tarski’s model-theoretic definition of logical consequence relies on a division of the expressions of the language under considerations into logical and non-logical. Finding a philosophically motivated and mathematically precise criterion to delineate the logical expressions of a language constitutes the *demarcation problem of the logical constants*.

In this talk, we propose a novel criterion of logicality designed to address the demarcation problem. It combines insights from the model-theoretic as well as from the inferentialist approaches to meaning. According to it a notion qualifies as logical if its inferential behaviour determines a unique denotation among logically acceptable interpretations.

In this talk, we propose a novel criterion of logicality designed to address the demarcation problem. It combines insights from the model-theoretic as well as from the inferentialist approaches to meaning. According to it a notion qualifies as logical if its inferential behaviour determines a unique denotation among logically acceptable interpretations.

Time: 15.30 – 17.00

- March 16, Jaap van Oosten (Utrecht)

* Partial Combinatory Algebras, between realizability and oracle computation*

Time: 16.00 – 17.30

Location: Stijlkamer (Janskerkhof 13, room 0.06)

- February 16, Giorgio Lenta (Genoa/FINO)

* The Hyperintensional Kaplan’s Paradox*

David Kaplan famously argued that mainstream semantics for modal logic, which identifies propositions with sets of possible worlds, is affected by a cardinality paradox. A new version of the paradox arises for every logical framework that validates an intuitive principle, when the semantics is extended with impossible worlds to deliver a hyperintensional account of propositions. I discuss two general approaches to a solution: giving up on sets and giving up on worlds, either in the semantics or in the corresponding picture of propositions. I argue that a truthmaker-based approach offers the most promising way to account for hyperintensional propositions, without facing the paradoxical outcome.

Time: 15.30 – 17.00

- January 26, Frederik Van De Putte (Rotterdam)

**Deontic Game Multiplication, Reduction Theorems, and Acceptability Voids**

Deontic games are normal form games equipped with a classification of action profiles into those that are acceptable and those that are not. These games have been used in past work to tackle various questions concerning individual and group obligation, group plans and coordination, and method- ological individualism. This paper is the first to develop a combinatorial perspective on such games. In particular, we define three ways to combine any two deontic games, resulting in a new game that represents the simulta- neous play of both original games. We then study the relation between the deontic status of group actions in the new game and the deontic status of the corresponding sub-actions in the original games, establishing a number of fundamental reduction theorems. From these, we derive several corollaries concerning the existence of acceptability voids in interaction scenarios.

Time: 15.30 – 17.00

Location: Ravensteynzaal (Kromme Nieuwegracht 80, room 1.06)

*A video recording of this talk is available on MS Teams, in the channel ‘Frederik van de Putte’ of the TULIPS team. If you would like to become a guest of the team, let us know.*

### 2022

- November 17, Diego Tajer (Buenos Aires / MCMP)

**Derivative normativity and logical pluralism**

In a recent article, Gillian Russell (2020) claims that logic isn’t normative: according to her, the usual bridge principles are just derived from general principles for truth and falsity, such as “believe the truth” or “avoid falsity”. For example, we should believe tautologies just because we should believe the truth. Russell argues that this rejection of logical normativity can avoid the collapse objection for logical pluralism. In a different paper, Russell and Blake Turner (2021) defend a telic pluralism, where different logics may correspond to different epistemic aims, without assuming that logic is normative.

In a response to that paper, Stei (2020) claims that even if logic is normative in this weak derivative sense, the collapse objection re-emerges. His main point is that the collapse argument can still work even if the bridge principles are derivative (they just need to be true).

In this talk I will argue against Stei’s point. I will show that there is a possible strategy which maintains the derivative normativity of logic and provides a non-trivial logical pluralism. My proposal is different from the telic pluralism, for it does not depend on the epistemic aims of the agent. The key of my approach is the possibility of having different normative sources for different logics. I will argue that the distinction between classical and relevant logic can be understood in this way.

References

Blake-Turner, C. and G. Russell, “Logical pluralism without the normativity”, Synthese 198, 2021, pp. 4859-4877.

Russell, G. “Logic isn’t normative”, Inquiry 63(3-4), 2020, pp. 371-388.

Stei, E. “Non-normative logical pluralism and the revenge of the normativity objection”, Philosophical Quarterly 70 (278), 2020, pp. 162–177.

Time: 15.30 – 17.00

Location: Ravensteynzaal (Kromme Nieuwegracht 80, room 1.06).

- September 29, Benjamin Rin (Utrecht)

**The Computational Complexity of Arimaa**

Arimaa is a two-player strategy game played on an 8 x 8 board. Like chess, checkers, and Go, it is a perfect-information, deterministic, turn-based game in which there is at most one winner. Arimaa has been a focus of much attention in applied AI research, as it was originally designed purposely to be difficult for computers to play.

This talk considers the more theoretical question, “Given a position in Arimaa and specified player, does that player have a winning strategy?” As with chess and checkers, this question is trivially solvable in constant time if the game is played on a standard 8 x 8 board (albeit for an impractically large constant). Accordingly, we focus instead on the question for the generalized case of an n x n board. For the aforementioned strategy games, the corresponding question is known to be PSPACE-hard. That is, solving (n x n) chess, checkers, etc. is at least as complex as any computational task in PSPACE–the class of problems solvable by Turing machines using an amount of space (memory) that grows as a polynomial function of the input size n. We prove in this talk that the same is true for Arimaa. Thus Arimaa is about as computationally complex as these other (classic) games. We prove this result by reduction from the known PSPACE-hard problem Generalized Geography, adapting a technique of Storer’s in his 1983 paper originally showing the PSPACE-hardness of (n x n) chess.

(Joint work with A. Schipper.)

Time: 15.30 – 17.00

Location: Stijlkamer (Janskerkhof 13, room 0.06).

- June 14, Nils Kürbis (Bochum and Lodz)

**A Theory of Definite Descriptions
**

According to Russell, a definite description is an expression of the form `The F’. They are incomplete symbols that mean nothing in isolation, and only in the context of complete sentences of the form `The F is G’, from which they disappear upon analysis. `The F is G’ is equivalent to `There is exactly one F and it is G’. For Russell, if there is no F, then any sentence of this form is false. Free logicians argue against Russell and that sometimes such sentences can be true. In free logic, definite descriptions are generally treated as genuine singular terms. But Russell surely had a point that we can draw distinctions of scope, for instance between `The F is not G’ and `It is not the case that the F is G’. This would require a means of introducing scope distinctions into the logic, which in free logic is generally not done. In my talk I will present a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means `The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown to be sound and complete for the semantics. The system has a number of novel features and is briefly compared to the usual approach of formalising `the F’ by a term forming operator in free logic. It does not coincide with Hintikka’s and Lambert’s preferred theories, but the divergence is well-motivated and attractive. Viewed from the perspective of proof theoretic semantics, the systems lets us decide various questions concerning the logic of definite descriptions in a principled way.

Time: 16.00 – 17.15

Location: Ravensteynzaal (Kromme Nieuwegracht 80, room 1.06).

- April 12, Andrew Tedder (Bochum)

**The Algebraic Structure of Mares-Goldblatt Models**

Mares and Goldblatt have introduced a general framework for providing frame-based semantics for which quantified relevant logics are complete (avoiding the incompleteness noted by Fine of these logics w.r.t. the simple `constant domain’ extensions of their usual frame-based semantics). In this talk, I’ll generalise and abstract away some of the frame-specific machinery of the Mares-Goldblatt framework in order to get a clearer idea of their algebraic structure. In so doing, I’ll consider issues relating to general completeness proofs for quantified extensions of logics complete w.r.t. certain classes of algebras (especially gaggles, following Dunn), mention some connections to related avenues of research in the model-theory of quantified non-classical logics, and suggest some potential applications of the resulting framework.

Time: 16.00 – 17.15

Location: Ravensteynzaal (Kromme Nieuwegracht 80, room 1.06).

- March 8, Revantha Ramanayake (Groningen)

**The first steps in cut-restriction**

Cut-elimination is a fundamental result of proof theory. It is the algorithm for eliminating cuts from a sequent calculus proof, leading to cut-free calculi and applications. Although the algorithm is remarkably robust in the sense that it applies with few amendments to many logics (irrespective of their semantics), it simply does not hold for most logics. Its importance is such that the invariable response is a move from the sequent calculus to richer proof formalisms in a bid to regain the cut-elimination. In this talk I will discuss the first steps in a radically different approach called cut-restriction: identifying how to adapt Gentzen’s age-old cut-elimination arguments to restrict the shape of the cut-formulas when elimination is not possible. I will present the “first level above cut-free”: restricting the standard sequent calculi for bi-intuitionistic logic and S5 to analytic cuts. These are two logics where (analytic) cuts are known to be essential.

This is joint work with Agata Ciabattoni (TU Wien) and Timo Lang (UCL).

Time: 16.00 – 17.15

Location: Online.

- February 22, Igor Sedlár (Czech Academy of Sciences)

**Generalized Scott-Montague Semantics for Hyperintensional Modal Logics**

In Montague–Scott semantics, the modal box operator represents a property of sentential intensions, that is, propositions or sets of possible worlds. It follows that all logics modelled by this kind of semantics are intensional: if A and B necessarily express the same proposition, then so do Box A and Box B. This is obejctionable on many readings of Box, notorious examples being propositional attitudes. A more realistic formalization of such examples, it is argued, calls for hyperintensional modal logics, where Box A and Box are are not necessarily equivalent even for necessarily equivalent A and B.

Different semantic frameworks for hyperintensional modal logics have been formulated. In a recent paper (Hyperintensional logics for everyone. Synthese 198, 933-956, 2021), I have introduced a generalization of Montague–Scott semantics in which the Box operator expresses properties of “semantic contents” which in turn determine propositions in the standard sense. The nature of these contents is left undetermined, which renders the semantic framework rather general.

In the first part of the talk, I will outline the generalized Scott–Montague semantic framework and I will show that many well-known semantics for hyperintensional modalities are special cases. In the second part of the talk, I outline recent joint work with M. Pascucci in which we use the framework to give a semantics for some weak modal logics.

Time: 16.00 – 17.15

Location: Online.

- January 25, Stipe Pandzic (Utrecht)

**Default justification logic as a logical theory of arguments**

In the 1980s, John Pollock’s work on defeasible reasons started the quest in the AI community for a formal system of defeasible argumentation. My goal in this talk is to present a logic of structured defeasible argumentation using the language of justification logic. One of the key features that is absent in standard justification logics is the possibility to weigh different epistemic reasons that might conflict with one another. To amend this, we develop a semantics for “defeaters”: conflicting reasons forming a basis to doubt the original conclusion or to believe an opposite statement. Formally, non-monotonicity of reasons is introduced through default rules with justification logic formulas.

Justification logic formulas are then interpreted as arguments and their acceptance semantics is given in analogy to Dung’s abstract argumentation framework semantics. In contrast to argumentation frameworks, determining arguments’ acceptance in default justification logic simply turns into finding (non-monotonic) logical consequences from a starting theory with justification assertions. We can show that a large subclass of Dung’s frameworks is a special case of default justification logic. By the end of the talk, I will briefly connect this logic with Pollock’s original motivation to deal with the justified-true-belief definition of knowledge.

Time: 16.00 – 17.15

Location: Online.

*A video recording of this talk is available on MS Teams, in the channel ‘Stipe Pandzic’ part of the TULIPS team. If you would like to become a guest of the team, let us know.*

- January 11, Iris van der Giessen (Utrecht)

**The form of proofs and structure of logics**

In this TULiPS talk, I would like to provide a high-level overview of the work of my PhD under supervision of Rosalie Iemhoff and Nick Bezhanishvili. I am studying two topics in the field of proof theory: uniform interpolation and admissible rules. I apply both topics to (intuitionistic) modal logics.

The first is used to describe the form of proof systems in terms of so-called negative results: if a logic does not have uniform interpolation then it cannot have a sequent calculus with certain nice properties. The aim of my research is to widen the scope to proof formalisms such as nested sequents. The second part is a study on the structure of logics. The admissible rules are those rules that you can add to a logic without changing its set of theorems. One of my main results is a characterization of the admissible rules of six interesting intuitionistic modal logics.

Time: 16.00 – 17.15

Location: Online.

### 2021

- December 14, Marcus Rossberg (Connecticut)

**An Inferentialist Redundancy Theory of Truth**

I present a “fully schematic”, proof-theoretic account of higher-order logic. The framework allows for the explicit definition of truth predicates for arbitrarily strong theories formulated in the framework. Thus, arguably, for any reasonable language, a truth predicate is explicitly definable with purely logical, proof-theoretic means. Enough “truth” should thus be available to the inferentialist to do the theoretical work that opponents claim is wanting. Furthermore, deflationists claim that the truth-predicate does not express a substantive property, but is only required to express generalizations (and such like). On the account presented here, truth-predicates are strictly purely logical, and indeed eliminable since they are logically definable. Deflationism appears to collapse into a redundancy theory of truth.

Time: 16.00 – 17.15

Location: Online.

- November 23, Natasha Alechina (Utrecht)

**Responsibility in multi agent teams**

Responsibility for team plan failures and other events arising in the context of multi-agent interaction is an interesting concept to model formally. I will talk about previous joint work with Joseph Halpern and Brian Logan on modelling responsibility for failure of team plans in causal models, and an on-going work in progress on expressing the same notion in logics of strategic ability.

Time: 16.00 – 17.15

Location: Online.

- November 9, Zoé Christoff (Groningen)

**Priority Merge and Intersection: from group attitudes to collective truth-tracking**

The logic part of the talk is based on joint work with Olivier Roy and Norbert Gratzl (Review of Symbolic Logic, 2021), and the formal learning theoretic part is based on ongoing joint work with Nina Gierasimczuk and Thomas Skafte.

Time: 16.00 – 17.15

Location: Ravensteynzaal (Kromme Nieuwegracht 80, room 1.06).

- October 26, Thomas Ferguson (ILLC, Amsterdam)

**Subject-Matter and Nested Topic-Sensitive Intentional Modals**

The framework of topic-sensitive intentional modal operators (TSIMs) described by Berto provides a general platform for representing agents’ intentional states of various kinds. For example, a TSIM can model doxastic states, capturing a notion that given the acceptance of antecedent information P, an agent will have a consequent belief Q. Notably, the truth conditions for TSIMs include a subject-matter filter so that the topic of the consequent Q must be “included” within that of the antecedent P. In practice, the types of intentional states modeled by TSIMs can be nested within one another–one can have beliefs about beliefs, one can imagine that one knows, etc. The device of the subject-matter filter, however, requires that modeling the semantics of such nested TSIMs requires an adequate account of the subject-matter of sentences in which a TSIM appears. In this talk, I will discuss extending earlier work on the subject-matter of intensional conditionals to the special case of TSIMs and argue that the account provided is adequate both formally and philosophically.

Time: 16.00 – 17.15

Location: Online.

- October 12, Sonia Marin (University College London)

**Ecumenical modal logic **

Recent works about ecumenical systems, where connectives from classical and intuitionistic logics can co-exist in peace, warmed the discussion of proof systems for combining logics, called Ecumenical systems by Prawitz and others.

In Prawitz’ system, the classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation, and the constant for the absurd, but they would each have their own existential quantifier, disjunction, and implication, with different meanings.

We extended this discussion to alethic K-modalities: using Simpson’s meta-logical characterization, necessity is shown to be independent of the viewer, while possibility can be either intuitionistic or classical.

We furthermore proposed an internal and pure calculus for ecumenical modalities, where every basic object of the calculus can be read as a formula in the language of the ecumenical modal logic.

(joint work with Elaine Pimentel, Luiz Carlos Pereira, and Emerson Sales, partially published in the proceedings of Dali’20 and WoLLiC’21)

Time: 16.00 – 17.15

Location: Online.

- September 14, Dominik Klein (Utrecht University)

**Worlds far apart: From Kripke Models to Dynamical Systems**

In this talk, we explore the universe of iterated information updates on a logical model. In particular, we show how iterated updates can be understood as a discrete time dynamic system.

In the first part of this talk, we show how to define distances between pointed Kripke models. These distances can be tailored to the modeler’s needs, putting much weight on propositions that are important for the purpose at hand and discounting those that are not. We then explore the resulting topological spaces and characterize compactness and when different metrics lead to the same topology.

In the second part, we show two applications of the metrics defined: First, our metrics allow to classify which sequences of Kripke Models converge in the limit. With this in hand, we can classify when a social protocol reaches its aim and whether this can be reached in finite time, in the limit or not at all. As a second application, we show that logical product updates with postconditions are continuous in the topology defined. Hence, the space of Kripke models together with iterated product updates forms a discrete time dynamical system.Time permitting we also show that the resulting dynamic system can display non-trivial limit behavior. This is joint work with Rasmus Rendsvig.

Time: 16.00 – 17.30

Location: Online

- June 8, Bjørn Jespersen (Utrecht University)

**Transparent quantification into hyperpropositional contexts de dicto (joint work with Mari Duží)**

We prove how to validly quantify into hyperpropositional contexts de dicto in Transparent Intensional Logic. Hyperpropositions are sentential meanings and attitude complements individuated more finely than up to logical equivalence. A hyperpropositional context de dicto is a context in which only co-hyperintensional propositions can be validly substituted. A de dicto attitude ascription is one that preserves the attributee’s perspective when one complement is substituted for another. Being an extensional logic of hyperintensions, Transparent Intensional Logic validates all the rules of extensional logic, including existential quantification. Yet the rules become more exacting when applied to hyperintensional contexts. The rules apply to only some types of entities, because the existence of only some types of entities is entailed. The insight that the paper offers is how a particular logic of hyperintensions is capable of validating quantifying-in in a principled and rigorous manner. This result advances the community-wide understanding of how to logically manipulate hyperintensions.

Time: 16.00 – 17.15

Location: Sweelinckzaal (Drift 21, room 005)

- May 25, Mark Jago(Nottingham)

**Metaphysical Structure**

Metaphysical structure is the way things hang together, in and of themselves, and aside from their causes and effects and propensities to behave. Examples include: truth depending on reality, the mind depending on the brain, sets depending on their members, disjunctions depending on their disjuncts, wholes depending on their parts, types being realised by their tokens, determinables being determined by their determinates. These might all be understood as cases of grounding – or rather, they might if we understood what grounding is. In this talk, I investigate parallels between metaphysical construction and familiar logical operators. First, there’s a link between composition (of parts into a whole) and conjunction. Second, I argue, there’s a link between some familiar metaphysical relations and disjunction. On the picture that emerges, metaphysical structure may be understood as logical structure, whilst remaining a genuine mind, concept, and language-independent feature of reality.

Time: 16.00 – 17.15

Location: Online

- May 11, Anthi Solaki (ILLC, Amsterdam)

**Actualizing Distributed Knowledge in Bounded Groups**

The idealizations resulting from the use of Kripke semantics in Epistemic Logic are inherited by formalizations of group epistemic notions. For example, distributed knowledge is often taken to reflect the potential knowledge of a group: what agents would know if they had unbounded means of communication and deductive ability. However, this does not specify whether/how this potential can be actualized, especially since real people are not unbounded reasoners. Inspired by experiments on group reasoning, we identify two dimensions of actualizing distributed knowledge: communication and inference. We build a dynamic framework with effortful actions accounting for both, combining impossible-worlds semantics and action models, and we provide a method for extracting a sound and complete axiomatization.

Time: 16.00 – 17.15

Location: Online.

- April 27, Pablo Cobreros (University of Navarra)

**Classicality and the ST approach to paradoxes**

This talk provides an overview on the ST approach to paradoxes detailed and defended in CERvR (2012) and CERvR (2013). The ST approach has a remarkable feature: it gives you (in a certain sense) classical logic for a classical vocabulary, but it doesn’t lead you to absurdities in the presence of tolerance principles or a truth-predicate. It follows from the previous that ST cannot be fully classical. Now explaining exactly what ‘full classicality’ means is much trickier than it might appear at first glance (cf. Barrio, Pailos and Szmuc (2020) and related papers). The non-classicality of ST can be investigated by looking at the validity of *metainferences*. Alternatively, the non-classicality of ST can be investigated by looking at inferences, but in relation to properties other than validity. There is a correspondence between these two approaches (this is stated, or at least, indicated in Cobreros, La Rosa and Tranchini).

**References:**

*JPL*, 49(1): 93-120.

*JPL*41(2): 347-385.

*Mind*122: 841-866.

Cobreros, P., La Rosa, E. and Tranchini, L. (2020) (I Can’t Get No) Antisatisfaction, *Synthese *https://rdcu.be/ciJmi

Time: 16.00 – 17.15

Location: Online

- April 13, Helle Hvid Hansen (Groningen)

**Complete Proof Systems for Parikh’s Game Logic**

Game logic was introduced by Rohit Parikh in the 1980s as a generalisation of propositional dynamic logic (PDL) for reasoning about outcomes that players can force in determined 2-player games. Semantically, the generalisation from programs to games is mirrored by moving from Kripke models to monotone neighbourhood models. Parikh proposed a natural PDL-style Hilbert system which was easily proved to be sound, but its completeness remained an open problem.

In our LISC 2019 paper, we introduce a cut-free sequent calculus for game logic, and two cut-free sequent calculi that manipulate annotated formulas, one for game logic and one for the monotone μ-calculus, the variant of the polymodal μ-calculus where the semantics is given by monotone neighbourhood models instead of Kripke structures. We show these systems are sound and complete, and that completeness of Parikh’s axiomatization follows. Our approach builds on ideas and results by Afshari & Leigh (LICS 2017) in that we obtain completeness via a sequence of proof transformations between the systems. A crucial ingredient is a validity-preserving translation from game logic to the monotone μ-calculus.

Joint work with Sebastian Enqvist, Johannes Marti, Clemens Kupke and Yde Venema.

Time: 16.00 – 17.15

Location: Online

- April 6, Nick Bezhanishvili (ILLC, Amsterdam)

**Linear bi-intuitionistic calculus**

In this talk I will overview the logic bi-LC obtained by adding the linearity (Goedel-Dummett) axiom to the bi-intuitionistic calculus bi-IPC. I will discuss some important properties of this logic and highlight the many differences with the Goedel-Dummett intermediate logic LC. I will also mention some open problems about bi-LC and related systems.

Time: 16.00 – 17.15

Location: Online

- March 23, Sebastian Melzer (ILLC, Amsterdam)

**Canonical Formulas for the Lax Logic**

In this talk, we will investigate the method of canonical formulas for propositional lax logic. We construct “lax canonical formulas” using the local finiteness of the variety of nuclear implicative semilattices. These formulas provide a uniform axoimatization method for lax logics. Then we extend generalized Esakia duality to account for nuclear implicative semilattice homomorphisms between nuclear Heyting algebras, and explore the feasibility of lax analogues of subframe logics. This leads to the introduction of steady logics — logics characterized by generalized lax canonical formulas that only partially encode the modal structure of nuclear Heyting algebras. Finally, we use these generalized lax canonical formulas to obtain a number of preservation theorems, for example, we will prove that for each Kripke-complete intermediate logic the least lax logic containing it is also Kripke-complete.

Time: 16.00 – 17.15

Location: Online

- March 9, Lucas Rosenblatt (CONICET, Buenos Aires)

**Recapture Results and Classical Logic**

The discussion on whether non-classical approaches to the semantics paradoxes can recover classical reasoning for non-problematic statements (what is sometimes referred to in the literature as ‘classical recapture’) is of the utmost importance for non-classical logicians. To show that classical logic can be recovered in certain contexts—and thus bolster the case for the suitability of their favored logic—these theorists sometimes establish so-called ‘recapture results’.

However, in a recent paper Jack Woods has argued that there is a problem with this strategy. In proving recapture results non-classical theorists typically employ classical principles that they themselves reject. In view of this one can conclude that these theorists are not entitled to these results, given that, presumably, they are not available unless classical logic is used. What non-classical logicians need to show, according to Woods, is that, by the standards of their own logic, classical recapture is possible. In this talk I will try to resist Woods’ objection. In particular, I will suggest that there is an ambiguity in his line of argument, one that can be made visible only if one focuses on the specific instances of the classical principles that are needed to obtain recapture results. Once the ambiguity is removed, one can see that there is no problem with the recapture strategy.

Time: 16.00 – 17.15

Location: Online

- February 9, Emil Jerabek (Czech Academy of Sciences)

**Disjunction properties in modal proof complexity**

When studying the proof complexity of classical logic, one of the basic tools is feasible interpolation, which gives a way to transform circuit lower bounds into length-of-proof lower bounds. A similar role in the proof complexity of modal logics is played by the feasible disjuction property, which is at the core of known lower bounds on modal Frege and extended Frege (EF) proof systems.

In this talk, we will discuss the feasibility of variants of the disjunction property (and more general extension rules) in some modal logics, and its application for length-of-proof separation of EF from SF (substitution Frege) proof systems for modal logics of unbounded branching. Finally, we will have a look at the complexity of the disjunction property in basic logics of bounded branching.

Time: 16.00 – 17.15

Location: Online

- January 26, Francesca Poggiolesi (Paris 1, CNRS, IHPST)

**Explanatory proofs (or grounding proofs): philosophical framework, core ideas and results**

In this talk we explore the concept of explanatory proofs, namely proofs that not only show that a theorem is true, but also provide reasons why it is true. After a philosophical introduction of this kind of proof, we provide a characterization and a formalization. We conclude the talk by offering a plethora of results/directions of future research that explanatory proofs lead to.

Time: 16.00 – 17.15

Location: Online

- January 12, Raheleh Jalali (Utrecht)

**On Hard Theorems**

Given a proof system, how can we specify the “hardness” of its theorems? One way to tackle this problem is taking the lengths of proofs as the corresponding hardness measure. Following this route, we call a theorem hard when even its shortest proof in the system is “long” in a certain formal sense. Finding hard theorems in proof systems for classical logic has been an open problem for a long time. However, in recent years as a significant progress, many super-intuitionistic and modal logics have been shown to have hard theorems.

In this talk, we will extend the aforementioned result to also cover a variety of weaker logics in the substructural realm. We show that there are theorems in the usual calculi for substructural logics that are even hard for the intuitionistic systems. More precisely, we provide a sequence of substructural tautologies {A_n}_{n=1}^{\infty} in a way that even their shortest intuitionistic proofs are exponentially long in the lengths of A_n.

Time: 16.00 – 17.15

Location: Online.

### 2020

- December 22, Edi Pavlovic (Helsinki) [joint work with Norbert Gratzl]

**A More Unified Approach to Free Logics**

Free logics is a family of first-order logics which came about as a result of examining the existence assumptions of classical logic. What those assumptions are varies, but the central ones are that (i) the domain of interpretation is not empty, (ii) every name denotes exactly one object in the domain and (iii) the quantifiers have existential import. Free logics usually reject the claim that names need to denote in (ii), and of the systems considered in this paper, the positive free logic concedes that some atomic formulas containing non-denoting names (including self-identity) are true, while negative free logic rejects even the latter claim.

Time: 16.00 – 17.15

Location: Online.

- December 8, Bogdan Dicher (Lisbon) [joint work with Francesco Paoli]

**Metainferential harmony: Harmony without Identity and Cut**

Proof-theoretic semantics aims to explain the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. One of its central concepts is that of *harmony*: roughly, the match between the rules stipulating the conditions for introducing a logical constant in a proof and those for eliminating it from a proof. There are many accounts of harmony, most of them are developed against a background that assumes the rules of Identity and Cut, taken to codify the reflexivity and transitivity of logical consequence. We have argued elsewhere that the proof-theoretic project should be approached relative to a *logic*, i.e., relative to a *consequence* relation, and that the consequence relation relevant for proof-theoretic semantics is the one given by the sequent-to-sequent derivability relation in Gentzen systems. This relation is always reflexive, monotonic, and transitive, but it being so does not depend on the availability of sequent rules codifying these properties. In this talk we investigate the prospects for an account of harmony adequate for logics that lack the structural rules of Identity and Cut.

Time: 16.00 – 17.15

Location: Online.

- November 24, Björn Lellmann (SBA Research, Vienna)

**Proof Theory for Modal Tense Logic and Symmetric Modal Logic via Linear Nested Sequents**

Modal logics offering the possibility of travelling backwards along the accessibility relation, such as modal tense logic Kt or symmetric modal logic KB, have often proved difficult to capture satisfactorily from a proof-theoretic point of view. In particular, while ordinary sequent systems, e.g., for KB exist, they rely on an analytic cut rule for completeness. Both tense logic Kt and symmetric modal logic KB have been given cut-free calculi in much more expressive frameworks, arguably the simplest being that of nested sequent calculi. However, the machinery necessary for nested sequents as well as the immediate connection to the semantics raise the question whether these logics can also be captured in a simpler framework.

As a possible contender, recently there has been a resurgence of work in the linear nested sequent framework, an intermediate framework between ordinary and full nested sequents. What was lacking so far, however, were convincing examples for the added expressivity of this frameworks over ordinary sequents, which did not depend on the linear structure of the models for the logics in question.

In this talk I will present joint work with Rajeev Gore showing that modal tense logic Kt and symmetric modal logic KB can indeed be captured in the linear nested sequent framework, thus providing positive answers to both of the above questions.

Time: 16.00 – 17.15

Location: Online

- October 13, Lorenzo Rossi(Munich), [joint work with Michael Glanzberg]

**Truth and Quantification**

Theories of self-applicable truth have been motivated in two main ways. First, if truth-conditions provide the meaning of (several kinds of) natural language expressions, then self-applicable truth is instrumental to develop the semantics of natural languages. Second, a self-applicable truth predicate is required to express generalizations that would not be expressible in natural languages without it. In order to fulfill their semantic and expressive roles, we argue, the truth predicate has to be studied in its interaction with linguistic constructs that are actually found in natural languages and extend beyond first-order logic — modals, indicative conditionals, arbitrary quantifiers, and more. Here, we focus on truth and quantification. We develop a Kripkean theory of self-applicable truth to for the language of Generalized Quantifiers Theory. More precisely, we show how to interpret a self-applicable truth predicate for the full class of type ⟨1, 1⟩ (and type ⟨1⟩) quantifiers to be found in natural languages. As a result, we can model sentences such as ‘Most of what Jane said is true’, or ‘infinitely many theorems of T are untrue’, and several others, thus expanding the scope of existing approaches to truth, both as a semantic and as an expressive device.

Time: 16.00 – 17.15

Location: Online

- October 6, Heinrich Wansing (Bochum)

**A Note on Synonymy in Proof-theoretic Semantics**

The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. The paper develops this idea.

Time: 16.00 – 17.15

Location: Online

- September 22, Erik Stei (Utrecht)

**Validity in Context. Logical Pluralism and 2D-Semantics**

Logical pluralism – the view that there is more than one correct logic – is typically connected to claims about the semantics of the logical vocabulary. A number of authors have claimed that the alleged plurality of correct logical systems can be traced back to the context-sensitivity of the expression “valid” in natural language. In the talk, I explore in what ways the most prominent account of context-sensitivity – Kaplan’s logic LD – can be employed to support this claim. I develop three possible readings of the Kaplanian character of “valid” and assess their weaknesses and strengths.

Time: 16.00 – 17.15

Location: Online.

- June 30, Giuliano Rosella(Torino), [joint work with Vita Saitta & Matteo Plebani]

**Truthmakers, Incompatibility and Modality**

We present an extension of Fine’s truthmaker semantics, obtained by adding an incompatibility relation to Fine’s state space. The resulting framework allows us to improve the semantic clauses for negation and define important notions such as those of (im)possible state and possible world in a new and natural way. We prove some interesting results concerning the interaction between incompatibility, negation and possible worlds, e. g. that possible worlds behave classically with respect to negation; we also give a semantics for the Logic of Exact Entailment, FDE and S5. At the end, we explore various attempts to use the resources of the framework to provide truthmaking clauses for modal sentences.

Time: 16.00 – 17.00

Location: Online

- June 23, Gijs Wijnholds(Utrecht University)

**Reasoning with words, types and tensors**

Computational linguists attempt to make a computer reason about natural language. For this, words and sentence need to be encoded in a suitable numerical form. This is where vector-based semantics comes in: by embedding words in a space in such a way that words similar in meaning will be measurably similar, we allow for efficient representations that encode (some sort of) relationships between words. This idea and its use in deep neural networks have led to successful application in the domain of natural language processing; anno 2020 we have access to several sentence encoders (e.g. Skip-Thoughts of Kiros 2015, InferSent of Conneau et al. 2017, Universal Sentence Encoder of Cer et al. 2018) and contextualised word embeddings (ELMo of Peters et al. 2018, BERT of Devlin et al. 2019). These neural vector approaches are able to map arbitrary text to some vectorial encoding, using state of the art deep learning techniques.

In contrast to purely neural approaches are formal compositional approaches to semantics, that take the meaning of a sentence to be built up by the meaning of individual words, and the way those are combined (Montague 1970). In a type-driven approach, words are assigned types that reflect their grammatical role in a sentence or text, and composition of words is driven by a logical system that assigns a function-argument structure to a sequence of words (Moortgat 2010). Such an approach can be neatly integrated with vector-based semantics of meaning, where individual word meaning is given by the way words are distributed in a large text corpus (Coecke et al. 2010, 2013, Moortgat & Wijnholds 2017).

Earlier talks in this series (Moortgat, Greco) discussed theoretical aspects of compositional distributional models; in this talk I will take the point of view of representation learning: how to learn representations for words and sentences in a way that aligns with some of the key ideas of typelogical grammar?

Compositional tensor-based distributional models assume that individual words are to be represented by tensors, whose order is determined by their grammatical type; such tensors represent multilinear maps, where composition is effectuated by function application. Learning such representations has been done, but often resulted in a large number of parameters to be learnt. We discuss some of these approaches (Grefenstette 2013, Polajnar 2014) as well as a recent new proposal (work in progress) that builds on the adjective skipgram model of (Maillard&Clark 2016).

I end with remarks on the feasibility of tensor-based representation learning, and some suggestions of the options that we are currently investigating, to create wide-coverage type-driven embeddings for Dutch (and beyond!).

Time: 16.00 – 17.00

Location: Online

- June 16, Paul Egré(Jean Nicod, ENS)

**Gibbardian Collapse and Trivalent Conditionals**

This paper discusses the scope and significance of a triviality result stated by Allan Gibbard for indicative conditionals, showing that any indicative conditional that satisfies the Law of Import-Export, is supraclassical, and stronger than the material conditional, must in fact collapse to the material conditional. Gibbard’s result is taken to pose a dilemma for a truth-functional account of conditionals: give up Import-Export, or embrace the two-valued analysis. We show that this dilemma can be averted in trivalent logics of the conditional based on Reichenbach and de Finetti’s idea that a conditional with a false antecedent is undefined. Import-Export and truth-functionality hold without triviality in such logics. We unravel some implicit assumptions in Gibbard’s proof, and discuss a recent generalization of Gibbard’s result due to Branden Fitelson.

Time: 16.00 – 17.00

Location: Online.

- May 12, Tadeusz Litak(University Erlangen-Nürnberg)

**Describable Nuclea, Negative Translations and Extension Stability**

What do soundness/completeness of negative translations of intutionistic modal logics, extension stability of preservativity/provability logics and the use of nuclea on Heyting Algebra Expansions (HAEs) to form other HAEs have in common? As it turns out, in all those cases one appears to deal with a certain kind of subframe property for a given logic, i.e., the question whether the logic in question survives a transition to at least some types of substructures of its Kripke-style or neighourhood-style frames. The nucleic perspective on subframe logics has been introduced by Silvio Ghilardi and Guram Bezhanishvili (APAL 2007) for the purely superintuitionistic syntax (without modalities or other additional connectives). It has not been used so much in the modal setting, mostly because the focus in the field tends to be on modal logics with classical propositional base, and nuclea are a rather trivial notion in the boolean setting. However, things are very different intuitionistically. Since the 1970’s, nuclea have been studied in the context of point-free topologies (lattice-complete Heyting algebras), sheaves and Grothendieck topologies on toposes, and finally arbitrary Heyting algebras (Macnab 1981). Other communities may know them as “lax modalities” or (a somewhat degenerate case of) “strong monads”.

We marry the nuclei view on subframe properties with the framework of “describable operations” introduced to study subframe logics in Frank Wolter’s PhD Thesis (1993). Wolter’s original setting was restricted to classical modal logics, but with minimal care his setup can be made to work intuitionistically and nuclea provide the missing ingredient to make it fruitful. From this perspective, we revisit the FSCD 2017 study soundness and completeness of negative translations in modal logic (joint work with Miriam Polzer and Ulrich Rabenstein) and our present study of extension stability for preservativity logics based on the constructive strict implication (jointly with Albert Visser). Various characterization and completeness results can be obtained in a generic way.

Time: 14.00 – 15.00

Location: Online.

This was a joint event with A|C, the Algebra|Coalgebra Seminar of the ILLC, Amsterdam. (http://events.illc.uva.nl/alg-coalg/)

- April 21, Giuseppe Greco (Utrecht University)

**Vector spaces as Kripke frames**

The compositional distributional approach in computational linguistics has opened the way for an integration of the lexical aspects of meaning into Lambek’s type-logical grammar program. This approach is based on the observation that a sound semantics for the associative, commutative and unital Lambek calculus can be based on vector spaces by interpreting fusion as the tensor product of vector spaces. We build on this observation and extend it to a ‘vector space semantics’ for the general modal Lambek calculus, based on modal algebras over a field K, i.e. vector spaces endowed with a bilinear binary product and a linear binary relation. We regard K-algebras as ‘Kripke frames’ the complex algebras of which are complete residuated lattices. This perspective makes it possible to establish a systematic connection between vector space semantics and the standard Routley-Meyer semantics of modal sub-structural logics.

Time: 16.00 – 17.00

Location: Online.

- March 10, Dominik Klein (Bayreuth/Bamberg), joint work with Soroush Rafiee Rad and Ondrej Majer.

**Four-Valued Probabilities**

First degree entailment (fde) is a four valued propositional logic that complements the classical truth values True and False with two non-classical truth values Neither and Both. The latter two account for the possibility of the available information being incomplete or containing contradictory evidence about some proposition. In this talk, we present a probabilistic extension of fde, i.e. we allow agents to have probabilistic beliefs about the truth and falsity of a proposition.

More specifically, we present two probabilistic versions of fde, one related to the bi-relational, the other to the four-valued semantics of first degree entailment. We provide sound and complete axiomatizations for both and identify a translation function between the two frameworks. Moreover, we identify policies for conditionalization and aggregation on the probability functions defined. More specifically, we analyze four-valued equivalents of Bayes’ and Jeffrey updating and also provide policies for aggregating information from different sources.

Time: 16.00 – 17.30

Location: 101, Drift 25

### 2019

- November 13, Michael Moortgat (Utrecht University)

*Words as tensors; proofs as multilinear maps*

In this talk, I report on a current NWO project that aims to combine the ‘proofs-as-programs’ view on derivational semantics as one finds it in typelogical grammars with a vector-based, distributional modelling of lexical semantics.

Typelogical grammars derive from the ‘Syntactic Calculus’ introduced by Lambek in 1958/1961. The Lambek calculus is a precursor of the ‘parsing as deduction’ method in computational linguistics: the conventional linguistic categories are turned into formulas of a grammar logic; the judgment whether a phrase is syntactically well-formed is the outcome of a process of deduction. Present-day categorial grammars address the expressive limitations of the original syntactic calculus by extending the formula language with control operations that allow for restricted forms of reordering and restructuring. These control operations play a role analogous to the exponentials/modalities of linear logic; they situate typelogical grammars in the broader family of substructural logics.

Compositional interpretation, in a typelogical grammar, takes the form of a structure-preserving map (a homomorphism) that sends types and proofs of the syntax to their counterparts in an appropriate semantic algebra. In the formal semantics approach in the tradition of Montague grammar, the target models are based on a set-theoretic universe of individuals, truth values, and function spaces over them. Semantics of open class lexical items (nouns, verbs, …) is ignored: these items are treated as unanalysed non-logical constants.

From a Natural Language Processing perspective, this agnostic attitude with respect to lexical semantics is disappointing. In fact, a core ingredient of the highly successful NLP applications we see today is the modelling of word meanings a vector in a high-dimensional semantic space representing a word’s context.

To obtain a vector-based compositional interpretation for typelogical grammars, the key idea is simple: a word with an atomic type, say a noun ‘cat’, is interpreted as a vector in Noun space; a word with an n-place functional type, say a transitive verb ‘chase’ requiring a subject and an object, is interpreted as a tensor of rank n+1; the derivation of a phrase ‘dogs chase cats’ then is interpreted as a multilinear map acting on the meanings of the constituting words to produce a vector in Sentence space, where the syntactic combination of the verb with its subject and object is modelled by tensor contraction.

I discuss some challenges for semantic modelling in terms of finite-dimensional vector spaces and (multi)linear maps arising from tensions between the demands of lexical and derivational aspects of meaning.

Time: 16.00 – 18.00

Location: 203, Drift 25

- September 25, Tadeusz Litak (University Erlangen-Nürnberg), joint work with Albert Visser (Utrecht University)

*Loeb constructively meets μ*

A famous result of Solovay identifies the classical modal Loeb system (GL) as the provability logic of Peano Arithmetic. Under this perspective, Goedel’s Second Incompleteness Theorem and Loeb’s Theorem correspond to explicit definability of

fixpoints of modalized formulas in GL. Van Benthem has observed that this definability of fixpoints entails that adding standard fixpoint operators of positive formulas does not increase the expressive power of GL. Visser has analyzed this observation syntactically and extended it to a proof that GL is a retract of the modal *μ*-calculus in a suitably defined category of interpretations. A fully polished theory of such embeddings and translations involving the fixpoint operator and similar binders is yet to be developed; our current efforts focus on utilizing the theory of higher-order rewrite systems (HRS).

Furthermore, we face some interesting problems when studying intuitionistic analogs of such results. First, while the fixpoint theorem for modalized formulas works in intuitionistic GL, the propositional reasoning underlying derivations of van Benthem and Visser is essentially classical. Deep results about the intuitionistic propositional calculus (IPC) established by Pitts and Ruitenburg can be used to overcome this limitation.

Second, over IPC (and sometimes even classically) it is for several reasons natural to look at a more general syntactic setup replacing the box with Lewis arrow, which arithmetically is standardly interpreted in terms of preservativity (although it does admit many other interpretations). As it turns out, there are two major incompatible ways of computing explicit fixpoints for formulas whose principal connective is the strict implication, each requiring a different base logic. Our approach here can be described as the first study of reverse mathematics of explicit fixpoints.

Time: 16.00 – 18.00

Location: 103, Drift 25

- October 23, Colin Caret (Utrecht University)

*Unifying Two Views of Conditionals*

In this talk, my goal is to draw together two traditions that often share similar motives, but reach different views about the logic of conditionals. Lewis and Stalnaker developed a semantics for conditionals based on selection functions, sometimes called the `variably-strict’ conditional. Routley and Meyer developed a semantics for conditionals based on a ternary relation, sometimes called an `enthymematic-relevant’ conditional. These traditions agree that the material and strict conditional are inadequate-and for similar reasons-but traditionally, these camps also disagree on some important details.

Time: 16.00 – 18.00

Location: 103, Drift 25

- June 4, Aybüke Özgün (ILLC), joint work with Francesco Bert (University of St Andrews)

*Dynamic Hyperintensional Belief Revision*

*topic-*or

*subject-*

*matter-sensitivity*: a feature of belief states which is gaining growing attention in the recent literature.

- May 7, Amir Tabatabai (Utrecht University)

**Steenen voor Brood: A Classical Interpretation of the Intuitionistic Logic**

In 1933, Gödel introduced a provability interpretation for the intuitionistic propositional logic, IPC, to establish a formalization for the BHK interpretation, reading intuitionistic constructions as the usual classical proofs [1]. However, instead of using any concrete notion of a proof, he used the modal system S4, as a formalization for the intuitive concept of provability and then translated IPC into S4 in a sound and complete manner. His work then suggested the problem to find the missing concrete provability interpretation of the modal logic S4 to complete his formalization of the BHK interpretation via classical proofs.

In this talk, we will develop a framework for such provability interpretations. We will first generalize Solovay’s seminal provability interpretation of the modal logic GL to capture other modal logics such as K4, KD4 and S4. The main idea is introducing a hierarchy of arithmetical theories to represent the informal hierarchy of meta-theories and then interpreting the nested modalities in the language as the provability predicates of the different layers of this hierarchy. Later, we will combine this provability interpretation with Gödel’s translation to propose a classical formalization for the BHK interpretation. The formalization suggests that the BHK interpretation is nothing but a plural name for different provability interpretations for different propositional logics based on different ontological commitments that we believe in. They include intuitionistic logic, minimal logic and Visser-Ruitenburg’s basic logic. Finally, as a negative result, we will first show that there is no provability interpretation for any extension of the logic KD45, and as expected, there is no BHK interpretation for the classical propositional logic.

[1]. K. Gödel, Eine Interpretation des Intuitionistichen Aussagenkalküls, Ergebnisse Math Colloq., vol. 4 (1933), pp. 39-40.

Time: 16:00 – 17:30

Location: Room 105, Drift 25

- April 16, Sam van Gool (Utrecht University)

*Monadic Second Order Logic as a Model Companion*

Time: 16:00 – 17:30

Location: Room 302, Drift 25

- April 2, Levin Hornischer (ILLC)

**Analyzing the Behavior of Transition Systems**

We develop a novel way to analyze the possible long-term behavior of transition systems. These are discrete, possibly non-deterministic dynamical systems. Examples range from computer programs, over neural- and social networks, to ‘discretized’ physical systems. We define when two trajectories in a system—i.e., possible sequences of states—exhibit the same type of behavior (e.g., agreeing on equilibria and oscillations). To understand the system we thus have to analyze the partial order of ‘types of behavior’: equivalence classes of trajectories ordered by extension.

We identify subsystems such that, if absent, this behavior poset is an algebraic domain—and we characterize these behavior domains. Next, we investigate the natural topology on the types of behavior, and we comment on connections to logic. Finally, and motivated by the ‘black box problem’ of neural networks, we mention ways to transform a system into a simple system with essentially the same behavior.

Time: 16:00 – 17:30

Location: Room 302, Drift 25

- March 19, Albert Visser (Utrecht University)

**Finite Axiomatizability and ****its**** Kin.**

In my talk I will first, briefly, discuss some background concerning finite axiomatizability. I will illustrate that some theories, like Peano Arithmetic and Zermelo Fraenkel Set Theory, are not finitely axiomatizable in particularly tenacious ways.

There are two notions that are quite close to finite axiomatizability. The first notion is axiomatizability by a finite scheme and the second notion is *finding a finitely axiomatized extension of the given theory in an expanded language such that the extension is conservative over the original theory*.

Vaught’s theorem tells us that a wide class of recursively enumerable theories is axiomatizable by a finite scheme. I will briefly discuss this result.

I present results by Kleene and Craig & Vaught that show that, for a wide class of recursively enumerable theories, a finitely axiomatized extension in an expanded language exists, such that the extension is conservative over the original theory. I discuss work by Pakhomov & Visser that tells us that, under reasonable assumptions, there is no best such extension.

The paper by Pakhomov & Visser can be found here: https://arxiv.org/abs/1712.01713

Time: 16:00 – 17:30

Location: Room 302, Drift 25

- March 5, Robert Passmann (ILLC)

*The De Jongh Property for Bounded Constructive Zermelo-Fraenkel Set Theory*

The theory BCZF is obtained from constructive Zermelo-Fraenkel set theory CZF by restricting the collection schemes to bounded formulas. We prove that BCZF has the de Jongh property with respect to every intermediate logic that is characterised by a class of Kripke frames. For this proof, we will combine Kripke semantics for subtheories of CZF (due to Iemhoff) and the set-theoretic forcing technique.

The paper is available for download under https://eprints.illc.uva.nl/1662/1/djp-illcpp.pdf

- February 19, Allard Tamminga (University of Groningen and Utrecht University)

*An Impossibility Result on Methodological Individualism*

We prove that the statement that a group of individual agents performs a deontically admissible group action cannot be expressed in a well-established multi-modal deontic logic of agency that models every conceivable combination of actions, omissions, abilities, obligations, prohibitions, and permissions of finitely many individual agents. Our formal result has repercussions for methodological individualism, the methodological precept that any social phenomenon is to be explained ultimately in terms of the actions and interactions of individuals. We show that by making the relevant social and individualistic languages fully explicit and mathematically precise, we can precisely determine the situations in which methodological individualism is tenable. (Joint work with Hein Duijf and Frederik Van De Putte)

- January 22, Daniel Cohnitz (Utrecht University), joint work with Carlo Nicolai (King’s College London)

*How to adopt a logic*

What is commonly referred to as the Adoption Problem is a challenge to the idea that the principles for logic can be rationally revised. The argument is based on a reconstruction of unpublished work by Saul Kripke. As the reconstruction has it, Kripke essentially extends the scope of William van Orman Quine’s regress argument against conventionalism to the possibility of adopting new logical principles. In this paper, we want to discuss the scope of this challenge. Are all revisions of logic subject to the regress problem? If not, are there interesting cases of logical revisions that are subject to the regress problem? We will argue that both questions should be answered negatively.