Workshop Friday 13th March 2026 13:00 - 17:00

Salle 001 IRIT 1 

13:00 - 13:40

Andreas Herzig, IRIT, CNRS, University of Toulouse

Dynamic Logic of Propositional Assignments

Dynamic Logic of Propositional Assignments (DL-PA) is a variant of PDL whose atomic programs are assignments of propositional variables. In DL-PA, quantification over a propositional variable p can be expressed straightforwardly as nondeterministic choice between assigning p to true and assigning p to false. The other way round, it is less obvious to find a polynomial translation from DL-PA to QBF. We start by eliminating the Kleene star and then put formulas into a normal form where all modal operators correspond to boolean quantifiers.

This concerns joint work with Abdallah Saffidine. 

13:40 - 14:00 

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14:00 - 14:40

Vicent Navarro Arroyo, University of Barcelona

On the Contingency of Logic in Possible World Semantics

In this talk we will develop the challenge to the tacit assumption in Standard Kripkean semantics that states that all possible worlds are governed by just one logic. In previous work mixed models were defined as models in which distinct possible worlds could be ruled by different logical systems. This study mixed classical propositional logic (CPC) and intuitionistic propositional logic (IPC) which are known to be comparable, that is, one of them is contained in the other. However, we investigate the mixing of two incomparable logics, Gödel-Dummett logic (LC) and Bounded Depth 2 (BD2) which are extensions of IPC.  We define the class of mixed models MM(LC,BD2) and a subclass of concrete mixed models CMM(LC,BD2). Also, we conjecture that the formulas valid in MM(LC,BD2) correspond precisely to the intuitionistic modal logic (iK) extended with the Box Excluded Middle Axiom and the 3-valued Gödel logic (iK + bem + G3), where G3 is just the union of LC and BD2.

14:40 - 15:20

Clara Lerouvillois, IRIT, CNRS, University of Toulouse

Representing dynamics in logic: from models to proof

Dynamic Epistemic Logic (DEL) extends modal logic to model both knowledge and its change through communication. A central example is Public Announcement Logic (PAL), where knowledge states are modeled by sets of possible worlds and announcements update these models by eliminating worlds. Thus, DEL’s semantics is inherently dynamic. In this talk, I develop a method to proof-theoretically represent the dynamic character of DEL in a fully natural way and with only syntactical means. I use it to construct a proof calculus for PAL that serves as a syntactic counterpart to epistemic models and their updates, and it enjoys strong structural properties such as admissibility of structural rules and cut-elimination.

The talk is based on joint work with Francesca Poggiolesi.

15:20 - 16:00

Rafael Ongaratto, University of Campinas, Brazil

Many-valuedness and Multimodalities

This presentation extends the six-valued Logic of Evidence and Truth LETK+ into a class of multimodal systems equipped with epistemic operators. The epistemic extensions of  LETK+ are shown to be complete with respect to Kripke-style semantics, using basilar systems based on the Lemmon–Scott schema G(a,b,c,d). We examine general features of this epistemic family and show how it gives rise to novel epistemic states when compared to the classical setting. We also discuss the problem of extensions of many-valued systems abstractly by providing a method to extend many-valued systems with minimal restrictions to modal extensions based on the Lemmon-Scott schema.

16:00 - 16:20 

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16:20 - 17:00

Hans van Ditmarsch, IRIT, CNRS, University of Toulouse

Simplicial Epistemic Semantics

All my working life as a logician epistemic logic came with Kripke models, in particular the kind for multiple agents with equivalence relations to interpret knowledge. Sure enough, I knew about enriched Kripke models, like subset spaces, or with topologies. But at some level of abstraction you get back your standard Kripke model. Imagine my surprise, around 2018, that there is an entirely dual sort of structure on which the epistemic logical language can be interpreted and that results in the same S5 logic: simplicial complexes. Instead of points that are worlds and links labeled with agents, we now have points that are agents and links labeled with worlds. Or, instead of edges (links), triangles, tetrahedrons, etcetera, that represent worlds. Simplicial complexes are well-known within combinatorial topology and have wide usage in distributed systems to model (a)synchronous computation. The link with epistemic modal logic is recent, spreading out from Mexico City and Paris to other parts of the world, like Bern, Prague and Vienna. Other logics are relevant too, for example KB4, in order to encode crashed processes/agents. Other epistemics are relevant too, and in particular distributed knowledge, which facilitates further generalizations from simplicial complexes to simplicial sets, and also belief instead of knowledge. It will be my pleasure to present my infatuation with this novel development connecting epistemic logic and distributed computing. Suggested introductory reading is:

https://arxiv.org/abs/2002.08863

https://link.springer.com/chapter/10.1007/978-3-030-75267-5_1

Knowledge and Simplicial Complexes

Hans van Ditmarsch, Eric Goubault, Jeremy Ledent, Sergio Rajsbaum

https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.7.34

Epistemic and Topological Reasoning in Distributed Systems (Dagstuhl Seminar 23272)

Armando Castañeda, Hans van Ditmarsch, Roman Kuznets, Yoram Moses, Ulrich Schmid

Section 4.3 Representing Epistemic Attitudes via Simplicial Complexes