Title: Cyclic Proof Theory

Abstract:  Proofs are a central tool in mathematics and a core concept in the study of formal reasoning. Traditionally, a proof is conceived as a finite object which is used to certify the correctness of our mathematical structures and their properties. Less common are so called cyclic proofs which, although infinitary, exhibit periodic patterns. Cyclic proof systems have proven to be a remarkably useful alternative in the mathematical study of computational systems, particularly in connection with algorithms, databases and programs. In this talk we will introduce cyclic proofs and study the extent to which these classes of proofs lend themselves to traditional proof theoretic techniques.

Title: Belief Revision and Modal Logic

Abstract: The belief change literature mainly considers the revision of belief bases consisting of sets of propositional logic formulas. When these bases are closed under logical consequence they are called belief sets. Revision operations on belief sets satisfy the postulate of extensionality: when two logically equivalent belief bases are revised by the same new piece of information then the outcomes are again logically equivalent. The main argument against extensionality is that while {p, q} and {p, p → q} are ‘statically equivalent’, they are not ‘dynamically equivalent’, in the sense that they have to be revised differently. We argue that this kind of non-equivalence should be made formal by considering logics where these two belief bases fail to be equivalent and that logics of strict implication are suitable candidates for such logic. We propose three rationality postulates for modal belief revision and provide a semantics that lifts the Hamming distance from a distance between valuations to a distance between pointed S5 models. 

Title: Modelling Knowledge-Action Interactions in Cops and Robbers

Abstract: The game of Cops and Robbers serves as a basic model for exploring computational challenges in pursuit-evasion scenarios. In this talk, we introduce the Epistemic Logic of Cops and Robbers (ELCR), a formal framework designed to precisely capture key aspects of the game, including players' positions, observational capabilities, and inferential processes. We develop a robust method for tracking the dynamic interactions between players, specifically focusing on how their knowledge evolves in response to their actions throughout the game.  We investigate important properties of ELCR, such as its axiomatization and decidability. This is a joint work with Dazhu Li and Sujata Ghosh.

Title: Craig Interpolation for Bi-intuitionistic Tense Logic

Abstract: Bi-intuitionistic stable tense logic (BiSKt), introduced by Stell et al. (2016), provides a logical framework for mathematical morphology on graphs. This talk establishes the Craig interpolation theorem for BiSKt from both a semantic and a proof-theoretic perspective. The theorem states that for any provable implication A -> B, there exists an interpolant I such that    A -> I and I -> B are both provable and the non-logical symbols of I are common to A and B.

From a semantic perspective, we use bisimulation product techniques, extending the methods of Maximova (1980) and Marx (1998). Although this approach does not directly yield an algorithm for computing interpolants, it demonstrates that a broad class of bi-intuitionistic tense logics satisfies the Craig interpolation theorem. From a proof-theoretic perspective, we introduce a sequent calculus with analytic cuts and apply Mints' (2001) symmetric interpolation method

to compute interpolants. This approach also simplifies Kowalski and Ono's (2017) proof for bi-intuitionistic logic. This research is part of an ongoing work together with Hiroakira Ono (JAIST).

A special keynote speaker: 

Title: Mathematical Logic meets Philosophy: the case of Beth and Craig

Abstract: One usually thinks of philosophical logic as the sole guardian of the interface of logic and philosophy. But classical results from mathematical logic also have a major role to play. We illustrate this for the case of the Beth Definability Theorem and Craig’s Interpolation Theorem, and the ways in which these have occurred in different areas of philosophy. On the way, we point

out new results and issues triggered by this encounter.

Ref: J. van Benthem, ‘Definability and Interpolation in Philosophy’, to appear in B. ten Cate, J. Jung, O. Koopmann, Ch. Wernhard & F. Wolter, eds., Theory and Applications of Craig Interpolation, Ubiquity Press.