Keynote Speakers:
Greg Restall (University of St Andrews)
Foundations for Truth-Conditional Semantics
This is the third lecture of Wendy Huang Lectures. For handout, see here.
Sonja Smets (Institute for Logic, Language and Computation, University of Amsterdam)
Comparing knowledge
Abstract: I present a philosophical analysis of comparative epistemic assertions between individuals or groups of agents. Such assertions can express that a group of agents collectively knows at least as much as another individual or group of agents. I will provide examples of epistemic comparison statements and analyze them in the context of different epistemic conditions. Formally, I introduce the logic obtained by adding a ‘group epistemic comparison’ operator to the standard multi-agent epistemic logic with distributed and common knowledge. I will report on the results obtained in [1], in which we axiomatized the resulting logic on the class of S5-models, and on recent work that generalizes the study of these group epistemic comparisons to the context of epistemic models including (besides S5) also KT and S4. In this context, I will pay special attention to what agents (collectively/individually) can deduce about their own epistemic position relative to that of other agents, who may know more or less than them. We will observe that the type of epistemic attitude that we attribute to individual agents and to groups of agents will play a crucial role. On the dynamic side, I discuss the informational events by which an epistemic advantage can be acquired. Such events subsume different kinds of actions via which agents gain access to other agents' information or data, and hence they can in principle learn everything known to those others. This presentation is based on joint work with A. Baltag at the University of Amsterdam on a philosophical discussion of the results in [1,2].
[1] Alexandru Baltag and Sonja Smets, Learning what Others Know, EPiC Series in Computing (LPAR23 proceedings of the International Conference on Logic for Programming AI and Reasoning), (Elvira Albert and Laura Kovacs, editors), vol. 73, Easy Chair, 2020, pp. 90-119.
[2] Logics for Data Exchange and Communication, AiML proceedings (Advances in Modal Logic, Prague), (Agata Ciabattoni, David Gabelaia and Igor Sedlar, editors), vol. 15, College Publications, 2024, pp. 147-170.
Invited Speakers:
Patrick Blackburn (Roskilde University)
The First Description Logic...?
Abstract: “Quasi-Propositions and Quasi-Individuals'' is a short paper which first appeared in 1968 as Paper XII in the first edition of Arthur Prior's book Papers on Time and Tense. Despite its brevity, it is important both logically and philosophically. Logically, Prior uses what he calls “quasi-modalities'' to build a small “egocentric logic'' for reasoning about taller and shorter; as we shall see, this is perhaps the earliest example of what computer scientists now call description logic. Moreover, partially inspired by his earlier work on the tense logic of special relativity, he shows how to hybridize this logic by defining a totalizing (universal) quasi-modality and quantifying over “people-propositions” (quasi-Individuals); that is, he quantifies over nominals. The philosophical discussion is equally interesting: the paper contains Prior's first critical reflections on his earlier claims, boldly stated in "Tense Logic and the Logic of Earlier and Later'' (Paper XI in the first edition of Papers on Time and Tense) on the significance of hybridization.
Wesley Holliday (University of California, Berkeley)
Fundamental Logic with Necessity
Abstract: Fundamental logic is a non-classical logic based only on the introduction and elimination rules for the connectives in a Fitch-style proof system (see https://arxiv.org/abs/2207.06993). Building on previous work that added modalities to fundamental logic (https://arxiv.org/abs/2403.14043), in this talk I will discuss the addition of a necessity operator to fundamental logic that makes possible a full and faithful translation of intuitionistic logic into fundamental logic. The main results concern relational semantics for this fundamental logic with necessity.
Peter Michael Hawke (Lingnan University)
De Morgan's Laws and Epistemic Language
Abstract: I argue that certain components of De Morgan’s Laws (typically taken to be innocuous) fail to hold for natural language reasoning, at least for languages equipped with information-sensitive vocabulary like ‘might’, ‘must’, ‘likely’, and ‘if’. In support, (i) I exhibit an intuitive counter-example to the components in question and (ii) I show that these components generate paradoxical reasoning when applied to sentences with information-sensitive vocabulary. I briefly exhibit a novel formal semantics that yields the subtle logical profile motivated by our discussion.
Takako Nemoto (Tohoku University)
Formal treatment of recursion theory over intuitionistic weak arithmetic
Abstract: Link
Katsuhiko Sano (Hokkaido University)
Uniform Interpolation of Basic Tense Logic
Abstract: This talk aims to establish the uniform interpolation theorem for basic tense logic, also known as two-way modal logic or modal logic with converse. Basic tense logic Kt was first introduced by Arthur Prior (1957, 1967, 1968). It can be viewed as a syntactic expansion of basic modal logic by adding a converse modality, whose corresponding accessibility relation is the converse of the ordinary accessibility relation in a given Kripke model. Interpreting a Kripke frame as representing a temporal order allows us to reason not only about the future but also about the past using this additional converse modality. A logic has the uniform interpolation property if, for every pair (A, p) consisting of a formula A and a propositional variable p, there exists a p-free formula B (the post-uniform interpolant) such that all propositional variables in B occur in A and the following equivalence holds: A proves C if and only if B proves C for every p-free formula C. To the best of the speaker’s knowledge, the uniform interpolation property of Kt has not yet been established. This talk extends Albert Visser’s (1996) semantic argument, which is formulated in terms of bounded bisimulation for the uniform interpolation property of basic modal logic K, to demonstrate that Kt also enjoys the uniform interpolation property. If time permits, we will also present a semantic sufficient condition for the Craig interpolation property of a normal tense logic.