Silvia De Toffoli (IUSS Pavia)

Title: Mathematics After AI

Abstract:

OpenAI's announcement of an AI-generated solution to the Navier–Stokes problem has intensified speculation that mathematics might soon be "solved," as many have said that chess and Go have been "solved." In this talk, I challenge this narrative by questioning two assumptions on which it rests: that AI has genuinely solved a mathematical problem, and that mathematics is fundamentally about solving problems. In short, I will suggest that mathematical solutions require intelligible proofs that advance human understanding and that mathematics itself is a human enterprise that encompasses far more than problem solving. Recent AI achievements should not be thought of as a "human defeat," as mathematics is not an adversarial game. Rather, they invite us to reconsider what mathematics is and what norms we should endorse to foster the flourishing of human mathematics. Finally, I will consider a future in which the production and appreciation of mathematics increasingly come apart. Drawing on analogies with aesthetic appreciation, I will ask whether part of the value of human mathematical practice is connected to the activity of engaging with mathematics itself – and, in particular, in the firsthand insights that such engagement can provide.

Sujata Ghosh (Indian Statistical Institute Chennai Centre)

Title: On epistemic reasoning in games on graphs

Abstract:

There is a long tradition of interaction between logic and games. In the past few decades, games played on graphs have proven to be a concise model for a wide range of interactive scenarios. These games have deep roots in the study of many areas, e.g., graph theory and algorithms, abstract argumentation theory, computational complexity among others.
These graph games have quite attractive analogies with respect to modal logic semantics and have motivated many new designs of logical systems that can capture crucial structures of these games. An important aspect is to define the desired logical tools to characterise key features of the games, including actions of the players, their winning strategies, and also, informational updates regarding players' uncertainties in the game plays. In recent years, many efforts have been made to explore the interactions between the two areas, but significant challenges remain. 

This talk will give an overview of the current research and future directions in the well-studied interaction between modal logic and graph games with a distinct focus on information available to players in the game play.

Andrzej Indrzejczak (University of Łódź)

Title: How Much Set Theory is in Logic? 

Abstract:
Logicism in its strong form, leading to an answer that all set theory belongs to logic, is rather difficult to defend. However, it was sometimes pointed out, recently by Tennant, that the mathematisation of set theory by Zermelo and his followers was premature. It abandoned too early the logicist project, at least in its weak form which deals with the concept of class/set rather than with the existential commitments of particular axiomatic set theories. In fact, we can say many things about arbitrary collections of objects without assuming their existence.

Is it possible to obtain a logic of our discourse on sets, based on principles existentially non-committal but meaning-conferring? In fact several proposals of such logics were provided by Bernays, Quine, Scott, Tennant, Bencivenga. Their common notion is that of a class expressed by means of set abstracts corresponding to predicate extensions, but they are different in many respects, partly rooted in the choice of an underlying logic (classical, free e.t.c.). Moreover, different criteria of demarcation between the logic of classes and set theory were proposed. In the talk we compare several logics of classes and propose proof-theoretic criteria for deciding where the border lies and which logic, if any, can be seen as the best option.

Takako Nemoto (Tohoku University)

Title: The role of De Morgan’s law in semi-intuitionistic weak arithmetic

Abstract

Hiroakira Ono (Japan Advanced Institute of Science and Technology)

Title: Some observations on bi-intermediate logics

Abstract

Graham Priest (Tohoku University, Shandong University & University of Melbourne)

Title: Connexive Logics and the Hyperconnexive Falsity Conditions for Conditionals  (joint work with Heinrich Wansing)

Abstract

Shawn Standefer (Tohoku University)

Title: S5-ish Relevant Modal Logics

Abstract:
While there are many presentations of the classically-based modal logic S5, in the context of non-classical logics, analogs of these presentations come apart. In this talk, we consider several S5-ish extensions of relevant logics, showing that many of them are incomparable. Adapting work of Ono, we define S5-type logics and show that a variety of extensions of relevant logics are S5-type. We then show that, depending on the axiomatization of adopted, the S5-ish logics may have differing numbers of distinct modalities. We then conclude with directions for future research.

Heinrich Wansing (Ruhr University Bochum & Tohoku University)

Title: A bimodal connexive logic of logical and metaphysical necessity

Abstract:
The notion of metaphysical necessity is controversial, and even if it is conceded that there is a distinct concept of metaphysical necessity along-side logical necessity, its exact relationship to logical necessity remains a matter of debate. In this paper, I propose to capture the distinction between metaphysical and logical necessity from the perspective of logical bilateralism. Whilst statements of logical and metaphysical necessity share the same (support of) truth conditions, they differ in their (support of) falsity conditions. The distinction is made precise by introducing a bimodal connexive propositional logic called ‘S5-ML’ (S5 with metaphysical and logical necessity). The system has a bilateralist semantics that enables a differentiation between ascriptions of metaphysical and logical necessity, and at the same time allows upholding modal monism, insofar as no distinction is drawn between metaphysically and logically possible worlds or states.   Another bimodal system aimed at capturing a distinction between logical and metaphysical necessity has recently been presented by Marcin Łyczak. Łyczak’s logic of logical necessity is a proper extension of the modal propositional logic S5 and is not closed under uniform substitution. In contrast to this, the bimodal logic S5-ML is closed under uniform substitution, whereas the class of necessities is not.

Zach Weber (University of Otago)

Title: On Methods for Infinitary Paradoxes (joint work with Ellie Ripley)

Abstract:
Substrucutral non-contractive logics have been proposed in part as responses to Curry's Paradox. Much attention has gone into facing Curry at the propositional level; but there are several newly threatening variants at the level of quantification. These range from omega-Currys to triviality proofs recently devised with the help of AI. We will outline four, looking for a common underlying structure. This leads to reconsidering principles for disjunction, universal quantification, and mathematical induction. More generally, we ask what this work tells us methodologically.  Have we been pushing boulders up a hill only to have them roll inevitably down again? Or are we improving our map of the line between trivial and non-trivial---converging on an ultimate Curry, and its ultimate resolution? To operationalise this, we conclude with prospects for non-triviality proofs using formal verification. 

Accepted Abstracts:

David Appadourai: Informal proof, tactic script, proof term: What formalization preserves, discards, and creates

Riccardo Borsetto: Strong inequality in observational type theory

Matthew Collinson, Timo Eckhardt & David Pym: Towards an inferentialist metaphysics of information security through proof-theoretic semantics

Blandine de Becker: A perspective on kinds of paradoxes

Christian Fermüller: Towards a logical framework for graded deontic reasoning

Rohan French: Semantics for a logic of structural properties

Ryo Ito: Many-sorted intensional logic and the Russell-Myhill Paradox

Purbita Jana & Prateek Kwatra: Continuous Logic: An algebraic treatment

Michael Kaminski: Intuitionistic logic of a binary modality

Junya Kitazono: The third value as modal status: A Suszkian reduction of Ł3 into the Boolean algebras with operators of Priorean branching time

Mateusz Klonowski & Tomasz Jarmużek: Some sequent calculi for the logic of demodalised analytic implication

Nils Kürbis: Neglected but plausible principles for free theories of definite descriptions

Tsubasa Kumasaka: Analytic cut property and subformula property for abstract provability structures

Anela Lolić: A note on a proof-theoretic limitation of first-order S5

Miguel Lopez Munive: A truth-theoretic approach to external negation

Paolo Maffezioli: Proof-theoretic aspects of stable logic

Ondrej Majer & Krishna Manoorkar: Probabilistic inquisitive logic

Shin Matsuura: The non-triviality of a connexive theory of truth

Satoru Niki & Mahan Vaz: Time, coherence and justification: Interpreting Kearns' semantics for intuitionistic logic

Yuki Nishimura & Sohei Iwata: Terminating sequent calculus for n-transitivity

Mashu Noguchi: Embeddings of propositional logics into the provability logics 𝐒 and 𝐃

Takuro Onishi: The star function as a free completion of negative accessibility

Elise Perrotin: On logics of S5 common knowledge

Sabeena PS: Normativity and logical pluralism: Reinterpreting Nyaya and Aristotelian logic

Vít Punčochář: Questions in mathematics

Takahiro Sawasaki & Yaroslav Petrukhin: A new positive free modal logic with definite descriptions

Igor Sedlár & Shawn Standefer: Time for relevant logic

Takahiro Seki: A hierarchy of non-associative substructural logics

Fatemeh Shirmohammadzadeh Maleki: Proof theory for some subintuitionistic logics

Ryan Simonelli: Does anything go? Structural conservativity on the Pittsburgh and Bochum Plans

Nobu-Yuki Suzuki: Variants of prenex normal form theorem in intermediate predicate logics

Nazanin R. Tavana, M. Pourmahdian & S.M.A. Khatami: The Craig interpolation property in first-order Gödel logic and some of its extensions

Mattia Vargas & Federico Faroldi: Truthmakers for Might counterfactuals

Ren-June Wang: Sequent calculus for FDE and its relative logics

Blane Worley: Saving logical consequence from identity

Emils Zavelis: Circularity in dialetheic classical recapture