Invited Speakers

[Invited Speakers]

• Ryo Kashima  (Tokyo Institute of Technology)
  Two topics on nested sequent calculi for modal logics
  Abstract: (1. Nested fragment of Negri's labelled sequent calculi): Nested sequent calculi have been introduced for many modal logics; for example, Brunnler[B09] gave fifteen nested sequent calculi for the modal cube. A feature of nested sequent calculi is that sequents have obvious corresponding formulas. On the other hand, Negri[N05] introduced labelled sequent calculi for infinitely many modal logics. Features of Negri's calculi are the uniformity of rules for infinitely many logics and the easiness of syntactic cut-elimination. In this talk, we give nested sequent calculi with all the abovementioned features.
  (2. Nested sequent calculi for the provability logics S and D): The provability logic S and D are extensions of the well-known provability logic GL. The semantics of S and D are defined by 'tail models', where a tail model consists of transitive and converse well-founded Kripke model (GL-model) with an infinite descending sequence of worlds (tail). There have been standard sequent calculi for GL, S, and D (see [KKI23]), and a nested (labelled) sequent calculus for GL (see [N05]). In this talk, we give nested sequent calculi for S and D.
  
  [B09] K. Brunnler, Deep Sequent Systems for Modal Logic, Archive for Mathematical Logic, 2009.
  [KKI23] R. Kashima, T. Kurahashi, and S. Iwata, Cut-free Sequent Calculi for the Provability Logic D, 2023. arXiv:2310.16369
  [N05] S. Negri, Proof Analysis in Modal Logic, Journal of Philosophical Logic, 2005.
  
  
  

• Shawn Standefer (National Taiwan University)
  Ignorance and the possibility of error in relevant epistemic logic
  Abstract: In this paper, I will present two approaches to epistemic logic in the setting of relevant logics. One uses the framework of equivalence classes representing indistinguishability, found in much work in epistemic logics. The other, does not use equivalence classes, but is more common in the area of relevant logics. I will argue that the former has many advantages over the latter while avoiding some of the standard criticisms leveled against the use of equivalence relations in classically based epistemic logic.
  
  
  

• Patrick Blackburn (University of Roskilde)
  This time, as grandfather...
  Abstract : Arthur Prior is best known as the father of tense logic, and (to a lesser extent) as the father of hybrid logic. In this talk, I will introduce Arthur Prior in a third role: this time, as grandfather of modal logics with propositional quantifiers.
  Arthur Prior made extensive use of modal logics with propositional quantifiers throughout his career. As we now know (since the groundbreaking work of Kit Fine, then Prior's PhD student, in the late 1960s) propositional quantifiers easily give rise to highly complex modal logics. But propositional quantifiers are syntactically simple and were philosophically attractive to Prior. I shall discuss how Prior put such quantifiers to work, ranging from his early work on paradoxes of knowledge to his late use of them to define nominals in hybrid logic. This discussion will lead to some recent joint work (with Torben Brauner and Julie Lundbak Kodod) on what we call Prior's Ideal Language (PIL), a hybrid modal logic enriched with propositional quantifiers.
  
  
  

• Fan Yang  (Utrecht University)
  Propositional logics based on team semantics
  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 Vaananen 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.

In this talk, we discuss some recent research on propositional logics based on team semantics and their applications.