Title: A Brief Introduction to First-order Modal Logic
Abstract:
In this survey talk, I will briefly survey the history of First-order Modal Logic and the relevant basic definitions and important results.
References:
Torben Braüner, Silvio Ghilardi, First-order modal logic, in Handbook of Modal Logic pp 594-620, Elsevier 2007
Melvin Fitting, Richard L. Mendelsohn: First-order Modal Logic (2nd ed.), Springer 2023
Title: Quantified Modal Logics: One Approach to Rule (Almost) them All!
Abstract:
We present a general approach to quantified modal logics that can simulate most other approaches. The language is based on operators indexed by terms which allow to express de re modalities and to control the interaction of modalities with the first- order machinery and with non-rigid designators. The semantics is based on a primitive counterpart relation holding between n-tuples of objects inhabiting possible worlds. This allows an object to be represented by one, many, or no object in an accessible world. Moreover by taking as primitive a relation between n-tuples we avoid some shortcoming of standard individual counterparts. Finally, we use cut-free labelled sequent calculi to give a proof-theoretic characterisation of the quantified extensions of each first-order definable propositional modal logic. In this way we show how to complete many axiomatically incomplete quantified modal logics.
Title: Frame Definability in First-Order Modal Logic
Abstract:
Correspondence theory is a fundamental aspect of the model theory of modal logic and has long been a topic of interest. A significant result in this field, established by Goldblatt and Thomason in the 1970s, characterizes modally definable classes of Kripke frames.
In this talk, we will delve into the model theory of first-order modal logic (FML). The integration of propositional modal logic with classical first-order logic presents additional challenges. We will specifically examine the intricacies of frame definability and present an appropriate version of the Goldblatt-Thomason theorem within this expanded logical framework.
This talk is based on a joint work with M. Pourmahdian.
Title: Bundled Fragments of First Order Modal Logic
Abstract:
First Order Modal Logic (FOML) extends First Order Logic (FO) with modal operators. FOML is suitable for many applications including planning, predicate epistemic logics among others. However, FOML is computationally unfriendly. Most of the decidable fragments of FO that are decidable (like the two variable fragment, guarded fragment, restriction to unary predicates) become undecidable when extended with modal operators. Until recently, the only known decidable fragment of FOML was the monodic fragment.
In this talk we will discuss some new and interesting decidable fragments of FOML called the bundled fragments where the quantifiers and modalities are 'bundled' together. The talk is based on a series of joint works with Mo Liu, R. Ramanujam and Yanjing Wang.
https://arxiv.org/abs/2202.01581