PP-2015-17: Instantial neighbourhood logic

PP-2015-17: van Benthem, Johan and Bezhanishvili, Nick and Enqvist, Sebastian and Yu, Junhua (2015) Instantial neighbourhood logic. [Report]

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Abstract

This paper explores a new language of neighborhood structures where existential information can be given about what kind of worlds occur in a neighborhood of a current world. The resulting system of `instantial neighborhood logic' INL has a non-trivial mix of features from relational semantics and from neighborhood semantics. We explore some basic model-theoretic behavior, provide a matching notion of bisimulation, and give a complete axiom system for which we prove completeness by a new normal form technique. In addition, we relate INL to other modal logics by means of translations, determine its precise SAT complexity, and formulate an adequate tableau calculus that can be used for automated deduction supporting INL inference. As for a broader setting, we discuss some motivations for INL in dynamic logics of evidence, consider some special cases in the realm of topology and of powers for players in games, and we point at general model-theoretic and especially, coalgebraic backgrounds for what is achieved in this paper. Many of these final themes suggest follow-up work of independent interest.

Item Type: Report
Report Nr: PP-2015-17
Series Name: Prepublication (PP) Series
Year: 2015
Uncontrolled Keywords: Modal logic, neighbourhood semantics, bisimulations, axiomatization, completeness, topological semantics, game logic, coalgebraic semantics
Subjects: Logic
Depositing User: Nick Bezhanishvili
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/528

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