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INQUISITIVE BISIMULATION

Part of: General logic Model theory

Published online by Cambridge University Press:  30 October 2020

IVANO CIARDELLI  and
MARTIN OTTO
IVANO CIARDELLI
Affiliation:
MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY (MCMP) LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHENMUNICH, GERMANYE-mail: ivano.ciardelli@lmu.de
MARTIN OTTO
Affiliation:
DEPARTMENT OF MATHEMATICS TECHNISCHE UNIVERSITAET DARMSTADTDARMSTADT, GERMANYE-mail: otto@mathematik.tu-darmstadt.de
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Abstract

Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic in the context of relational structures with two sorts, one for worlds and one for information states, and characterise inquisitive modal logic as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures.

Keywords

inquisitive modal logicbisimulationteam semanticsvan Benthem theoremexpressive completenessmodel theory of modal logicsfinite model theory

MSC classification

Primary: 03B45: Modal logic (including the logic of norms)
Secondary: 03B42: Logics of knowledge and belief (including belief change) 03C07: Basic properties of first-order languages and structures 03C80: Logic with extra quantifiers and operators 03C98: Applications of model theory 03B70: Logic in computer science
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 1 , March 2021 , pp. 77 - 109
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Copyright
© The Association for Symbolic Logic 2020

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