Strong Noncontingency: On the Modal Logics of an Operator Expressively Weaker Than Necessity

Notre Dame Journal of Formal Logic 60 (3):407-435 (2019)
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Abstract

Operators can be compared in at least two respects: expressive strength and deductive strength. Inspired by Hintikka’s treatment of question embedding verbs, the variations of noncontingency operator, and also the various combinations of modal operators and Boolean connectives, we propose a logic with strong noncontingency operator as the only primitive modality. The novel operator is deductively but not expressively stronger than both noncontingency operator and essence operator, and expressively but not deductively weaker than the necessity operator. The frame-definability power of this new logic is in between standard modal logic and noncontingency logic. A notion of bisimulation is proposed to characterize this logic within standard modal logic and first-order logic. Axiomatizations over various frame classes are presented, among which the minimal logic is related to the treatment of an alternative semantics of the agreement operator proposed by Lloyd Humberstone.

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Citations of this work

A note on logics of essence and accident.David R. Gilbert & Giorgio Venturi - 2020 - Logic Journal of the IGPL 28 (5):881-891.
Logics of (In)sane and (Un)reliable Beliefs.Jie Fan - 2022 - Logic Journal of the IGPL 30 (1):78-100.
A Logic for Disjunctive Ignorance.Jie Fan - 2021 - Journal of Philosophical Logic 50 (6):1293-1312.

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References found in this work

Syntax and semantics of questions.Lauri Karttunen - 1977 - Linguistics and Philosophy 1 (1):3--44.
Contingency and knowing whether.Jie Fan, Yanjing Wang & Hans van Ditmarsch - 2015 - Review of Symbolic Logic 8 (1):75-107.
Minimal Non-contingency Logic.Steven T. Kuhn - 1995 - Notre Dame Journal of Formal Logic 36 (2):230-234.
Completeness and Definability in the Logic of Noncontingency.Evgeni E. Zolin - 1999 - Notre Dame Journal of Formal Logic 40 (4):533-547.

View all 13 references / Add more references