August 2019 Strong Noncontingency: On the Modal Logics of an Operator Expressively Weaker Than Necessity
Jie Fan
Notre Dame J. Formal Logic 60(3): 407-435 (August 2019). DOI: 10.1215/00294527-2019-0010


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 (deductively) 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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Jie Fan. "Strong Noncontingency: On the Modal Logics of an Operator Expressively Weaker Than Necessity." Notre Dame J. Formal Logic 60 (3) 407 - 435, August 2019.


Received: 3 September 2015; Accepted: 17 May 2017; Published: August 2019
First available in Project Euclid: 12 July 2019

zbMATH: 07120748
MathSciNet: MR3985619
Digital Object Identifier: 10.1215/00294527-2019-0010

Primary: 03B45
Secondary: 03B42

Keywords: bisimulation , completeness , expressivity , frame definability , strong noncontingency

Rights: Copyright © 2019 University of Notre Dame


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Vol.60 • No. 3 • August 2019
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