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CONTINGENCY AND KNOWING WHETHER

Published online by Cambridge University Press:  09 January 2015

JIE FAN ,
YANJING WANG  and
HANS VAN DITMARSCH
JIE FAN*
Affiliation:
Department of Philosophy, Peking University
YANJING WANG*
Affiliation:
Department of Philosophy, Peking University
HANS VAN DITMARSCH*
Affiliation:
LORIA-CNRS/Univeristy of Lorraine
*
*DEPARTMENT OF PHILOSOPHY, PEKING UNIVERSITY, BEIJING 100871, CHINA E-mail: [email protected]
†DEPARTMENT OF PHILOSOPHY, PEKING UNIVERSITY, BEIJING 100871, CHINA E-mail: [email protected]
‡LORIA-CNRS/UNIVERSITY OF LORRAINE, 54506 VANDUVRE-LÈS-NANCY, FRANCE E-mail: [email protected]
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Abstract

A proposition is noncontingent, if it is necessarily true or it is necessarily false. In an epistemic context, ‘a proposition is noncontingent’ means that you know whether the proposition is true. In this paper, we study contingency logic with the noncontingency operator Δ but without the necessity operator □. This logic is not a normal modal logic, because Δ(φ → ψ) → (Δφ → Δψ) is not valid. Contingency logic cannot define many usual frame properties, and its expressive power is weaker than that of basic modal logic over classes of models without reflexivity. These features make axiomatizing contingency logics nontrivial, especially for the axiomatization over symmetric frames. In this paper, we axiomatize contingency logics over various frame classes using a novel method other than the methods provided in the literature, based on the ‘almost-definability’ schema AD proposed in our previous work. We also present extensions of contingency logic with dynamic operators. Finally, we compare our work to the related work in the fields of contingency logic and ignorance logic, where the two research communities have similar results but are apparently unaware of each other’s work. One goal of our paper is to bridge this gap.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 1 , March 2015 , pp. 75 - 107
Copyright
Copyright © Association for Symbolic Logic 2014 

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