Open AccessTwo Temporal Logics of Contingency
Author(s) -
Matteo Pascucci
Publication year - 2017
Publication title -
australasian journal of logic
Language(s) - English
Resource type - Journals
ISSN - 1448-5052
DOI - 10.26686/ajl.v12i2.4140
Subject(s) - transitive relation , contingency , extension (predicate logic) , modal logic , class (philosophy) , computer science , constant (computer programming) , temporal logic , linear temporal logic , propositional calculus , mathematics , theoretical computer science , calculus (dental) , artificial intelligence , algebra over a field , epistemology , modal , programming language , pure mathematics , philosophy , medicine , chemistry , dentistry , combinatorics , polymer chemistry
This work concerns the use of operators for past and future con-tingency in Priorean temporal logic. We will develop a system namedCt, whose language includes a propositional constant and prove that(i) Ct is complete with respect to a certain class of general frames and(ii) the usual operators for past and future necessity are denable insuch system. Furthermore, we will introduce the extension Ctlin thatcan be interpreted on linear and transitive general frames. The theo-retical result of the current work is that contingency can be treatedas a primitive notion in reasoning about temporal modalities.