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Discrete Tense Logic with Infinitary Inference Rules and Systematic Frame Constants: A Hilbert-Style Axiomatization

Lennart Äqvist
Journal of Philosophical Logic
Vol. 25, No. 1 (Feb., 1996), pp. 45-100
Published by: Springer
Stable URL: http://www.jstor.org/stable/30227089
Page Count: 56
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Discrete Tense Logic with Infinitary Inference Rules and Systematic Frame Constants: A Hilbert-Style Axiomatization
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Abstract

The paper deals with the problem of axiomatizing a system T1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 ("immediate successor") and-1 ("immediate predecessor"). T1 is like the Segerberg-Sundholm system WI in working with so-called infinitary inference ruldes; on the other hand, it differs from W I with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a "now" operator, and, most importantly, with respect to (iii) the presence in T1 of so-called systematic frame constants, which are meant to hold at exactly one point in a temporal structure and to enable us to express the irreflexivity of such structures. Those frame constants will be seen to play a paramount role in our axiomatization of T1.

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