Abstract
The paper deals with the problem of axiomatizing a system τ1 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”). τ1 is like the Segerberg-Sundholm system W1 in working with so-called infinitary inference rules; on the other hand, it differs from W1 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 τ 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 τ1.
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The present contribution reports research done under the auspices of the Swedish Council for Research in the Humanities and the Social Sciences (HSFR), project “On the Legal Concepts of Rights and Duties: an Analysis Based on Deontic and Causal Conditional Logic”. I wish to thank the anonymous referee for his/her extremely patient and accurate revision work, and Krister Segerberg for his helpful suggestions.
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Åqvist, L. Discrete tense logic with infinitary inference rules and systematic frame constants: A Hilbert-style axiomatization. Journal of Philosophical Logic 25, 45–100 (1996). https://doi.org/10.1007/BF00357842
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DOI: https://doi.org/10.1007/BF00357842