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arXiv · 2310.20069

Strong completeness of a first-order temporal logic for real time

Robert Goldblatt
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Abstract

Propositional temporal logic over the real number time flow is finitely axiomatisable, but its first-order counterpart is not recursively axiomatisable. We study the logic that combines the propositional axiomatisation with the usual axioms for first-order logic with identity, and develop an alternative ``admissible'' semantics for it, showing that it is strongly complete for admissible models over the reals. By contrast there is no recursive axiomatisation of the first-order temporal logic of admissible models whose time flow is the integers, or any scattered linear ordering.

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Robert Goldblatt. 2023-10-30. Strong completeness of a first-order temporal logic for real time. https://doi.org/10.1017/s1755020324000121

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