Incompleteness of a first-order G��del logic and some temporal logics of programs (original) (raw)

Computer Science Logic, 1996

Abstract

It is shown that the infinite-valued first-order G��del logic G�� based on the set of truth values {1/k: kw {0}} U {0} is not re The logic G�� is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kr��ger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal logic of linear discrete time with gaps follows.

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