Finite trees in tense logic

Studia Logica 62 (2):121-140 (1999)
Abstract
In this paper we show the adequacy of tense logic with unary operators for dealing with finite trees. We prove that models on finite trees can be characterized by tense formulas, and describe an effective method to find an axiomatization of the theory of a given finite tree in tense logic. The strength of the characterization is shown by proving that adding the binary operators "Until" and "Since" to the language does not result in a better description than that given by unary tense logic; although the greater expressive power of "Until" and "Since" can be exploited by using the semantics of e-frames instead of traditional Kripke semantics
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