Bi-intuitionistic linear temporal logic
Brett McLean
Authors: David Fernández-Duque, Brett McLean and Lukas Zenger
We investigate an intuitionistic propositional logic extended with both the co-implica-tion connective of Hilbert–Brouwer logic and with the modalities of linear temporal logic. We use a semantics based on intuitionistic Kripke frames equipped with an order-preserving function representing the temporal dynamics. By using the technical notion of a quasimodel, a type of nondeterministic encoding of a linear-time model, first introduced in [1], we establish the decidability of our bi-intuitionistic linear temporal logic and give a sound and complete Hilbert-style calculus for it. This work builds on that of [2], where the decidability of various bi-intuitionistic modal logics was established.
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