Abstract
In this work we propose a proof-system for propositional Linear Time Temporal Logic over Finite Temporal Frames (LTL Fin) in the tableau style, where formulae are equipped with labels in order to explicitly embed some semantic information in the inference rules. The labels mark formulae as true in a given time interval and linear inequality constraints (temporal constraints) are used to express ordering relations between time points. Branch closure is reduced to unsatisfiability over the integers of the set of temporal constraints in the branch. The proposed tableau calculus checks whether a finite set of formulae has a finite model whose cardinality is bounded by a constant given in input, and constructs such a model, if any. From a theoretical standpoint, the method can also be used to check finite satisfiability tout court. The following properties of the proposed proof-system are proved: termination, soundness and completeness w.r.t. both bounded and finite validity. This work is a revised and extended version of [6].
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Cerrito, S., Mayer, M.C. (2000). Labelled Tableaux for Propositional Linear Time Logic Over Finite Frames. In: Basin, D., D’Agostino, M., Gabbay, D.M., Matthews, S., Viganò, L. (eds) Labelled Deduction. Applied Logic Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4040-9_6
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