Bounded Model Search in Linear Temporal Logic and Its Application to Planning

In this work a tableau calculus is proposed, that checks whether a finite set of formulae in propositional linear temporal logic (LTL) 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 calculus are proved: termination, soundness and completeness w.r.t. finite model construction. The motivation behind this work is the design of a logical language to model planning problems and an associated calculus for plan construction, integrating the declarativity, expressiveness and flexibility typical of the logical languages with the capability of embedding search-based techniques well established in the planning community.