Finite satisfiability of propositional interval logic formulas with multi-objective evolutionary algorithms

Interval temporal logics provide a natural framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as the primitive ontological entities. Despite being relevant for a broad spectrum of application domains, ranging from temporal databases to artificial intelligence and verification of reactive systems, interval temporal logics still misses algorithms and tools capable of supporting them in an efficient way. In this paper, we approach the finite satisfiability problem for the simplest meaningful interval temporal logic (which is NEXPTIME-complete), namely A (also known as Right Propositional Neighborhood Logic), by means of a multi-objective combinatorial optimization model solved with three different multi-objective evolutionary algorithms. As a result we obtain a decision procedure that, although incomplete, turns out to be unexpectedly suitable and easy to implement with respect to classical complete algorithms. Moreover, this approach allows one to effectively search for the minimal model that satisfy a set of A-formulas without using any kind of normal form.