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

Abstract

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

A Tableau System for Right Propositional Neighborhood Logic over Finite Linear Orders: An Implementation

“…Despite being a prototypical implementation, our system runs reasonably well on the COMBINATORICS benchmark, being able to produce a result in a short time for formulas up to 20 conjuncts (and up to a model size of 23 points). The results of the RANDOMIZED benchmark allows for a first comparison with the Evolutionary algorithm in [5], and shows that the two algorithms have similar performances on the considered formulas. The tableau system was able to prove that problem 31 is unsatisfiable, while the evolutionary algorithm (being incomplete) can only provide positive answers.…”

“…First, we tested the scalability of the program with respect to a set of combinatorial problems of increasing complexity (COMBI-NATORICS), where the n-th combinatorial problem is defined as the problem of finding a model for the formula that contains n conjuncts, each one of the type A p i (0 ≤ i ≤ n), plus n(n+1) 2 formulas of the type [A]¬(p i ∧ p j ) (i = j). Then, we considered the set of 36 "easy" purely randomized formulas used in [5] to evaluate an Evolutionary Computation algorithm for RPNL finite satisfiability (RANDOMIZED). Table 1 summarizes the outcome of our experiments.…”