Increasing Model Building Capabilities by Constraint Solving on Terms with Integer Exponents

We extend a former method for simultaneous search for refutations and models, based on the use of constraints, by extending the expressive power of the constraints. Our extension uses the language ofI-terms, in which it is possible to denote infinite sequences of structurally similar terms. Our work generalizes the results of Comon (1995). Comon gives only aunificationalgorithm for ‘‘one holeʹʹI-terms, while we present a decision procedure for term constraints with integer exponents (only decidability of the positive existential fragment was known so far). We show that the formalism ofI-terms can be profitably integrated into our method for model building. In particular, it allows us to specify all the resolvents of some kinds of self-resolvent clauses. This feature is especially useful in model building. We illustrate our approach with two non-trivial examples, showing that the extension presented here increases the power of our method, i.e. the class of formulae for which it is able to build models.