A new method for automated finite model building exploiting failures and symmetries

Abstract

A method for building nite models is proposed. It combines enumeration of the set of interpretations on a nite domain with strategies in order to prune signi cantly the search space. The main new ideas underlying our method are to bene t from symmetries and from the information extracted from the structure of the problem and from failures of model veri cation tests. The algorithms formalizing the approach are given and the standard properties (termination, completeness, and soundness) are proven. The method can deal with rst-order logic with equality. In contrast to existing ones, it does not require to transform the initial problem into a normal form and can be easily extended to other logics. Experimental results and comparisons with related works are reported.

Proving Failure of Queries for Definite Logic Programs Using XSB-Prolog

“…Of the model generators, the system FMC AT IN F is the weakest on the class of problems we consider. This result contrasts with the results in [7] where it is the best on several problems.…”

“…Incorporating these features in the current approach which relies on direct execution with XSB of the transformed query, requires special care. First let us formalize the notion of conflict set (refutation in first order model generators [7,10]). …”

“…The general idea underlying all methods is the generation of a finite model of the definite program in which the query is false. However the approach developed in [2] is quite different from that used in general purpose model generators for first order logic such as FINDER [10], SEM [12], and FMC AT IN F [7]. Whereas the latter systems search for a model in the space of interpretations, the former searches in the smaller space of pre-interpretations and applies a topdown proof procedure using tabulation to verify whether the query is false in the least model of the Horn theory based on the candidate pre-interpretation.…”

Symmetry in Constraint Programming

“…This is less the case in Automated Theorem Proving, where there is a substantial literature in adapting proof systems to deal with symmetry, e.g. [3,71,86,24,117]. There have also been substantial efforts in Model Checking over some years, e.g.…”

Combining Enumeration and Deductive Techniques in order to Increase the Class of Constructible Infinite Models

“…-Enumeration methods (Slaney, 1993;McCune, 1994;Slaney, 1994;Zhang and Zhang, 1995;Peltier, 1997b;Zhang, 1997;Peltier, 1998b). The principle of these methods is a very simple one: enumerate a class of interpretations (usually interpretations defined on a finite domain) and check whether these interpretations validate the considered formula.…”