Detecting Unsolvable Queries for Definite Logic Programs

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In solving a query, the SLD proof procedure for definite programs sometimes searches an infinite space for a non existing solution. For example, querying a planner for an unreachable goal state. Such programs motivate the development of methods to prove the absence of a solution. Considering the definite program and the query ``<- Q'' as clauses of a first order theory, one can apply model generators which search for a finite interpretation in which the program clauses as well as the clause ``false <- Q'' are true. This paper develops a new approach which exploits the fact that all clauses are definite. It is based on a goal directed abductive search in the space of finite pre-interpretations for a pre-interpretation such that ``Q'' is false in the least model of the program based on it. Several methods for efficiently searching the space of pre-interpretations are presented. Experimental results confirm that our approach find solutions with less search than with the use of a first order model generator.