On Computational Representations of Herbrand Models

Computationally feasible representations of models of rst-order formulas are of interest in various elds like e.g. in automated model building, automated deduction, deductive databases, etc. For representing a Herbrand model symbolically we only need to represent the true ground atoms of the model. Many mechanisms for representing such (term) sets appear as candidates for model representations. We are particularly interested in expressiveness and in algorithmic issues like the availability (and complexity) of ground atom evaluation, equivalence test and clause evaluation. We give a survey of recent work on this topic and then we focus on tree automata as a suitable device for model representations { a device that appears in many notations such as automata, grammars, logic programs, etc. We show that for this representation clause evaluation is EXPTIME-complete. We describe an improved algorithm for clause evaluation that avoids the explicit determinization of the automaton and we sketch why this is of beneet in many practical situations.