Automated Model Building
Springer Science & Business Media, Sep 13, 2004 - Philosophy - 341 pages
On the history of the book: In the early 1990s several new methods and perspectives in au- mated deduction emerged. We just mention the superposition calculus, meta-term inference and schematization, deductive decision procedures, and automated model building. It was this last ?eld which brought the authors of this book together. In 1994 they met at the Conference on Automated Deduction (CADE-12) in Nancy and agreed upon the general point of view, that semantics and, in particular, construction of models should play a central role in the ?eld of automated deduction. In the following years the deduction groups of the laboratory LEIBNIZ at IMAG Grenoble and the University of Technology in Vienna organized several bilateral projects promoting this topic. This book emerged as a main result of this cooperation. The authors are aware of the fact, that the book does not cover all relevant methods of automated model building (also called model construction or model generation); instead the book focuses on deduction-based symbolic methods for the construction of Herbrand models developed in the last 12 years. Other methods of automated model building, in particular also ?nite model building, are mainly treated in the ?nal chapter; this chapter is less formal and detailed but gives a broader view on the topic and a comparison of di?erent approaches. Howtoreadthisbook: In the introduction we give an overview of automated deduction in a historical context, taking into account its relationship with the human views on formal and informal proofs.
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algorithm applied arity atomic representation automated deduction c-clauses called CARM clash clause logic clause sets computation consider contains corresponding defined definition with constraints deletion denoted disequations disjunction dissubsumption EQ(A equational clause equational formulae equational problems equivalent example exists false finite model building finite set first-order formula first-order logic formal function symbols GEARM ground atoms ground clauses ground instances ground terms Herbrand interpretation Herbrand model Herbrand universe Horn clauses Horn logic hyper-linking hyperresolution induction inference infinite Leitsch Lemma linear literals MBEQ method model representation normal form obtain occurring orthogonal paramodulation Peltier positive clauses predicate symbols Proof PROP-operator Proposition prove RAMC replaced resolution satisfiable set semantics set of clauses set of ground signature solution solved form subsumes subsumption subterm tableaux terminates theorem provers tion transformation tree automaton trivial true iff truth values unifiable unification unit clauses unsatisfiable variables
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