Automated Theorem Proving Proof and Model Generation with Disconnection Tableaux

We present the disconnection tableau calculus, which is a free-variable clausal tableau calculus where variables are treatedin a nonrigidmanner. The calculus essentially consists of a single inference rule, the so-called linking rule, which strongly restricts the possible clauses in a tableau. The method can also be viewed as an integration of the linking rule as used in Plaisted’s linking approach into a tableau format. The calculus has the proof-theoretic advantage that, in the case of a satisfiable formula, one can characterise a model of the formula, a property which most of the free-variable tableau calculi lack. In the paper, we present a rigorous completeness proof and give a procedure for extracting a model from a finitely failed branch.

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