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Semantic tableaux

The method of semantic tableaux is an efficient decision procedure for satisfiability (and by duality validity) in propositional logic.

The principle behind semantic tableaux is very simple: search for a model (satisfying interpretation) by decomposing the formula into sets of atoms [e.g. propositional letters : $p, q, \ldots$] and negations of atoms. It is easy to check if there is an interpretation for each set: a set of atoms and negations of atoms is satisfiable iff the set does not contain an atom $p$ and its negation $¬p$. The formula is satisfiable iff one of these sets is satisfiable.

For each formula, every step is uniquely defined, because you have to decompose the formula according to the principal connective.

Automated Reasoning with Analytic Tableaux and Related Methods: International Conference, TABLEAUX 2005, Koblenz, Germany, September 14-17, 2005, ... / Lecture Notes in Artificial Intelligence)
Book (Springer)
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