Pruning the search space and extracting more models in tableaux
Nicolas Peltier · Logic Journal of IGPL · 1999
An extension of tableaux is presented. The extension is threefold: a new rule allowing the use of information deduced during the building of the tableau in order to simplify formulae occurring in it, integration of semantic strategies (i.e. strategies based on the use of interpretations) that prune the search space and a new way of extracting a model for a given (possible infinite) branch. These features are combined with a former method for simultaneous search for refutations and models. The capabilities of the new method w.r.t. the original one are clearly stated. A non-trivial extension of the standard proof using Hintikka sets is introduced in order to prove the refutational completeness of our method. Finally, it is shown that the method is able to build models for any formula having a model that can be specified by equational constraints. This class contains many existing decidable classes of formulae such as the Bernays-Schönfinkel class, the PVD and OCC1N classes etc. Key words: Automated Deduction, Model Building, Tableux, Equational Constraints.