Abstract
Quasitautologies are formulas valid solely by the properties of identity and of propositional connectives. In connection with Herbrand's theorem the quasitautologies are central to the automated theorem proving with identity. It is a matter of folklore in logic that the predicate of being a quasitautology is decidable. We present a finitary proof of this fact by a powerful method of transformation of tableaux with identity rules. This should shed some light on the subtleties of tableaux with identity. We have extended this method in a separate paper to a much harder finitary proof of the conservativity of Skolem axioms. The question of why we should prefer finitary over model-theoretic proofs occurs frequently in logic. The answer is always simple: we obtain more information from a finitary proof than from a model-theoretic one. In our case, we get that quasitautologies can be proved by tableaux with a subterm property.
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Komara, J., Voda, P.J. (1997). On quasitautologies. In: Galmiche, D. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1997. Lecture Notes in Computer Science, vol 1227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027417
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DOI: https://doi.org/10.1007/BFb0027417
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