Abstract
The problem of automatically reasoning using a knowledge base containing axioms, definitions and theorems from a first-order theory is recurrent in automated reasoning research. Here we present a sound and complete method for reasoning over an arbitrary first-order theory using the tableau calculus. A natural, well-motivated and simple restriction (implemented in IPR) to the method provides a powerful framework for the automation of the selection of theorems from a knowledge base for use in theorem proving [22]. The restrictions are related to semantic resolution restrictions and the set-of-support restriction in resolution, and to hyper-tableaux and the weak connection condition in tableaux. We also present additional tableau rules used by the IPR prover for handling some equality which is not complete but is sufficient for handling the problems in its intended domain of problem solving.
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Shults, B. (1997). A framework for using knowledge in tableau proofs. 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/BFb0027424
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DOI: https://doi.org/10.1007/BFb0027424
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