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A Tableau System for First-Order Logic with Standard Names
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DOI：10.1007/978-3-032-06085-3_2.png)
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Abstract
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Levesque and Lakemeyer proposed a logic called L as a first-order logic for knowledge representation and reasoning in knowledge-based systems. A characteristic feature of this logic is that it uses a countably infinite set of what are called standard names, which are syntactically treated like constants, but which are also isomorphic to a fixed universe of discourse. Quantifiers in L are then given a substitutional interpretation. This non-standard semantics not only simplifies the proofs for certain meta-theoretic properties, but is also exploited in dedicated reasoning procedures for modal extensions of L that include notions of belief, actions, time, and more. However, the only sound and complete proof system provided for L so far is a Hilbert-style axiom system, as well as an iterative reasoning mechanism based on resolution and clause subsumption. In this paper, we present a tableau system for L, and show its soundness and completeness. Completeness is proved first by reduction to the existing axiom system, and involves the cut rule, and then via Hintikka sets, which does not require the cut rule.
Keywords:
Tableau
First-Order Logic
Standard Names
Substitutional Quantification
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