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FreeVariable Tableaux for ConstantDomain Quantified Modal Logics with Rigid and NonRigid Designation
, 2001
"... This paper presents a sound and complete freevariable tableau calculus for constantdomain quantified modal logics, with a propositional analytical basis, i.e. one of the systems K, D, T, K4, S4. The calculus is obtained by addition of the classical freevariable rule and the "liberalized" + rule ..."
Abstract

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This paper presents a sound and complete freevariable tableau calculus for constantdomain quantified modal logics, with a propositional analytical basis, i.e. one of the systems K, D, T, K4, S4. The calculus is obtained by addition of the classical freevariable rule and the "liberalized" + rule [14] to a standard set of propositional rules. Thus, the proposed system characterizes prooftheoretically the constantdomain semantics, which cannot be captured by "standard" (nonpre xed, nonannotated) ground tableau calculi. The calculi are extended so as to deal also with nonrigid designation, by means of a simple numerical annotation on functional symbols, conveying some semantical information about the worlds where they are meant to be interpreted.