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Analytic Tableau Systems and Interpolation for
"... Abstract. We give complete sequentlike tableau systems for the modal logics KB, KDB, K 5, and KD5. Analytic cut rules are used to obtain the completeness. Our systems have the analytic superformula property and can thus give a decision procedure. Using the systems, we prove the Craig interpolation ..."
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Abstract. We give complete sequentlike tableau systems for the modal logics KB, KDB, K 5, and KD5. Analytic cut rules are used to obtain the completeness. Our systems have the analytic superformula property and can thus give a decision procedure. Using the systems, we prove the Craig interpolation
Analytic tableau systems and interpolation for the modal logics
 KB, KDB, K5, KD5. Studia Logica
"... Abstract. We give complete sequentlike tableau systems for the modal logics KB, KDB, K 5, and KD5. Analytic cut rules are used to obtain the completeness. Our systems have the analytic superformula property and can thus give a decision procedure. Using the systems, we prove the Craig interpolation ..."
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Cited by 14 (12 self)
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Abstract. We give complete sequentlike tableau systems for the modal logics KB, KDB, K 5, and KD5. Analytic cut rules are used to obtain the completeness. Our systems have the analytic superformula property and can thus give a decision procedure. Using the systems, we prove the Craig interpolation
Analytic Tableau Systems for Propositional Bimodal Logics of Knowledge and Belief
 Proceedings of TABLEAUX 2002, LNAI 2381
, 2002
"... We give sound and complete analytic tableau systems for the propositional bimodal logics KB , KB C , KB 5 , and KB 5C . These logics have two universal modal operators K and B , where K stands for knowing and B stands for believing. The logic KB is a combination of the modal logic S5 (for K ) an ..."
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Cited by 5 (4 self)
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) and KD45 (for B ) with the interaction axioms I : K ! B and C : B ! K B . The logics KB C , KB 5 , KB 5C are obtained from KB respectively by deleting the axiom C (for KB C ), the axioms 5 (for KB 5 ), and both of the axioms C and 5 (for KB 5C ). As analytic sequentlike tableau systems, our
Intuitionisitic Tableau Extracted
"... Abstract. This paper presents a formalization of a sequent presentation of intuitionisitic propositional logic and proof of decidability. The proof is implemented in the Nuprl system and the resulting proof object yields a “correctbyconstruction ” program for deciding intuitionisitc propositional ..."
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sequents. The extracted program turns out to be an implementation of the tableau algorithm. If the argument to the resulting decision procedure is a valid sequent, a formal proof of that fact is returned, otherwise a counterexample in the form of a Kripke Countermodel is returned. The formalization
How to Synthesize a Tableau
"... We synthesize a refutationally complete tableau calculus for propositional logic by a new method, using ordered resolution as a procedural framework at the meta level. Algebraically, the calculus solves the word problem for free distributive lattices. Goaldirectedness of the construction is enforce ..."
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We synthesize a refutationally complete tableau calculus for propositional logic by a new method, using ordered resolution as a procedural framework at the meta level. Algebraically, the calculus solves the word problem for free distributive lattices. Goaldirectedness of the construction
Controlled Integrations of the Cut Rule into Connection Tableau Calculi
"... In this paper techniques are developed and compared which increase the inferential power of tableau systems for classical firstorder logic. The mechanisms are formulated in the framework of connection tableaux, which is an amalgamation of the connection method and the tableau calculus, and a genera ..."
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Cited by 65 (3 self)
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In this paper techniques are developed and compared which increase the inferential power of tableau systems for classical firstorder logic. The mechanisms are formulated in the framework of connection tableaux, which is an amalgamation of the connection method and the tableau calculus, and a
A Tableau Calculus for Equilibrium Entailment
 In Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2000, LNAI 1847
, 2000
"... We apply tableau methods to the problem of computing entailment in the nonmonotonic system of equilibrium logic, a generalisation of the inference relation associated with the stable model and answer set semantics for logic programs. We describe tableau calculi for the nonclassical logics undery ..."
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Cited by 13 (8 self)
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We apply tableau methods to the problem of computing entailment in the nonmonotonic system of equilibrium logic, a generalisation of the inference relation associated with the stable model and answer set semantics for logic programs. We describe tableau calculi for the nonclassical logics
A Tableau Calculus for Partial Functions
, 1996
"... Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using a threevalued logic decades ago, but there has not been a satisfactory mechanization. R ..."
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Cited by 6 (5 self)
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logics. This paper presents a tableau calculus that combines the proper treatment of partial functions with the efficiency of sorted calculi.
PPCtab: an automated Tableau prover for PPC.
"... An automated tableau prover for the Partial Predicate Calculus(PPC) has been implemented and integrated in Isabelle. It is based on the LK objectlogic but is extended to the threevalued logic of PPC. It provides three tactics: the tablo tac which offers the opportunity to trace every step in the p ..."
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An automated tableau prover for the Partial Predicate Calculus(PPC) has been implemented and integrated in Isabelle. It is based on the LK objectlogic but is extended to the threevalued logic of PPC. It provides three tactics: the tablo tac which offers the opportunity to trace every step
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