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22
A tutorial on Stålmarck's proof procedure for propositional logic
 Formal Methods in System Design
, 1998
"... We explain Stalmarck's proof procedure for classical propositional logic. The method is implemented in a commercial tool that has been used successfully in real industrial verification projects. Here, we present the proof system underlying the method, and motivate the various design decisions th ..."
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Cited by 64 (1 self)
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We explain Stalmarck's proof procedure for classical propositional logic. The method is implemented in a commercial tool that has been used successfully in real industrial verification projects. Here, we present the proof system underlying the method, and motivate the various design decisions that have resulted in a system that copes well with the large formulas encountered in industrialscale verification. 1
HigherOrder Tableaux
, 1995
"... Even though higherorder calculi for automated theorem proving are rather old, tableau calculi have not been investigated yet. This paper presents two free variable tableau calculi for higherorder logic that use higherorder unification as the key inference procedure. These calculi differ in the ..."
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Cited by 16 (6 self)
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Even though higherorder calculi for automated theorem proving are rather old, tableau calculi have not been investigated yet. This paper presents two free variable tableau calculi for higherorder logic that use higherorder unification as the key inference procedure. These calculi differ in the treatment of the substitutional properties of equivalences. The first calculus is equivalent in deductive power to the machineoriented higherorder refutation calculi known from the literature, whereas the second is complete with respect to Henkin's general models.
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 12 (10 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 lemma for the mentioned logics. 1
Are Tableaux an Improvement on TruthTables? CutFree proofs and Bivalence
, 1992
"... We show that Smullyan's analytic tableaux cannot psimulate the truthtables. We identify the cause of this computational breakdown and relate it to an underlying semantic difficulty which is common to the whole tradition originating in Gentzen's sequent calculus, namely the dissonance between cutf ..."
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Cited by 12 (0 self)
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We show that Smullyan's analytic tableaux cannot psimulate the truthtables. We identify the cause of this computational breakdown and relate it to an underlying semantic difficulty which is common to the whole tradition originating in Gentzen's sequent calculus, namely the dissonance between cutfree proofs and the Principle of Bivalence. Finally we discuss some ways in which this principle can be built into a tableaulike method without affecting its "analytic" nature. 1 Introduction The truthtable method, introduced by Wittgenstein in his Tractatus LogicoPhilosophicus, provides a decision procedure for propositional logic which is immediately implementable on a machine. However this timehonoured method is usually mentioned only to be immediately dismissed because of its incurable inefficiency. The wellknown tableau method (which is closely related to Gentzen's cutfree sequent calculus) is commonly regarded as a "shortcut" in testing the logical validity of complex propositions...
Clausal tableau systems and space bounds for the modal logics
 KD, T, KB, KDB, and B. Submitted to Journal of Logic and Computation
, 1999
"... Abstract. We propose so called clausal tableau systems for the common modal logics K, KD, T, KB, KDB and B. There is a measure such that for each tableau rule of these systems the measure of all its denominators is smaller than the measure of its numerator. Basing on these systems, we give a decisio ..."
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Cited by 7 (5 self)
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Abstract. We propose so called clausal tableau systems for the common modal logics K, KD, T, KB, KDB and B. There is a measure such that for each tableau rule of these systems the measure of all its denominators is smaller than the measure of its numerator. Basing on these systems, we give a decision procedure for the logics, which uses O(n 2)space for the logics T, KB, KDB and B, and O(n. log n)space for the logics K and KD. We also show that the problem of checking satisfiability in T, KB, KDB, or B for formulae with finitely bounded modaldepth is decidable in O(n. log n)space. We are the first who explicitly establish space requirements for the logics KB, KDB and B. 1
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. ..."
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Cited by 6 (5 self)
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. 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. Recent years have seen a thorough investigation of the framework of manyvalued truthfunctional logics. However, strong Kleene logic, where quantification is restricted and therefore not truthfunctional, does not fit the framework directly. We solve this problem by applying recent methods from sorted logics. This paper presents a tableau calculus that combines the proper treatment of partial functions with the efficiency of sorted calculi. Keywords: Partial functions, manyvalued logic, sorted logic, tableau. 1 Introduction Many practical applications of deduction systems in mathematics and computer science rely on the correct and efficient treatment of partial functions. For this purpose...
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 4 (4 self)
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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 ) 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 calculi give simple decision procedures for reasoning about both knowledge and belief in the mentioned logics.
A New Space Bound for the Modal Logics K4, KD4 and S4
"... We propose so called clausal tableau systems for the common modal logics K4, KD4 and S4. Basing on these systems, we give more efficient decision procedures than those hitherto known for the considered logics. In particular space requirements for our logics are reduced from the previously establishe ..."
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Cited by 4 (2 self)
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We propose so called clausal tableau systems for the common modal logics K4, KD4 and S4. Basing on these systems, we give more efficient decision procedures than those hitherto known for the considered logics. In particular space requirements for our logics are reduced from the previously established bound O(n 2 : log n) to O(n: log n).
Cutsimulation in impredicate logics
 PROC. OF IJCAR 2006
, 2006
"... We investigate cutelimination and cutsimulation in impredicative (higherorder) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic — in our case a sequent calculus for classical type theory — is like adding cut. The phenomenon equally ..."
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Cited by 3 (3 self)
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We investigate cutelimination and cutsimulation in impredicative (higherorder) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic — in our case a sequent calculus for classical type theory — is like adding cut. The phenomenon equally applies to prominent axioms like Boolean and functional extensionality, induction, choice, and description. This calls for the development of calculi where these principles are builtin instead of being treated axiomatically.