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18
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
Stalmarck's algorithm as a HOL derived rule
 Verlag LNCS 1125
, 1996
"... Abstract. St˚almarck’s algorithm is a patented technique for tautologychecking which has been used successfully for industrialscale problems. Here we describe the algorithm and explore its implementation as a HOL derived rule. 1 ..."
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Abstract. St˚almarck’s algorithm is a patented technique for tautologychecking which has been used successfully for industrialscale problems. Here we describe the algorithm and explore its implementation as a HOL derived rule. 1
Sequent Calculi for Nominal Tense Logics: A Step Towards Mechanization?
, 1999
"... . We define sequentstyle calculi for nominal tense logics characterized by classes of modal frames that are firstorder definable by certain \Pi 0 1 formulae and \Pi 0 2 formulae. The calculi are based on d'Agostino and Mondadori's calculus KE and therefore they admit a restricted cutrule ..."
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Cited by 15 (4 self)
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. We define sequentstyle calculi for nominal tense logics characterized by classes of modal frames that are firstorder definable by certain \Pi 0 1 formulae and \Pi 0 2 formulae. The calculi are based on d'Agostino and Mondadori's calculus KE and therefore they admit a restricted cutrule that is not eliminable. A nice computational property of the restriction is, for instance, that at any stage of the proof, only a finite number of potential cutformulae needs to be taken under consideration. Although restrictions on the proof search (preserving completeness) are given in the paper and most of them are theoretically appealing, the use of those calculi for mechanization is however doubtful. Indeed, we present sequent calculi for fragments of classical logic that are syntactic variants of the sequent calculi for the nominal tense logics. 1 Introduction Background. The nominal tense logics are extensions of Prior tense logics (see e.g. [Pri57, RU71]) by adding nomina...
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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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...
Theorem Proving and Model Building with the Calculus KE
, 1996
"... A Prolog implementation of a new theoremprover for firstorder classical logic is described. The prover is based on the calculus KE and the rules used for analysing quantifiers in free variable semantic tableaux. A formal specification of the rules used in the implementation is described, for which ..."
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Cited by 9 (5 self)
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A Prolog implementation of a new theoremprover for firstorder classical logic is described. The prover is based on the calculus KE and the rules used for analysing quantifiers in free variable semantic tableaux. A formal specification of the rules used in the implementation is described, for which soundness and completeness is straightforwardly verified. The prover has been tested on the first 47 problems of the Pelletier set, and its performance compared with a state of the art semantic tableaux theoremprover. It has also been applied to model building in a prototype system for logical animation, a technique for symbolic execution which can be used for validation. The interest of these experiments is that they demonstrate the value of certain `characteristics' of the KE calculus, such as the significant spacesaving in theoremproving, the mutual inconsistency of open branches in KE trees, and the relation of the KE rules to `traditional' forms of reasoning. 1 Introduction 1.1 Ov...
How to prove properties of recursively defined circuits using Stalmarck's method
, 1998
"... . We present a technique for proving properties of recursively defined circuits using Stalmarck's method. We consider instances of circuits defined according to a particular inductive scheme and show how extra definitions of fresh propositional variables can be added automatically in such a way that ..."
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Cited by 6 (2 self)
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. We present a technique for proving properties of recursively defined circuits using Stalmarck's method. We consider instances of circuits defined according to a particular inductive scheme and show how extra definitions of fresh propositional variables can be added automatically in such a way that an automatic theorem prover is able to find short proofs of correctness of the resulting circuits. We show how regular circuits, such as adders and multipliers, fit into the inductive scheme. 1 Introduction Stalmarck's method is an effective algorithm for proving formulas in propositional logic extended with some arithmetic. The method was patented by Stalmarck in 1992 and has since been used to verify complex systems in many real industrial projects, particularly in the area of railway signalling [4]. Stalmarck defines a notion of proof hardness, the number of simultaneously free assumptions in a proof. It turns out that many real verification problems have easy proofs (hardness 0 or 1), a...
A reduplication and loop checking free proof system for S4
 Department of Computer Science, University of Milan
, 1996
"... Most of the sequent/tableau based proof systems for the modal logic S4 need to duplicate formulas and thus are required to adopt some method of loop checking [7, 13, 10]. In what follows we present a tableaulike proof system for S4, based on D’Agostino and Mondadori’s classical KE [3], which is fre ..."
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Most of the sequent/tableau based proof systems for the modal logic S4 need to duplicate formulas and thus are required to adopt some method of loop checking [7, 13, 10]. In what follows we present a tableaulike proof system for S4, based on D’Agostino and Mondadori’s classical KE [3], which is free of duplication and loop checking. The key
Tableau TheoremProving, Default Logic and the Parallel ATMS
, 1993
"... : In this paper we demonstrate a connection between semantic tableaux and the parallel ATMS of Dixon and deKleer. We show how this enables the ATMS to be used as a propositional theoremprover. We also show the connection between the ATMS and a subclass of default logic theories called free normal d ..."
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: In this paper we demonstrate a connection between semantic tableaux and the parallel ATMS of Dixon and deKleer. We show how this enables the ATMS to be used as a propositional theoremprover. We also show the connection between the ATMS and a subclass of default logic theories called free normal default theories. 1 Introduction. Assumptionbased Truth Maintenance, [dK86a, dK86b, dK86c], has become a widely used basis for a variety of problem and constraintsolving programs. DeKleer 's original ATMS was described in terms that were complicated by the necessity for efficient implementation on a serial machine. Since then Dixon and deKleer [DdK88] have described a Connection Machine implementation and have shown that abstracting away from details of the serial implementation leads to a simpler, more general, model of the ATMS and has the advantage over the serial version of being complete without the extra mechanism of hyperresolution. We have implemented an ATMS along the lines descri...
MacKE: Yet Another Proof Assistant Automated Pedagogic Tool
, 1995
"... . In this paper, we describe the implementation of (yet another) proof assistant and/or automated pedagogic tool. This one is based on the calculus KE and our Prolog implementation of free variable KE. The new system is written in LPA MacProlog TM , and features an interactive interface via menus, ..."
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. In this paper, we describe the implementation of (yet another) proof assistant and/or automated pedagogic tool. This one is based on the calculus KE and our Prolog implementation of free variable KE. The new system is written in LPA MacProlog TM , and features an interactive interface via menus, dialogues and graphics tools, a graphics window for constructing and displaying proofs, and on and offline proof checking. The ease of use and the visual satisfaction of the interface should make the system very convenient for fulfilling its primary intended function: teaching logic and reasoning through KE. 1 Introduction In this paper, we describe the implementation of (yet another) proof assistant and/or automated pedagogic tool. This one is based on the calculus KE [4] and our Prolog implementation of free variable KE [11]. KE is reviewed in Sect. 2.1, and our implementation is described in Sect. 2.2. The new system is written in LPA MacProlog TM , and features an interactive inter...