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42
Building decision procedures for modal logics from propositional decision procedures  The case study of modal K(m)
, 1996
"... The goal of this paper is to propose a new technique for developing decision procedures for propositional modal logics. The basic idea is that propositional modal decision procedures should be developed on top of propositional decision procedures. As a case study, we consider satisfiability in m ..."
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Cited by 95 (29 self)
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The goal of this paper is to propose a new technique for developing decision procedures for propositional modal logics. The basic idea is that propositional modal decision procedures should be developed on top of propositional decision procedures. As a case study, we consider satisfiability in modal K(m), that is modal K with m modalities, and develop an algorithm, called Ksat, on top of an implementation of the DavisPutnamLongemannLoveland procedure. Ksat is thoroughly tested and compared with various procedures and in particular with the stateoftheart tableaubased system Kris. The experimental results show that Ksat outperforms Kris and the other systems of orders of magnitude, highlight an intrinsic weakness of tableaubased decision procedures, and provide partial evidence of a phase transition phenomenon for K(m).
A Tableau Calculus for Minimal Model Reasoning
 Proceedings of the Fifth Workshop on Theorem Proving with Analytic Tableaux and Related Methods
, 1996
"... . The paper studies the automation of minimal model inference, i.e., determining whether a formula is true in every minimal model of the premises. A novel tableau calculus for propositional minimal model reasoning is presented in two steps. First an analytic clausal tableau calculus employing a rest ..."
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Cited by 53 (6 self)
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. The paper studies the automation of minimal model inference, i.e., determining whether a formula is true in every minimal model of the premises. A novel tableau calculus for propositional minimal model reasoning is presented in two steps. First an analytic clausal tableau calculus employing a restricted cut rule is introduced. Then the calculus is extended to handle minimal model inference by employing a groundedness property of minimal models. A decision procedure based on the basic calculus is devised and then it is extended to minimal model inference. The basic decision procedure and its extension enjoy some interesting properties. When deciding logical consequence, the basic procedure explores the search space of countermodels with a preference to minimal models and each countermodel is not generated more than once. The procedures can be implemented to run in polynomial space, and they provide polynomial time decision procedures for Horn clauses. The extended decision procedure...
Applying the DavisPutnam procedure to nonclausal formulas
 In Proc. AI*IA'99, number 1792 in Lecture Notes in Arti Intelligence
, 1999
"... . Traditionally, the satisability problem for propositional logics deals with formulas in Conjunctive Normal Form (CNF). A typical way to deal with nonCNF formulas requires (i) converting them into CNF, and (ii) applying solvers usually based on the DavisPutnam (DP) procedure. A well known problem ..."
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Cited by 27 (6 self)
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. Traditionally, the satisability problem for propositional logics deals with formulas in Conjunctive Normal Form (CNF). A typical way to deal with nonCNF formulas requires (i) converting them into CNF, and (ii) applying solvers usually based on the DavisPutnam (DP) procedure. A well known problem of this solution is that the CNF conversion may introduce many new variables, thus greatly widening the space of assignments in which the DP procedure has to search in order to nd solutions. In this paper we present two variants of the DP procedure which overcome the problem outlined above. The idea underlying these variants is that splitting should occur only for the variables in the original formula. The CNF conversion methods employed ensure their correctness and completeness. As a consequence, we get two decision procedures for nonCNF formulas (i) which can exploit all the present and future sophisticated technology of current DP implementations, and (ii) whose space of assignments t...
Labelled Tableaux for Nonmonotonic Reasoning: Cumulative Consequence Relations
 Journal of Logic and Computation
, 2002
"... In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the ..."
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Cited by 25 (10 self)
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In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the latter. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The basic inference rules are provided by the propositional system KE a tableaulike analytic proof system devised to be used both as a refutation method and a direct method of proof that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.
Simplification  A general constraint propagation technique for propositional and modal tableaux
, 1998
"... . Tableau and sequent calculi are the basis for most popular interactive theorem provers for formal verification. Yet, when it comes to automatic proof search, tableaux are often slower than DavisPutnam, SAT procedures or other techniques. This is partly due to the absence of a bivalence principle ..."
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Cited by 24 (2 self)
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. Tableau and sequent calculi are the basis for most popular interactive theorem provers for formal verification. Yet, when it comes to automatic proof search, tableaux are often slower than DavisPutnam, SAT procedures or other techniques. This is partly due to the absence of a bivalence principle (viz. the cutrule) but there is another source of inefficiency: the lack of constraint propagation mechanisms. This paper proposes an innovation in this direction: the rule of simplification, which plays for tableaux the role of subsumption for resolution and of unit for the DavisPutnam procedure. The simplicity and generality of simplification make possible its extension in a uniform way from propositional logic to a wide range of modal logics. This technique gives an unifying view of a number of tableauxlike calculi such as DPLL, KE, HARP, hypertableaux, BCP, KSAT. We show its practical impact with experimental results for random 3SAT and the industrial IFIP benchmarks for hardware ve...
Implementing Circumscription Using a Tableau Method
, 1996
"... . A tableau calculus for firstorder circumscriptive reasoning is developed. Parallel circumscription with fixed and varying predicates with respect to Herbrand models is treated. First a new clausal tableau calculus for firstorder reasoning is developed where a hypertype rule is combined with a r ..."
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Cited by 23 (5 self)
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. A tableau calculus for firstorder circumscriptive reasoning is developed. Parallel circumscription with fixed and varying predicates with respect to Herbrand models is treated. First a new clausal tableau calculus for firstorder reasoning is developed where a hypertype rule is combined with a restricted analytical cut rule. The use of a cut rule offers the advantages that when deciding logical consequence the space of countermodels is searched with a preference to (subset) minimal (Herbrand) models and each countermodel is not generated more than once. Then the calculus is extended to handle parallel circumscription. The circumscriptive calculus is sound in the general case and complete when no function symbols are allowed. Low space complexity is obtained by employing a groundedness property of minimal models that enables a one branch at a time approach to constructing tableaux for circumscriptive inference. 1 INTRODUCTION We study the automation of firstorder circumscriptive...
Towards an efficient tableau method for boolean circuit satisfiability testing
 Computational Logic  CL 2000; First Internatinal Conference
, 2000
"... Boolean circuits oer a natural, structured, and compact representation of Boolean functions for many application domains. In this paper a tableau method for solving satisfiability problems for Boolean circuits is devised. The method employs a direct cut rule combined with deterministic deduction r ..."
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Cited by 21 (7 self)
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Boolean circuits oer a natural, structured, and compact representation of Boolean functions for many application domains. In this paper a tableau method for solving satisfiability problems for Boolean circuits is devised. The method employs a direct cut rule combined with deterministic deduction rules. Simplification rules for circuits and a search heuristic attempting to minimize the search space are developed. Experiments in symbolic model checking domain indicate that the method is competitive against stateoftheart satisfiability checking techniques and a promising basis for further work.
Labelled Tableaux for MultiModal Logics
 Theorem Proving with Analytic
, 1995
"... this paper we present a tableaulike proof system for multimodal logics based on D'Agostino and Mondadori's classical refutation system KE [DM94]. The proposed system, that we call KEM , works for the logics S5A and S5P(n) which have been devised by Mayer and van der Hoek [MvH92] for formalizing th ..."
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Cited by 17 (9 self)
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this paper we present a tableaulike proof system for multimodal logics based on D'Agostino and Mondadori's classical refutation system KE [DM94]. The proposed system, that we call KEM , works for the logics S5A and S5P(n) which have been devised by Mayer and van der Hoek [MvH92] for formalizing the notions of actuality and preference. We shall also show how KEM works with the normal modal logics K45, D45, and S5 which are frequently used as bases for epistemic operators  knowledge, belief (see, for example [Hoe93, Wan90]), and we shall briefly sketch how to combine knowledge and belief in a multiagent setting through KEM modularity