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36
On evaluating decision procedures for modal logic
, 1997
"... {hustadt, schmidt} topisb.mpg.de This paper investigates the evaluation method of decision procedures for multimodal logic proposed by Giunchiglia and Sebastiani as an adaptation from the evaluation method of Mitchell et al of decision procedures for propositional logic. We compare three different ..."
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Cited by 52 (7 self)
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{hustadt, schmidt} topisb.mpg.de This paper investigates the evaluation method of decision procedures for multimodal logic proposed by Giunchiglia and Sebastiani as an adaptation from the evaluation method of Mitchell et al of decision procedures for propositional logic. We compare three different theorem proving approaches, namely the DavisPutnambased procedure KSAT, the tableauxbased system KTUS and a translation approach combined with firstorder resolution. Our results do not support the claims of Giunchiglia and Sebastiani concerning the computational superiority of KSAT over KRIS, and an easyhardeasy pattern for randomly generated modal formulae. 1
An Empirical Analysis Of Modal Theorem Provers
"... This paper reports on an empirical performance analysis of four modal theorem provers on benchmark suites of randomly generated formulae. The theorem provers tested are the DavisPutnambased procedure Ksat, the tableauxbased system KRIS, the sequentbased Logics Workbench, and a translation appro ..."
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Cited by 23 (10 self)
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This paper reports on an empirical performance analysis of four modal theorem provers on benchmark suites of randomly generated formulae. The theorem provers tested are the DavisPutnambased procedure Ksat, the tableauxbased system KRIS, the sequentbased Logics Workbench, and a translation approach combined with the firstorder theorem prover SPASS.
EXPTime tableaux with global caching for description logics with transitive roles, inverse roles and role hierarchies
 IN PROC. TABLEAUX 2007, AIX EN PROVENCE
, 2007
"... The description logic SHI extends the basic description logic ALC with transitive roles, role hierarchies and inverse roles. The known tableaubased decision procedure [9] for SHI exhibit (at least) NEXPTIME behaviour even though SHI is known to be EXPTIMEcomplete. The automatabased algorithms fo ..."
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Cited by 21 (11 self)
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The description logic SHI extends the basic description logic ALC with transitive roles, role hierarchies and inverse roles. The known tableaubased decision procedure [9] for SHI exhibit (at least) NEXPTIME behaviour even though SHI is known to be EXPTIMEcomplete. The automatabased algorithms for SHI often yield optimal worstcase complexity results, but do not behave well in practice since good optimisations for them have yet to be found. We extend our method for global caching in ALC to SHI by adding analytic cut rules, thereby giving the first EXPTIME tableaubased decision procedure for SHI, and showing one way to incorporate global caching and inverse roles.
Cutfree Sequent and Tableau Systems for Propositional Diodorean Modal Logics
"... We present sound, (weakly) complete and cutfree tableau systems for the propositional normal modal logics S4:3, S4:3:1 and S4:14. When the modality 2 is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of po ..."
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Cited by 20 (3 self)
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We present sound, (weakly) complete and cutfree tableau systems for the propositional normal modal logics S4:3, S4:3:1 and S4:14. When the modality 2 is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points. Although cutfree, the last two systems do not possess the subformula property. But for any given finite set of formulae X the "superformulae" involved are always bounded by a finite set of formulae X L depending only on X and the logic L. Thus each system gives a nondeterministic decision procedure for the logic in question. The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive. Each tableau system has a cutfree sequent analogue proving that Gentzen's cutelimination theorem holds for these latter systems. The techniques are due to Hi...
Optimised EXPTime tableaux for ALC using sound global caching, propagation and cutoffs
 In Proceedings of the 2nd International Conference on Language Resources and Evaluation
, 2007
"... Abstract. We show that global caching can be used with propagation of both satisfiability and unsatisfiability in a sound manner to give an EXPTIME algorithm for checking satisfiability w.r.t. a TBox in the basic description logic ALC. Our algorithm is based on a simple traditional tableau calculus ..."
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Cited by 19 (12 self)
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Abstract. We show that global caching can be used with propagation of both satisfiability and unsatisfiability in a sound manner to give an EXPTIME algorithm for checking satisfiability w.r.t. a TBox in the basic description logic ALC. Our algorithm is based on a simple traditional tableau calculus which builds an andor graph where no two nodes of the graph contain the same formula set. When a duplicate node is about to be created, we use the preexisting node as a proxy, even if the proxy is from a different branch of the tableau, thereby building global caching into the algorithm from the start. Doing so is important since it allows us to reason explicitly about the correctness of global caching. We then show that propagating both satisfiability and unsatisfiability via the andor structure of the graph remains sound. In the longer paper, by combining global caching, propagation and cutoffs, our framework reduces the search space more significantly than the framework of [1]. Also, the freedom to use arbitrary search heuristics significantly increases its application potential. A longer version with all optimisations is currently under review for a journal. An extension for SHI will appear in TABLEAUX 2007.
Constructing the Least Models for Positive Modal Logic Programs
, 2000
"... We give algorithms to construct the least Lmodel for a given positive modal logic program P , where L can be one of the modal logics KD, T , KDB, B, KD4, S4, KD5, KD45, and S5. If L 2 fKD5;KD45;S5g, or L 2 fKD;T ; KDB;Bg and the modal depth of P is finitely bounded, then the least Lmodel of P can ..."
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Cited by 18 (16 self)
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We give algorithms to construct the least Lmodel for a given positive modal logic program P , where L can be one of the modal logics KD, T , KDB, B, KD4, S4, KD5, KD45, and S5. If L 2 fKD5;KD45;S5g, or L 2 fKD;T ; KDB;Bg and the modal depth of P is finitely bounded, then the least Lmodel of P can be constructed in PTIME and coded in polynomial space. We also show that if P has no flat models then it has the least models in KB, K5, K45, and KB5. As a consequence, the problem of checking the satisfiability of a set of modal Horn formulae with finitely bounded modal depth in KD, T , KB, KDB, or B is decidable in PTIME. The known result that the problem of checking the satisfiability of a set of Horn formulae in K5, KD5, K45, KD45, KB5, or S5 is decidable in PTIME is also studied in this work via a different method. 1.
Resolution is a Decision Procedure for Many Propositional Modal Logics
, 1997
"... The paper shows satisfiability in many propositional modal systems can be decided by ordinary resolution procedures. This follows from a general result that resolution and condensing is a decision procedure for the satisfiability problem of formulae in socalled path logics. Path logics arise from p ..."
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Cited by 14 (4 self)
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The paper shows satisfiability in many propositional modal systems can be decided by ordinary resolution procedures. This follows from a general result that resolution and condensing is a decision procedure for the satisfiability problem of formulae in socalled path logics. Path logics arise from propositional and normal uni and multimodal logics by the optimised functional translation method. The decision result provides an alternative decision proof for the relevant modal logics (including K, KD, KT and KB, their combinations ...
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
On the complexity of fragments of modal logics
 Advances in Modal Logic  Volume 5
, 2005
"... abstract. We study and give a summary of the complexity of 15 basic normal monomodal logics under the restriction to the Horn fragment and/or bounded modal depth. As new results, we show that: a) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by k ≥ 2 in the modal ..."
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Cited by 9 (2 self)
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abstract. We study and give a summary of the complexity of 15 basic normal monomodal logics under the restriction to the Horn fragment and/or bounded modal depth. As new results, we show that: a) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by k ≥ 2 in the modal logics K 4 and KD4 is PSPACEcomplete, in K is NPcomplete; b) the satisfiability problem of modal formulas with modal depth bounded by 1 in K 4, KD4, and S4 is NPcomplete; c) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by 1 in K, K 4, KD4, and S4 is PTIMEcomplete. In this work, we also study the complexity of the multimodal logics Ln under the mentioned restrictions, where L is one of the 15 basic monomodal logics. We show that, for n ≥ 2: a) the satisfiability problem of sets of Horn modal clauses in K5n, KD5n, K45n, and KD45n is PSPACEcomplete; b) the satisfiability problem of sets of Horn modal clauses with modal depth bounded by k ≥ 2 in Kn, KBn, K5n, K45n, KB5n is NPcomplete, and in KDn, Tn, KDBn, Bn,
Admissibility of Cut in Coalgebraic Logics
 CMCS
, 2008
"... We study sequent calculi for propositional modal logics, interpreted over coalgebras, with admissibility of cut being the main result. As applications we present a new proof of the (already known) interpolation property for coalition logic and establish the interpolation property for the conditional ..."
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Cited by 8 (7 self)
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We study sequent calculi for propositional modal logics, interpreted over coalgebras, with admissibility of cut being the main result. As applications we present a new proof of the (already known) interpolation property for coalition logic and establish the interpolation property for the conditional logics CK and CK Id.