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25
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 56 (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
MSPASS: Modal Reasoning by Translation and FirstOrder Resolution
, 2000
"... mspass is an extension of the firstorder theorem prover spass, which can be used as a modal logic theorem prover, a theorem prover for description logics and a theorem prover for the relational calculus. ..."
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Cited by 44 (4 self)
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mspass is an extension of the firstorder theorem prover spass, which can be used as a modal logic theorem prover, a theorem prover for description logics and a theorem prover for the relational calculus.
PSpace Reasoning for Graded Modal Logics
, 1999
"... We present a PSpace algorithm that decides satisfiability of the graded modal logic Gr(KR)  a natural extension of propositional modal logic KR by counting expressions  which plays an important role in the area of knowledge representation. The algorithm employs a tableaux approach and is the rst k ..."
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Cited by 36 (1 self)
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We present a PSpace algorithm that decides satisfiability of the graded modal logic Gr(KR)  a natural extension of propositional modal logic KR by counting expressions  which plays an important role in the area of knowledge representation. The algorithm employs a tableaux approach and is the rst known algorithm which meets the lower bound for the complexity of the problem. Thus, we exactly fix the complexity of the problem and refute an ExpTimehardness conjecture. We extend the results to the logic Gr(K R 1 \ ), which augments Gr(KR) with inverse modalities and intersection of accessibility relations. This establishes a kind of "theoretical benchmark" that all algorithmic approaches can be measured with.
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 26 (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.
A PSpace Algorithm for Graded Modal Logic
 In Proc. of CADE16, LNCS
, 1999
"... We present a PSpace algorithm that decides satisfiability of the graded modal logic Gr(K_R)a natural extension of propositional modal logic KR by counting expressionswhich plays an important role in the area of knowledge representation. The algorithm employs a tableaux approach and is the firs ..."
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Cited by 14 (6 self)
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We present a PSpace algorithm that decides satisfiability of the graded modal logic Gr(K_R)a natural extension of propositional modal logic KR by counting expressionswhich plays an important role in the area of knowledge representation. The algorithm employs a tableaux approach and is the first known algorithm which meets the lower bound for the complexity of the problem. Thus, we exactly fix the complexity of the problem and refute a ExpTimehardness conjecture. This establishes a kind of "theoretical benchmark" that all algorithmic approaches can be measured with.
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 ...
A Survey of Decidable FirstOrder Fragments and Description Logics
 Journal of Relational Methods in Computer Science
, 2004
"... The guarded fragment and its extensions and subfragments are often considered as a framework for investigating the properties of description logics. There are also other, some less wellknown, decidable fragments of firstorder logic which all have in common that they generalise the standard tran ..."
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Cited by 14 (2 self)
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The guarded fragment and its extensions and subfragments are often considered as a framework for investigating the properties of description logics. There are also other, some less wellknown, decidable fragments of firstorder logic which all have in common that they generalise the standard translation of to firstorder logic. We provide a short survey of some of these fragments and motivate why they are interesting with respect to description logics, mentioning also connections to other nonclassical logics.
A Resolution Decision Procedure for Fluted Logic
 In Proc. CADE17
, 2000
"... Fluted logic is a fragment of firstorder logic without function symbols in which the arguments of atomic subformulae form ordered sequences. A consequence of this restriction is that, whereas firstorder logic is only semidecidable, fluted logic is decidable. In this paper we present a sound, comp ..."
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Cited by 13 (10 self)
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Fluted logic is a fragment of firstorder logic without function symbols in which the arguments of atomic subformulae form ordered sequences. A consequence of this restriction is that, whereas firstorder logic is only semidecidable, fluted logic is decidable. In this paper we present a sound, complete and terminating inference procedure for fluted logic. Our characterisation of fluted logic is in terms of a new class of socalled fluted clauses. We show that this class is decidable by an ordering refinement of firstorder resolution and a new form of dynamic renaming, called separation.