{hustadt, schmidt} topi-sb.mpg.de This paper investigates the evaluation method of decision procedures for multi-modal 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 Davis-Putnam-based procedure KSAT, the tableaux-based system KTUS and a translation approach combined with first-order resolution. Our results do not support the claims of Giunchiglia and Sebastiani concerning the computational superiority of KSAT over KRIS, and an easy-hard-easy pattern for randomly generated modal formulae. 1

mspass is an extension of the first-order 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.

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 ExpTime-hardness 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.

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 Davis-Putnam-based procedure Ksat, the tableaux-based system KRIS, the sequent-based Logics Workbench, and a translation approach combined with the first-order theorem prover SPASS.

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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 expressions---which 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 ExpTime-hardness conjecture. This establishes a kind of "theoretical benchmark" that all algorithmic approaches can be measured with.

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 so-called path logics. Path logics arise from propositional and normal uni- and multi-modal 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 ...

Fluted logic is a fragment of first-order logic without function symbols in which the arguments of atomic subformulae form ordered sequences. A consequence of this restriction is that, whereas first-order logic is only semi-decidable, 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 first-order resolution and a new form of dynamic renaming, called separation.

.24> existential and universal role restriction operations: some and all, as well as domain and range, ffl additional role operators: comp (composition), sum (relative sum), conv (converse), id (identity), div (diversity) , and ffl test (test), domrestr (domain restriction) and ranrestr (range restriction). mspass supports terminological axioms in their most general form, which includes generalised inclusion and equivalence axioms, for both concepts and roles. In addition, because the first-order symbol associated by the translation mapping to a propositional symbol can be declared, it is possible to specify ABox statements as well as any first-order restrictions on concepts and roles. Translation mappings A number of different translatio

. This paper is concerned with the unification problem in the path logics associated by the optimised functional translation method with the propositional modal logics K, KD, KT, KD4, S4 and S5. It presents improved unification algorithms for certain forms of the right identity and associativity laws. The algorithms employ mutation rules, which have the advantage that terms are worked off from the outside inward, making paramodulating into terms superfluous. 1 Introduction An area of application for unification theory which has not been explored much is modal logic. Modal inference can be facilitated by theory resolution via the socalled functional translation or its variation for propositional modal logics, the optimised functional translation approach. The functional translation method was proposed independently in the late eighties by a number of groups. Fari~nas del Cerro and Herzig (1989, 1995) describe a transformation of quantified modal logics into so-called deterministic logi...