Many of the formalisms used in Attribute Value grammar are notational variants of languages of propositional modal logic, and testing whether two Attribute Value Structures unify amounts to testing for modal satisfiability. In this paper we put this observation to work. We study the complexity of the satisfiability problem for nine modal languages which mirror different aspects of AVS description formalisms, including the ability to express re-entrancy, the ability to express generalisations, and the ability to express recursive constraints. Two main (...) techniques are used: either Kripke models with desirable properties are constructed, or modalities are used to simulate fragments of Propositional Dynamic Logic. Further possibilities for the application of modal logic in computational linguistics are noted. (shrink)

Generally speaking, it appears correct to say that in a formulation of first order logic in which a large number of connectives are taken as primitive which allows us to have our cake and eat it too.

ABSTRACT 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 KRZIS, the sequent-based Logics Workbench, and a translation approach combined with the first-order theorem prover SPASS. Our benchmark suites are sets of multi-modal formulae in a certain normal form randomly generated according to the scheme of Giunchiglia and Sebastiani [GS 96a, GS 96b]. We investigate the quality of (...) the random modal formulae and show that the scheme has some shortcomings, which may lead to mistaken conclusions. We propose improvements to the evaluation method and show that the translation approach provides a viable alternative to the other approaches. (shrink)

Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have connections with computational complexity, theories of arithmetic, and satisfiability algorithms. This is article includes a broad survey of the field, and a technical exposition of some recently developed techniques for proving lower bounds on proof sizes.

ABSTRACT This paper follows on previous papers which present and evaluate various decision procedures for modal logics. We consider new test sets and systems that have been recently proposed in the literature. This new experimental analysis confirm previous experimental results in showing that SAT based decision procedures, i.e., the procedures built on top of decision procedures for propositional satisfiability, are more efficient than tableau based decision procedures. They also confirm previous evidence of an easy-hard-easy pattern in the satisfiability curve for (...) modal K. Finally, on these tests, SAT based decision procedures are also more efficient than the recently proposed decision procedures based on translation methods. These results contradict some of the claims presented in previous papers by other authors. (shrink)