tailieunhanh - Báo cáo khoa học: "Decidability and Undecidability in stand-alone Feature Logics"

This paper investigates the complexity of the satisfiability problem for feature logics strong enough to code entire grammars unaided. We show that feature logics capable of both enforcing re-entrancy and stating linguistic generalisations will have undecidable satisfiability problems even when most Boolean expressivity has been discarded. We exhibit a decidable fragment, but the restrictions imposed to ensure decidability render it unfit for stand-alone use. The import of these results is discussed, and we conclude that there is a need for feature logics that are less homogeneous in their treatment of linguistic structure. . | Decidability and Undecidability in stand-alone Feature Logics Patrick Blackburn Department of Philosophy University of Utrecht Heidelberglaan 8 3584 cs Utrecht The Netherlands Email patrick@ Edith Spaan Department of Computer Science SUNY at Buffalo 226 Bell Hall Buffalo NY 14260 United States of America Email spaan@ Abstract This paper investigates the complexity of the satisfiability problem for feature logics strong enough to code entire grammars unaided. We show that feature logics capable of both enforcing re-entrancy and stating linguistic generalisations will have undecidable satisfiability problems even when most Boolean expressivity has been discarded. We exhibit a decidable fragment but the restrictions imposed to ensure decidability render it unfit for stand-alone use. The import of these results is discussed and we conclude that there is a need for feature logics that are less homogeneous in their treatment of linguistic structure. 1 Introduction This paper investigates decidability and undecidability in stand-alone feature logics that is feature logics strong enough to express entire grammars without the assistance of a phrase-structure backbone. Our results are predominately negative and seem applicable to most existing stand-alone formalisms. We strengthen a result of Blackburn and Spaan 1991 1992 to show that the ability to express re-entrancy and the ability to express generalisations about feature structures interact in ways that lead to undecidability even if most Boolean expressivity has been dropped from the logic. Even our positive results have a negative flavour. We exhibit a decidable fragment but the restrictions imposed to attain decid ability render it incapable of encoding interesting grammars unaided. But what is the import of such results This is the question we turn to in the last section of the paper. Basically we regard such results as a sign that existing feature logics treat linguistic structure too .