Abstract
Feature logics are the logical basis for so-called unification grammars studied in computational linguistics. We investigate the expressivity of feature terms with negation and the functional uncertainty construct needed for the description of long-distance dependencies and obtain the following results: satisfiability of feature terms is undecidable, sort equations can be internalized, consistency of sort equations is decidable if there is at least one atom, and consistency of sort equations is undecidable if there is no atom.
Similar content being viewed by others
References
Baader, F., 1991, “Augmenting concept languages by transitive closure of roles: An alternative to terminological cycles,”Proceedings of the 12th International Joint Conference on Artificial Intelligence, pp. 446–451, Sydney, Australia.
Blackburn, P. and Spaan, E., 1992, “A modal perspective on the computational complexity of attribute value grammar,” Logic Group Preprint Series No. 77, Department of Philosophy, Utrecht University, The Netherlands.
Boone, W. W., 1959, “The word problem,”Ann. of Mat. 70, 207–265.
Brachman, R. J. and Schmolze, J. G., 1985, “An overview of the KL-ONE knowledge representation system.”Cognitive Science,9(2), 171–216.
Goldblatt, R., 1987,Logics of Time and Computation, CSLI Lecture Notes 7. Center for the Study of Language and Information, Stanford University, California, USA.
Johnson, M., 1988,Attribute-Value Logic and the Theory of Grammar, CSLI Lecture Notes 16. Center for the Study of Language and Information, Stanford University, California, USA.
Kaplan, R. M. and Bresnan, J., 1982, “Lexical-Functional Grammar: A formal system for grammatical representation,” pp. 173–381 inThe Mental Representation of Grammatical Relations, J. Bresnan, ed., Cambridge, Mass.: MIT Press.
Kaplan, R. M. and Maxwell III, J. T., 1989, “An algorithm for functional uncertainty,” pp. 297–302 inProceedings of the 12th International Conference on Computational Linguistics, Budapest, Hungary.
Kaplan, R. M. and Maxwell III, J. T., 1989, “Constituent coordination in lexical-functional grammar,” pp. 303–305 inProceedings of the 12th International Conference on Computational Linguistics, Budapest, Hungary.
Kasper, R. T. and Rounds, W. C., 1986, “A logical semantics for feature structures,” pp. 257–265 inProceedings of the 24th Annual Meeting of the ACL, Columbia University, New York, N.Y.
Kay, M., 1979, “Functional grammar,” inProceedings of the Fifth Annual Meeting of the Berkeley Linguistics Society, Berkeley, Cal.: Berkeley Linguistics Society.
Kozen, R. and Tiuryn, J., 1990, “Logics of programs,” pp. 789–840 inHandbook of Theoretical Computer Science, Volume B: Formal Models and Semantics, J. van Leeuwen, ed., Elsevier: Amsterdam and MIT Press: Cambridge, Mass.
Levesque, H. J. and Brachman, R. J., 1987, “Expressiveness and tractability in knowledge representation and reasoning.”Computational Intelligence,3, 78–93.
Nebel, B. and Smolka, G., 1990, “Representation and reasoning with attributive descriptions,” pp. 112–139 inSorts and Types in Artificial Intelligence, volume 418 ofLectures Notes in Computer Science, K. Bläsius, U. Hedtstück and C.-R. Rollinger, eds., Berlin, Germany: Springer-Verlag.
Novikov, P. S., 1955, “On the algorithmic unsolvability of the word problem (in Russian),”Dokl. Akad. Nauk SSSR Mathematičeskii Institut Trudy, 44, Moscow.
Pollard, C. and Sag, I. A., 1987,Information-Based Syntax and Semantics, volume 13 ofCSLI Lecture Notes. Center for the Study of Language and Information, Stanford University, Cal.
Rounds, W. C. and Kasper, R. T., 1986, “A complete logical calculus for record structures representing linguistic information,” pp. 38–43, inProceedings of the 1st IEEE Symposium on Logic in Computer Science, Boston, Mass.
Schild, K., 1991, “A correspondence theory for terminological logics: Preliminary report,”Proceedings of the 12th International Joint Conference on Artificial Intelligence, 466–471, Sydney, Australia.
Schmidt-Schauß, M. and Smolka, G., 1991, “Attributive concept descriptions with complements,”Artificial Intelligence,48, 1–26.
Shieber, S. M., 1986,An Introduction to Unification-Based Approaches to Grammar, volume 4 ofCSLI Lecture Notes. Center for the Study of Language and Information, Stanford University, Cal.
Shieber, S. M., Uszkoreit, H., Pereira, F. C., Robinson, J. and Tyson, M., 1983, “The siformalism and implementation of PATR-II,” inResearch on Interactive Acquisition and Use of Knowledge, B. J. Grosz and M. Stickel, eds., SRI International, Artificial Intelligence Center, Menlo Park, Cal.
Smolka, G., 1988, “A feature logic with subsorts,” LILOG Report 33, IWBS, IBM Germany, Stuttgart, Germany.
Smolka, G., 1992, “Feature constraint logics for unification grammars,”Journal of Logic Programming,12, 51–87.
Stillwell, J., 1982, “The word problem and the isomorphism problem for groups,”Bulletin AMS,6, 33–56.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Baader, F., Bürckert, HJ., Nebel, B. et al. On the expressivity of feature logics with negation, functional uncertainty, and sort equations. J Logic Lang Inf 2, 1–18 (1993). https://doi.org/10.1007/BF01051766
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01051766