×

Language in action. (English) Zbl 0743.03018

The author gives detailed arguments to some valuable ideas which we briefly outline here: Logic has reached such a state of “inter- translatability”, that almost all known variant logics can be embedded into each other, via suitable translations. Thus all systems of dynamic interpretation or inference proposed so far admit a direct embedding into an ordinary ‘static’ predicate logic having explicit transition predicates. The author emphasizes that the issue is not \(whether\) the new systems of information structure or processing are more ‘expressive’ than the traditional logical systems (since they are not), but rather \(which\) interesting phenomena and questions will be put into the right focus for them. In this context, the paper makes some interesting concrete proposals for information-oriented or dynamic semantics: from a Gentzen- type “Lambek calculus” in the context of Categorial Grammar and extended to families of languages (\(L\)-models), to modal logic-based models or relational algebras (\(R\)-models). What matters is an increased sensitivity to configurations of dynamic logics, e.g., the author’s categorial hierarchy of calculi in Categorial Grammar, an (ascending) family of logics whose interconnections reveal intra-linguistic, or cross-linguistic, comparisons of complexity between syntactic phenomena. Finally, the new framework (of natural language as a programming language), because of its differences from standard logic, arise a lot of new kinds of questions when regarding propositions as programs: program synthesis, determinism, quering.
Reviewer: N.Curteanu (Iaşi)

MSC:

03B65 Logic of natural languages
03B70 Logic in computer science
68T50 Natural language processing
Full Text: DOI

References:

[1] Abrusci, V. M., 1988a, ?Sequent Calculus for Intuitionistic Linear Propositional Logic?, report 1, Department of Philosophy of Science, University of Bari. · Zbl 0787.03005
[2] Abrusci, V. M., 1988b, ?A Comparison between Lambek Syntactic Calculus and Intuitionistic Linear Propositional Logic?, report 2, Department of Philosophy of Science, University of Bari. · Zbl 0719.03005
[3] Avron, A., 1988, ?The Semantics and Proof Theory of Linear Logic?, Theoretical Computer Science 57, 161-184. · Zbl 0652.03018 · doi:10.1016/0304-3975(88)90037-0
[4] Barwise, J., 1987, ?Noun Phrases, Generalized Quantifiers and Anaphora?, in P. Gardenfors, ed., 1987, 1-29. · Zbl 0723.03011
[5] Benthem, J.van, 1985. Modal Logic and Classical Logic. Bibliopolis, Napoli/The Humanities Press, Atlantic Heights. · Zbl 0639.03014
[6] Benthem, J.van, 1986, Essays in Logical Semantics, D. Reidel, Dordrecht. · Zbl 0619.03021
[7] Benthem, J. van, 1987, ?Categorial Grammar and Type Theory?, report 87-07, Institute for Language, Logic and Information, University of Amsterdam. Also appeared in Journal of Philosophical Logic 19, 115-168. · Zbl 0695.03016
[8] Benthem, J. van, 1987*, ?Polyadic Quantifiers?, report 87-04, Institute for Language, Logic and Information, University of Amsterdam. Also appeared in Linguistics and Philosophy 12, 437-464.
[9] Benthem, J. van, 1988a, ?The Lambek Calculus?, in R. Oehrle et al., eds., 1988, 35-68.
[10] Benthem, J. van, 1988b, ?Semantic Parallels in Natural Language and Computation?, report 88-06, Institute for Language, Logic and Information, University of Amsterdam. Also appeared in H.-D. Ebbinghaus et al., eds., 1989, 331-375.
[11] Benthem, J. van, 1988c, ?Logical Constants across Varying Types?, report LP-88-05, Institute for Language, Logic and Information, University of Amsterdam. Also appeared in Notre Dame Journal of Formal Logic 30, 315-342. · Zbl 0694.03023
[12] Benthem, J. van, 1989a, ?The Fine-Structure of Categorial Semantics?, report LP-89-01, Institute for Language, Logic and Information, University of Amsterdam. (To appear in M. Rosner, ed., Lugano Workshop on Computational Linguistics and Formal Semantics, Cambridge University Press.)
[13] Benthem, J. van, 1989b, ?Relational Algebra from The Perspective of Modal Logic?, Institute of Language, Logic and Information, University of Amsterdam.
[14] Benthem, J. van, 1989c, ?Modal Logic as a Theory of Information?, to appear in J. Copeland, ed., Proceedings Prior Memorial Conference, Christchurch, New Zealand.
[15] Benthem, J.van, 1991, Language in Action: Categories, Lambdas and Dynamic Logic, North-Holland, Amsterdam (Studies in Logic). · Zbl 0717.03001
[16] Buszkowski, W., 1982, Lambek’s Categorial Grammars, dissertation, Institute of Mathematics, Adam Mickiewicz University, Poznan.
[17] Buszkowski, W., 1986, ?Completeness Results for Lambek Syntactic Calculus?, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 32, 13-28. · Zbl 0594.03015 · doi:10.1002/malq.19860320104
[18] Buszkowski, W., Marciszewski, W., and Benthem, J.van, eds., 1988, Categorial Grammar, John Benjamin, Amsterdam and Philadelphia.
[19] Dalla Chiara, M.-L., 1985, ?Quantum Logic?, in Gabbay & Guenthner, eds., 1985, 427-469.
[20] Do?en, K., 1985, ?A Completeness Theorem for the Lambek Calculus of Syntactic Categories?, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 31, 235-281. · Zbl 0564.03029 · doi:10.1002/malq.19850311405
[21] Dunn, M., 1985, ?Relevance Logic and Entailment?, in Gabbay & Guenthner, eds., 1985, 117-224. · Zbl 0875.03051
[22] Ebbinghaus, H.-D., et al., eds., 1989, Logic Colloquium, Granada 1987, North-Holland, Amsterdam, (Studies in Logic).
[23] Fitch, F. B., 1952, Symbolic Logic: an Introduction, New York. · Zbl 0049.00504
[24] Gabbay, D. and Guenthner, F., eds., 1984, Handbook of Philosophical Logic, vol. II (Extensions of Classical Logic), D. Reidel, Dordrecht. · Zbl 0572.03003
[25] Gabbay, D. and Guenthner, F., eds., 1985, Handbook of Philosophical Logic, vol. III (Alternatives to Classical Logic), D. Reidel, Dordrecht. · Zbl 0603.03001
[26] Gabbay, D., Hogger, C. and Robinson, J., eds., 1990, Handbook of Logic in Artificial Intelligence and Logic Programming, Oxford University Press, Oxford. · Zbl 0889.03001
[27] Gabbay, D., Pnueli, A., Shelah, S., and Stavi, Y., 1980, ?On the Temporal Analysis of Fairness?, ACM Symposium on Principles of Programming Languages, 163-173.
[28] Gärdenfors, P., ed., 1987, Generalized Quantifiers. Linguistic and Logical Approaches, D. Reidel, Dordrecht.
[29] Gärdenfors, P., 1988, Knowledge in Flux: Modelling the Dynamics of Epistemic States, Bradford Books/MIT Press, Cambridge (Mass.). · Zbl 1229.03008
[30] Gärdenfors, P. and Makinson, D., 1988, ?Revision of Knowledge Systems Using Epistemic Entrenchment?, in M. Vardi, ed., 1988, 83-95.
[31] Gargov, G., Passy, S., and Tinchev, T., 1987, ?Modal Environment for Boolean Speculations?, in D. Skordev, ed., 1987, 253-263. · Zbl 0701.03008
[32] Girard, J.-Y., 1987, ?Linear Logic?, Theoretical Computer Science 50, 1-102. · Zbl 0625.03037 · doi:10.1016/0304-3975(87)90045-4
[33] Groenendijk, J. and Stokhof, M., 1988, ?Dynamic Predicate Logic?, Institute for Language, Logic and Information, University of Amsterdam. (To appear in Linguistics and Philosophy.) · Zbl 0726.03024
[34] Harel, D., 1984, ?Dynamic Logic?, in Gabbay & Guenthner, eds, 1984, 497-604. · Zbl 0875.03076
[35] Heim, I., 1982, The Semantics of Definite and Indefinite Noun Phrases, dissertation, Department of Linguistics, University of Massachusetts, Amherst.
[36] Hopcroft, J. and Ullman, J., 1979, Introduction to Automata Theory, Languages and Computation, Addison-Wesley, Reading (Mass.). · Zbl 0426.68001
[37] Immerman, N. and Kozen, D., 1987, ?Definability with Bounded Number of Bound Variables?, Proceedings IEEE 1987, 236-244.
[38] Jónsson, B. and Tarski, A., 1951, ?Boolean Algebra with Operators I?, American Journal of Mathematics 73, 891-939. · Zbl 0045.31505 · doi:10.2307/2372123
[39] Jónsson, B., 1984, ?The Theory of Binary Relations?, Department of Mathematics, VanderBilt University, Nashville (Tenn.). · Zbl 0546.06006
[40] Koymans, R., 1989, Specifying Message Passing and Time-Critical Systems with Temporal Logic, dissertation, Department of Computer Science, Technological University, Eindhoven. · Zbl 0666.03023
[41] Lafont, Y., 1988, ?The Linear Abstract Machine?, Theoretical Computer Science 59, 157-180. · Zbl 0648.68016 · doi:10.1016/0304-3975(88)90100-4
[42] Lambek, J., 1958, ?The Mathematics of Sentence Structure?, American Mathematical Monthly 65, 154-170. · Zbl 0080.00702 · doi:10.2307/2310058
[43] Maddux, R., 1983, ?A Sequent Calculus for Relation Algebras?, Annals of Pure and Applied Logic 25, 73-101. · Zbl 0528.03016 · doi:10.1016/0168-0072(83)90055-6
[44] Makinson, D., 1988, ?General Non-Monotonic Logic?, to appear in Gabbay et al., eds., 1990.
[45] Moortgat, M., 1988, Categorial Investigations. Logical and Linguistic Aspects of the Lambek Calculus, Foris, Dordrecht (GRASS series).
[46] Oehrle, R., Bach, E., and Wheeler, D., eds. 1988. Categorial Grammars and Natural Language Structures, D. Reidel, Dordrecht (Studies in Linguistics and Philosophy).
[47] Ono, H., 1988, ?Structural Rules and a Logical Hierarchy?, Faculty of Integrated Arts and Sciences, Hiroshima University.
[48] Quine, W. V. O., 1946, ?Concatenation as a Basis for Arithmetic?, Journal of Symbolic Logic 11, 105-114. · Zbl 0063.06362 · doi:10.2307/2268308
[49] Sambin, G., 1988, ?Intuitionistic Formal Spaces and their Neighbourhood?, Mathematical Institute, University of Padova. · Zbl 0677.03006
[50] Skordev, D., ed., 1987, Mathematical Logic and its Applications, Plenum Press, New York. · Zbl 0695.00003
[51] Troelstra, A. and Dalen, D.van, 1988, Constructivism in Mathematics: an Introduction. North-Holland, Amsterdam (Studies in Logic). · Zbl 0653.03040
[52] Urquhart, A., 1972, ?Semantics for Relevant Logics?, Journal of Symbolic Logic 37, 159-169. · Zbl 0245.02028 · doi:10.2307/2272559
[53] Vardi, M., ed., 1988, Proceedings 2d Conference on Theoretical Aspects of Reasoning about Knowledge, Morgan Kaufmann Publishers, Los Altos. · Zbl 0699.00012
[54] Veltman, F., 1989, ?Update Semantics?. Institute for Language, Logic and Information, University of Amsterdam. · Zbl 0860.03025
[55] Wansing, H., 1989, ?The Adequacy Problem for Sequential Propositional Logic?, Institute for Language, Logic and Information, University of Amsterdam.
[56] Zucker, J. and Tragesser, R., 1978, ?The Adequacy Problem for Inferential Logic?, Journal of Philosophical Logic 7, 501-516. · Zbl 0408.03020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.