zbMATH — the first resource for mathematics

A categorial type logic. (English) Zbl 1285.03017
Casadio, Claudia (ed.) et al., Categories and types in logic, language, and physics. Essays dedicated to Jim Lambek on the occasion of his 90th birthday. Berlin: Springer (ISBN 978-3-642-54788-1/pbk). Lecture Notes in Computer Science 8222, 331-352 (2014).
Summary: In logical categorial grammar syntactic structures are categorial proofs and semantic structures are intuitionistic proofs, and the syntax-semantics interface comprises a homomorphism from syntactic proofs to semantic proofs. Thereby, logical categorial grammar embodies in a pure logical form the principles of compositionality, lexicalism, and parsing as deduction. Interest has focused on multimodal versions but the advent of the (dis)placement calculus of G. Morrill et al. [J. Logic Lang. Inf. 20, No. 1, 1–48 (2011; Zbl 1233.03035)] suggests that the role of structural rules can be reduced, and this facilitates computational implementation. In this paper we specify a comprehensive formalism of (dis)placement logic for the parser/theorem prover CatLog integrating categorial logic connectives proposed to date and illustrate with a cover grammar of the Montague fragment.
For the entire collection see [Zbl 1284.03016].

03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
03B65 Logic of natural languages
CatLog; Grail
Full Text: DOI
[1] Bach, E.: Discontinuous constituents in generalized categorial grammars. In: Burke, V.A., Pustejovsky, J. (eds.) Proceedings of the 11th Annual Meeting of the North Eastern Linguistics Society, pp. 1–12. GLSA Publications, Department of Linguistics, University of Massachussets at Amherst, Amherst (1981)
[2] Bach, E.: Some Generalizations of Categorial Grammars. In: Landman, F., Veltman, F. (eds.) Varieties of Formal Semantics: Proceedings of the Fourth Amsterdam Colloquium, Foris, Dordrecht, pp. 1–23 (1984); Reprinted in Savitch, W.J., Bach, E., Marsh, W., Safran-Naveh, G. (eds.) The Formal Complexity of Natural Language, pp. 251–279. D. Reidel, Dordrecht (1987)
[3] Barry, G., Hepple, M., Leslie, N., Morrill, G.: Proof Figures and Structural Operators for Categorial Grammar. In: Proceedings of the Fifth Conference of the European Chapter of the Association for Computational Linguistics, Berlin (1991) · doi:10.3115/977180.977215
[4] Dowty, D.R., Wall, R.E., Peters, S.: Introduction to Montague Semantics. Synthese Language Library, vol. 11. D. Reidel, Dordrecht (1981)
[5] Lambek, J.: On the Calculus of Syntactic Types. In: Jakobson, R. (ed.) Structure of Language and its Mathematical Aspects, Proceedings of the Symposia in Applied Mathematics XII, pp. 166–178. American Mathematical Society, Providence (1961) · doi:10.1090/psapm/012/9972
[6] Moortgat, M., Oehrle, R.T.: Adjacency, dependency and order. In: Dekker, P., Stokhof, M. (eds.) Proceedings of the Ninth Amsterdam Colloquim, pp. 447–466. ILLC, Amsterdam (1994)
[7] Morrill, G.: Grammar and Logical Types. In: Stokhof, M., Torenvelt, L. (eds.) Proceedings of the 1989 Seventh Amsterdam Colloquium, pp. 429–450 (1989)
[8] Moortgat, M.: Multimodal linguistic inference. Journal of Logic, Language and Information 5(3,4), 349–385 (1996); Also in Bulletin of the IGPL 3(2,3), 371–401 (1995) · Zbl 0919.03023
[9] Moortgat, M.: Categorial Type Logics. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, pp. 93–177. Elsevier Science B.V. and The MIT Press, Amsterdam and Cambridge (1997) · doi:10.1016/B978-044481714-3/50005-9
[10] Moortgat, M., Morrill, G.: Heads and phrases: Type calculus for dependency and constituent structure. Manuscript, Universiteit Utrecht (1991)
[11] Moot, R.: Grail: An automated proof assistant for categorial grammar logics. In: Backhouse, R.C. (ed.) Proceedings of the 1998 User Interfaces or Theorem Provers Conference (1998)
[12] Moot, R., Retoré, C.: The Logic of Categorial Grammars: A Deductive Account of Natural Language Syntax and Semantics. Springer, Heidelberg (2012) · Zbl 1261.03001 · doi:10.1007/978-3-642-31555-8
[13] Morrill, G.: Intensionality and Boundedness. Linguistics and Philosophy 13(6), 699–726 (1990) · doi:10.1007/BF00627513
[14] Morrill, G.: Categorial Formalisation of Relativisation: Pied Piping, Islands, and Extraction Sites. Technical Report LSI-92-23-R, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya (1992)
[15] Morrill, G.: Logic Programming of the Displacement Calculus. In: Pogodalla, S., Prost, J.-P. (eds.) LACL 2011. LNCS (LNAI), vol. 6736, pp. 175–189. Springer, Heidelberg (2011) · Zbl 1333.03099 · doi:10.1007/978-3-642-22221-4_12
[16] Morrill, G.: CatLog: A Categorial Parser/Theorem-Prover. In: LACL 2012 System Demonstrations, Logical Aspects of Computational Linguistics 2012, pp. 13–16 (2012)
[17] Morrill, G., Merenciano, J.-M.: Generalising discontinuity. Traitement automatique des langues 37(2), 119–143 (1996)
[18] Morrill, G., Valentín, O.: Displacement Calculus. Linguistic Analysis 36(1-4), 167–192 (2010); Special issue Festschrift for Joachim Lambek, http://arxiv.org/abs/1004.4181
[19] Morrill, G., Valentín, O.: On Anaphora and the Binding Principles in Categorial Grammar. In: Dawar, A., de Queiroz, R. (eds.) WoLLIC 2010. LNCS (LNAI), vol. 6188, pp. 176–190. Springer, Heidelberg (2010) · Zbl 1253.03055 · doi:10.1007/978-3-642-13824-9_15
[20] Morrill, G., Valentín, O., Fadda, M.: Dutch Grammar and Processing: A Case Study in TLG. In: Bosch, P., Gabelaia, D., Lang, J. (eds.) TbiLLC 2007. LNCS (LNAI), vol. 5422, pp. 272–286. Springer, Heidelberg (2009) · Zbl 1236.03026 · doi:10.1007/978-3-642-00665-4_22
[21] Morrill, G., Valentín, O., Fadda, M.: The Displacement Calculus. Journal of Logic, Language and Information 20(1), 1–48 (2011), doi:10.1007/s10849-010-9129-2 · Zbl 1233.03035 · doi:10.1007/s10849-010-9129-2
[22] Morrill, G.V.: Type Logical Grammar: Categorial Logic of Signs. Kluwer Academic Publishers, Dordrecht (1994) · Zbl 0848.03007 · doi:10.1007/978-94-011-1042-6
[23] Morrill, G.V.: Categorial Grammar: Logical Syntax, Semantics, and Processing. Oxford University Press, New York (2011)
[24] Oehrle, R.T.: Multi-Modal Type-Logical Grammar. In: Borsley, R.D., Börjars, K. (eds.) Non-transformational Syntax: Formal and Explicit Models of Grammar. Wiley-Blackwell, Oxford (2011), doi:10.1002/9781444395037.ch6 · doi:10.1002/9781444395037.ch6
[25] Oehrle, R.T., Zhang, S.: Lambek calculus and preposing of embedded subjects. In: Chicago Linguistics Society, Chicago, vol. 25 (1989)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.