Abstract
Categorial grammars are driven by resource logics in a proof format Benthem, 1991; Mootrgat, 1997). Thus, they revolve around derivation and computation, with theCurry-Howard. 1997 Gestalt switch taking proofs to type-theoretic denotions for the expression analyzed. But over thye past decades, categorial logics have also been analyzed model-theoretically in modal logics with standard possible worlds-style models (cf. Kurtonina, 1995). Then, e.g., a categorial product A•B ‘true ‚ of some objects, t, u satisfying A,B, respectively. This is a standard binary modality, which needs a ternary accessibility relation R for its abstract truth condition: M,8⊨ A•B iff ∃t, υ: Rs, tu & M,t ⊨ A & M,u ⊨ B Modal logic is a world of research rather different from the usual concerns in categorial grammar. What happens when we put the two agendas side by side?
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adriaans, Pieter (1990). Categoriale modellen voor kennissystemen. Informatie, pages 118–126.
Aiello, Marco and van Benthem, Johan (2002). A modal walk through space. Journal of Applied Non-Classical Logics, 12(3/4):319–363.
Andréka, Hajnal and Mikulás, Szabolcs (1994). Lambek calculus and its relational semantics: completeness and incompleteness. Journal of Logic, Language and Information, 3:1–37.
Blackburn, Patrick, de Rijke, Maarten, and Venema, Yde (2001). Modal Logic. Cambridge University Press, Cambridge.
Buszkowski, Wojciech (1997). Mathematical linguistics and proof theory. In van Benthem, Johan and ter Meulen, Alice, editors, Handbook of Logic and Language, pages 638–738. Elsevier Science Publishers, Amsterdam.
de Haas, Erik (2001). Logics for OO Information Systems. PhD thesis, Institute for Logic, Language and Computation, University of Amsterdam. DS-2001–03.
Gabbay, Dov and Shehtman, Valentin (1998). Products of modal logics, part 1. Logic Journal of the IGPL, 6: 73–146.
Harel, David, Kozen, Dexter, and Tiuryn, Jerzy (2000). Dynamic Logic. Foundations of Computing. MIT Press, Cambridge, Massachusetts.
Kerdiles, Gwen (2001). Saying it with Pictures, a logical landscape of conceptual graphs. PhD thesis, Institute for Logic, Language and Computation, University of Amsterdam. DS-2001–09.
Kurtonina, Natasha (1995). Frames and Labels. A Modal Analysis of Catego-rial Inference. PhD thesis, OTS Utrecht and ILLC Amsterdam.
Kurtonina, Natasha and de Rijke, Maarten (1996). Bisimulations for temporal logic. Journal of Logic, Language and Information, 6:403–425.
Moortgat, Michael (1997). Categorial type logics. In van Benthem, Johan and ter Meulen, Alice, editors, Handbook of Logic and Language. Elsevier, Amsterdam.
Németi, Istvan (1985). The equational theory of cylindric relativized set algebras is decidable. Technical report, Mathematical Institute, Hungarian Academy of Sciences, Budapest. Preprint No 63/85.
Pentus, M. (1995). Models for the Lambek calculus. Annals of Pure and Applied Logic, 75(1–2): 179–213.
Spaan, Edith (1993). Complexity of Modal Logics. PhD thesis, Institute for Logic, Language and Computation, University of Amsterdam.
Spaan, Edith (2000). Poor man’s modal logic. In Gerbrandy, Jelle, Marx, Maarten, de Rijke, Maarten, and Venema, Yde, editors, JFAK, essays dedicated to Johan van Benthem on the occasion of his 50th birtday. Institute for Logic, Language and Computation, University of Amsterdam.
van Benthem, Johan (1991). Language in Action: Categories, Lambdas, and Dynamic Logic. North-Holland, Amsterdam. Reprint with addenda, MIT Press, Cambridge, Massachusetts, 1995.
van Benthem, Johan (1996). Exploring Logical Dynamics. Studies in Logic, Language, and Information. CSLI Publications, Stanford, California.
van Benthem, Johan (1999). Logical structures in mathematical morphology. manuscript, Institute for Logic, Language and Computation, Amsterdam.
van Benthem, Johan (2003). The categorial fine-structure of natural language. In Casadio, Claudia and Scott, Philip J., editors, Festschrift on the Occasion of Jim Lambek’s 80th Birthday. CSLI Publications, Stanford, California.
Venema, Yde (1996). A crash course in arrow logic. In Marx, Maarten, Pólos, László, and Masuch, Michael, editors, Arrow Logic and Multi-Modal Logic, Studies in Logic, Language and Information, pages 3–34. CSLI Publications, Stanford, California.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
van Benthem, J. (2003). Categorial Grammar at a Cross-Roads. In: Kruijff, GJ.M., Oehrle, R.T. (eds) Resource-Sensitivity, Binding and Anaphora. Studies in Linguistics and Philosophy, vol 80. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0037-6_1
Download citation
DOI: https://doi.org/10.1007/978-94-010-0037-6_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-1692-9
Online ISBN: 978-94-010-0037-6
eBook Packages: Springer Book Archive