Introduction
The topic of this paper concerns a particular extension of Lambek’s syntactic calculus [5] that was proposed by Grishin [4]. Roughly, the usual residuated family ( ⊗ ,/,\) is extended by a coresiduated triple (
) mirroring its behavior in the inequality sign:
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Brünnler, K., McKinley, R.: An algorithmic interpretation of a deep inference system. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS, vol. 5330, pp. 482–496. Springer, Heidelberg (2008)
Cockett, J.R.B., Seely, R.A.G.: Weakly distributive categories. Journal of Pure and Applied Algebra, 45–65 (1991)
Foret, A.: On the computation of joins for non associative Lambek categorial grammars. In: Levy, J., Kohlhase, M., Niehren, J., Villaret, M. (eds.) Proceedings of the 17th International Workshop on Unification Valencia, UNIF 2003, Spain, June 8-9 (2003)
Grishin, V.N.: On a generalization of the Ajdukiewicz-Lambek system. In: Mikhailov, A.I. (ed.) Studies in Nonclassical Logics and Formal Systems, Nauka, Moscow, pp. 315–334 (1983)
Lambek, J.: On the calculus of syntactic types. In: Jakobson, R. (ed.) Structure of Language and its Mathematical Aspects, Proceedings of the Twelfth Symposium in Applied Mathematics (1961)
Lambek, J., Scott, P.J.: Introduction to Higher-Order Categorical Logic. Cambridge Studies in Advanced Mathematics. Cambridge University Press (1988)
Curien, P.L.: Categorical Combinators, Sequential Algorithms and Functional Programming. Progress in Theoretical Computer Science. Birkhäuser, Boston (1993)
Moortgat, M.: Symmetric categorial grammar. Journal of Philosophical Logic 38(6), 681–710 (2009)
Moortgat, M., Pentus, M.: Type similarity for the Lambek-Grishin calculus. In: Proceedings of the Twelfth Conference on Formal Grammar (2007)
Pentus, M.: The conjoinability relation in Lambek calculus and linear logic. ILLC Prepublication Series ML–93–03, Institute for Logic, Language and Computation, University of Amsterdam (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bastenhof, A. (2014). Type Similarity for the Lambek-Grishin Calculus Revisited. In: Casadio, C., Coecke, B., Moortgat, M., Scott, P. (eds) Categories and Types in Logic, Language, and Physics. Lecture Notes in Computer Science, vol 8222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54789-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-54789-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-54788-1
Online ISBN: 978-3-642-54789-8
eBook Packages: Computer ScienceComputer Science (R0)