Powerset residuated algebras

Mirosława Kołowska-Gawiejnowicz

DOI: http://dx.doi.org/10.12775/LLP.2013.029

Abstract


We present an algebraic approach to canonical embeddings of arbitrary residuated algebras into powerset residuated algebras. We propose some construction of powerset residuated algebras and prove a representation theorem for symmetric residuated algebras.

Keywords


residuated algebra; symmetric residuated algebra; powerset residuated algebra; canonical embedding

Full Text:

PDF

References


Abrusci, V.M., “Phase semantics and sequent calculus for pure noncommutative classical linear propositional logic”, The Journal of Symbolic Logic, 56 (1991), 4: 1403–1451. DOI: 10.2307/2275485

Bimbó, K., and J.M. Dunn, Generalized Galois Logics: Relational Semantics of Nonclassical Logical Calculi, CSLI Publications, 2008.

Bimbó, K., and J.M. Dunn, “Symmetric generalized Galois logics”, Logica Universalis, 3 (2009): 125–152. DOI: 10.1007/s11787-009-0004-3

Buszkowski, W., “Interpolation and FEP for logics of residuated algebras”, Logic Journal of the IGPL, 19 (2011), 3: 437–454. DOI: 10.1093/jigpal/jzp094

Buszkowski, W., “Many-sorted gaggles”, Link

Galatos, N., P. Jipsen, T. Kowalski and H. Ono, Residuated Lattices: An Algebraic Glimpse at Substructural Logics, vol. 151, Elsevier, Amsterdam, 2007.

Grishin, V.N., “On a generalization of the Ajdukiewicz-Lambek system”, pp. 315–343 in Studies in Non-Commutative Logics and Formal Systems (in Russian), Nauka, Moscow, 1983.

Kołowska-Gawiejnowicz, M., “Powerset residuated algebras and generalized Lambek calculus”, Mathematical Logic Quarterly, 43 (1997): 60–72. DOI: 10.1002/malq.19970430108

Kołowska-Gawiejnowicz, M., “On canonical embeddings of residuated groupoids”, to appear.

Kurtonina, N., and M. Moortgat, “Relational semantics for the Lambek-Grishin calculus”, pp. 210–222 in The Mathematics of Language, Ch. Ebert, G. Jäger and J. Michaelis (eds.), Lectures Notes in Computer Science, vol. 6149, 2010.

Lambek, J., “On the calculus of syntactic types”, pp. 166–178 in Structure of Language and Its Mathematical Aspects, R. Jacobson (ed.), AMS, Providence, 1961.

Moortgat, M., “Symmetries in natural language syntax and semantics: Lambek-Grishin calculus”, pp. 264–284 in Proceedings 14th Workshop on Logic, Language, Information and Computation, Lectures Notes in Computer Science, vol. 4576, Springer, 2007.

Orłowska, E., and I. Rewitzky, “Algebras for Galois-style connections and their discrete duality”, Fuzzy Sets and Systems, 161 (2010): 1325–1342. DOI: 10.1016/j.fss.2009.12.013




Bookmark and Share




Print ISSN: 1425-3305
Online ISSN: 2300-9802

Partnerzy platformy czasopism