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2014 | 23 | 1 | 69–80

Article title

Powerset residuated algebras

Title variants

Languages of publication

EN

Abstracts

EN
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.

Year

Volume

23

Issue

1

Pages

69–80

Physical description

Dates

published
2014-03-01
online
2013-09-17

Contributors

  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University ul. Umultowska 87, 61-614 Poznań, Poland

References

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  • 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

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.desklight-bbdc82ba-d6ae-4716-ae6b-2cdf37ab3685
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