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Mikulás, Szabolcs (2015)
Publisher: Springer
Languages: English
Types: Article
Subjects: csis

Classified by OpenAIRE into

arxiv: Computer Science::Logic in Computer Science, Mathematics::Logic
We look at lower semilattice-ordered residuated semigroups and, in particular, the representable ones, i.e., those that are isomorphic to algebras of binary relations. We will evaluate expressions (terms, sequents, equations, quasi-equations) in representable algebras and give finite axiomatizations for several notions of validity. These results will be applied in the context of substructural logics.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • x y (x y) = (x y) A.R. Anderson, N.D. Belnap and J.M. Dunn, Entailment. The Logic of Relevance and Necessity. Vol. II., Princeton University Press. 1992.
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    • H. Andreka and Sz. Mikulas, \Axiomatizability of positive algebras of binary relations", Algebra Universalis, 66:7{34, 2011.
    • H. Andreka, Sz. Mikulas and I. Nemeti, \Residuated Kleene algebras", in R.L. Constable and A. Silva (eds.), Kozen Festschrift, pages 1{11, SpringerVerlag, 2012.
    • K. Bimbo, J.M. Dunn and R.D. Maddux, \Relevance logic and relation algebras", Review of Symbolic Logic, 2(1):102{131, 2009.
    • R. Hirsch and Sz. Mikulas, \Representable semilattice-ordered monoids", Algebra Universalis, 57:333{370, 2007.
    • R. Hirsch and Sz. Mikulas, \Positive fragments of relevance logic and algebras of binary relations", Review of Symbolic Logic, 4(1):81{105, 2011.
    • J. Lambek, \The mathematics of sentence structure" American Mathematical Monthly, 65:154{170, 1958.
    • R.D. Maddux, \Relevance logic and the calculus of relations", Review of Symbolic Logic, 3(01):41{70, 2010.
    • Sz. Mikulas, \Algebras of relations and relevance logic", Journal of Logic and Computation, 19:305{321, 2009.
    • Sz. Mikulas, \On representable ordered residuated semigroups", Logic Journal of the IGPL, 19(1):233{240, 2011.
    • V. Pratt, \Action logic and pure induction", in J. van Eijck (editor), Logics in AI: European Workshop JELIA '90, pages 97{120. Springer-Verlag, 1990.
    • R. Routley and R.K. Meyer, \The semantics of entailment (I)", in H. Leblanc (ed.), Truth, Syntax and Modality, pages 199{243, North-Holland, 1973.
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