Abstract
We show that the equational theory of representable lower semilattice-ordered residuated semigroups is finitely based. We survey related results.
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References
Anderson, A. R., & Belnap, N. D. (1975). Entailment: The logic of relevance and necessity (Vol. 1). Princeton: Princeton University Press.
Anderson, A. R., Belnap, N. D., & Dunn, J. M. (1992). Entailment: The logic of relevance and necessity (Vol. 2). Princeton: Princeton University Press.
Andréka, H., & Mikulás, S. (1994). Lambek calculus and its relational semantics. Journal of Logic, Language and Information, 3, 1–37.
Andréka, H., Mikulás, S., & Németi, I. (2012). Residuated Kleene algebras. In R. L. Constable & A. Silva (Eds.), Kozen Festschrift. Berlin: Springer.
Burris, S., & Sankappanavar, H. P. (1981). A course in universal algebra. New York: Springer.
Lambek, J. (1958). The mathematics of sentence structure. American Mathematical Monthly, 65, 154–170.
Mikulás, S. (2011). On representable ordered residuated semigroups. Logic Journal of the IGPL, 19(1), 233–240.
Mikulás, S. Lower semilattice-ordered residuated semigroups and substructural logics, submitted. Manuscript available at http://www.dcs.bbk.ac.uk/~szabolcs/MeetLambek.pdf.
Pratt, V. (1990). Action logic and pure induction. In J. van Eijck (Ed.), Logics in AI: European workshop JELIA ’90 (pp. 97–120). Amsterdam: Springer.
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The author is grateful to the two anonymous referees for their useful comments.
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Mikulás, S. The equational theories of representable residuated semigroups. Synthese 192, 2151–2158 (2015). https://doi.org/10.1007/s11229-014-0513-3
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DOI: https://doi.org/10.1007/s11229-014-0513-3