Variable Sharing in Substructural Logics: an Algebraic Characterization
DOI:
https://doi.org/10.18778/0138-0680.47.2.03Keywords:
relevant logic, algebraic characterizations of logical properties, variable sharing property, substructural logicsAbstract
We characterize the non-trivial substructural logics having the variable sharing property as well as its strong version. To this end, we find the algebraic counterparts over varieties of these logical properties.
References
[1] A. R. Anderson and N. D. Belnap, Entailment. The Logic of Relevance and Necessity, I, Princeton University Press, 1975.
Google Scholar
[2] A. Avron, The basic relevance criterion, talk given at the Third Workshop in Edmonton, Canada, May 2016.
Google Scholar
[3] M. Dunn and G. Restall, Relevance Logic [in:] D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Kluwer, 2002, pp. 1–128.
Google Scholar
[4] N. Galatos, P. Jipsen, T. Kowalski and H. Ono, Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Elsevier, 2007.
Google Scholar
[5] H. Kihara and H. Ono, Algebraic characterizations of variable separation properties, Reports on Mathematical Logic 43 (2008), pp. 43–63.
Google Scholar
[6] L. L. Maksimova, Craig’s theorem in superintuitionistic logics and amalgamable varieties of pseudo-Boolean algebras, Algebra i Logika 16 (1977), pp. 643–681.
Google Scholar
[7] L. L. Maksimova, On variable separation in modal and superintuitionistic logics, Studia Logica 55 (1995), pp. 99–112.
Google Scholar
[8] L. L. Maksimova, Interrelation of algebraic, semantical and logical properties for superintuitionistic and modal logics, Logic, Algebra and Computer Science, Banach Center Publications, Vol. 46, Polish Academy of Science, Warszawa (1999), pp. 159–168.
Google Scholar
[9] J. M. Méndez and G. Robles, A General Characterization of the Variable-Sharing Property by Means of Logical Matrices, Notre Dame Journal of Formal Logic, Vol. 53(2) (2012), pp. 223–244.
Google Scholar
[10] D. Souma, An algebraic approach to the disjunction property of substructural logics, Notre Dame Journal of Formal Logic, Vol. 48(4) (2007), pp. 489–495.
Google Scholar
[11] A. Wroński, Remarks on Halldén-completeness of modal and intermediate logics, Bulletin of the Section of Logic, Vol. 5/4 (1976), pp. 126–129.
Google Scholar
[12] E. Yang, R and Relevance Principle Revisited, Journal of Philosophical Logic 42(5) (2013), pp. 767–782.
Google Scholar
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