A Semantic Analysis of some Distributive Logics with Negation
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RIS BIB ENDNOTEA Semantic Analysis of some Distributive Logics with Negation
Publication date: 26.11.2013
Reports on Mathematical Logic, 2013, Number 48, pp. 81-100
https://doi.org/10.4467/20842589RM.13.004.1256Authors
A Semantic Analysis of some Distributive Logics with Negation
In this paper we shall study some extensions of the semilattice based deductive systems S (N) and S (N, 1), where N is the variety of bounded distributive lattices with a negation operator. We shall prove that S (N) and S (N, 1) are the deductive systems generated by the local consequence relation and the global consequence relation associated with ¬-frames, respectively. Using algebraic and relational methods we will prove that S (N) and some of its extensions are canonical and frame complete.
[1] F. Bou, F. Esteva, J. M. Font, A. Gil, L. Godo, A. Torrens, A., and V. Verd´ u, Logics preserving degrees of truth from varieties of residuated lattices, Journal of Logic and Computation 19 (2009), pp. 1031–1069.
[2] R. Ertola, M. Sagastume, Subminimal logic and weak algebras, Reports on Math. Logic 44 (2009), pp. 153-166.
[3] R. Dwinger and P.H. Balbes, Distributive Lattices, University of Missouri Press, Columbia, MO, 1974.
[4] P. Blackburn, M. de Rijke, Y. Venema, Modal Logic, Cambridge Tracts in Theoretical Computer Science 53, Cambridge University Press, 2001.
[5] S. A. Celani, Distributive lattices with a negation operator, Math. Logic Quarterly 45 (1999), pp. 207-218.
[6] S. A. Celani,Notes on the representation of distributive modal algebras, Miskolc Mathematical Notes 9:2 (2008), pp. 81–89.
[7] S A. Celani and L. M. Cabrer, Weak-quasi-Stone algebras, Math. Logic Quarterly 55:3 (2009), pp. 288-298.
[8] K. Dosˇen:. Negative modal operator in intuitionistic logic, Publications de L’Institut Math´ematique (Beograd) (N.S) 35:49 (1984), pp. 3-14.
[9] K. Dosˇen, Negation as a modal operator, Reports on Mathematical Logic 20 (1986), pp. 15-27.
[10] J. Michael Dunn, C. Zhou, Negation in the Context of Gaggle Theory, Studia Logica 80:2-3 (2005), pp. 235–264.
[11] J. M. Font, On semilattice-based logics with an algebraizable assertional companion, Reports on Mathematical Logic 46 (2011), pp. 109–132.
[12] R. Jansana, Selfextensional Logics with a Conjunction, Studia Logica 84:1 (2006), pp. 63–104.
[13] S. P. Odintsov, Combining intuitionistic connectives and Routley negation, Siberian Electronic Mathematical Reports (2010), pp. 21-41.
[14] H. A. Priestley, Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. 3:24 (1972), pp. 507-530.
[15] N. A. Sankappanavar and H. P. Sankappanavar, Quasi-Stone algebras, Math. Logic Quarterly 39 (1993), pp. 255-268.
[16] Y. Shramko, Dual Intuitionistic Logic and a Variety of Negations. The Logic of Scientific Research, Studia Logica 80:2-3 (2005), pp. 347-367.
Information: Reports on Mathematical Logic, 2013, Number 48, pp. 81-100
Article type: Original article
CONICET and Escuela de Ciencia y Tecnologica, Universidad de San Marteen, Campus Miguelete (CP1650). San Martn, Provincia de Buenos Aires, Argentina
Published at: 26.11.2013
Article status: Open
Licence: None
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