A Duality for the Algebras of a Lukasiewicz n + 1-valued Modal System

Teheux, Bruno

doi:10.1007/s11225-007-9074-5

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A Duality for the Algebras of a Lukasiewicz n + 1-valued Modal System

Teheux, Bruno

2007 • In Studia Logica, 87 (1), p. 13-36

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https://hdl.handle.net/2268/4341

DOI
10.1007/s11225-007-9074-5

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Keywords :

modal logic; many-valued logic; topological duality

Abstract :

[en] We develop a duality for the varieties of a Lukasiewicz n + 1-valued modal system. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory. . . ) are the derived and we propose some ideas for future research.

Disciplines :

Mathematics

Author, co-author :

Teheux, Bruno ; Université de Liège - ULiège > Département de mathématique > Algèbre et logique

Language :

English

Title :

A Duality for the Algebras of a Lukasiewicz n + 1-valued Modal System

Publication date :

October 2007

Journal title :

Studia Logica

ISSN :

0039-3215

eISSN :

1572-8730

Publisher :

Kluwer Academic Publishers, Netherlands

Volume :

Issue :

Pages :

13-36

Peer reviewed :

Peer reviewed

Available on ORBi :

since 19 January 2009

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Bibliography

Blackburn Patrick, Maarten de Rijke, Yde Venema (2001) Modal logic, vol. 53 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge
Burris Stanley, Sankappanavar H.P. (1981) A course in universal algebra, vol. 78 of Graduate Texts in Mathematics. Springer-Verlag, New York
Chagrov Alexander, Michael Zakharyaschev (1997) Modal logic, vol. 35 of Oxford Logic Guides. Oxford Science Publications, The Clarendon Press Oxford University Press, New York
Chang C.C. (1958) 'Algebraic analysis of many valued logics', Trans. Amer. Math. Soc. 88: 467-490
Chang C.C. (1959) 'A new proof of the completeness of the Łukasiewicz axioms', Trans. Amer. Math. Soc. 93: 74-80
Cignoli R. (1996) 'Natural dualities for the algebras of Łukasiewicz finite-valued logics', Bull. Symbolic Logic 2(2): 218
Cignoli Roberto, Eduardo J. Dubuc, Daniele Mundici (2004) 'Extending Stone duality to multisets and locally finite MV-algebras', J. Pure Appl. Algebra 189(1-3): 37-59
Cignoli Roberto L.O., Itala M.L. D'Ottaviano, Daniele Mundici (2000) Algebraic foundations of many-valued reasoning, vol. 7 of Trends in Logic-Studia Logica Library. Kluwer Academic Publishers, Dordrecht
Clark David M., Brian A. Davey (1998) Natural dualities for the working algebraist, vol 57. of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge
Esakia Leo, Revaz Grigolia (1977) 'The criterion of Brouwerian and closure algebras to be finitely generated', Polish Acad. Sci. Inst. Philos. Sociol. Bull. Sect. Logic 6(2): 46-52
Fitting Melvin (1992) 'Many-valued modal logics. II', Fund. Inform. 17(1-2): 55-73
Fitting Melvin (1995) 'Tableaus for many-valued modal logic', Studia Logica 55(1): 63-87
Fitting M. (1991) 'Many-valued modal logics', Fund. Inform. 15(3-4): 235-254
Gehrke Mai, Bjarni Jónsson (2004) 'Bounded distributive lattice expansions', Math. Scand. 94(1): 13-45
Gehrke Mai, Hideo Nagahashi, Yde Venema (2005) 'A Sahlqvist theorem for distributive modal logic', Ann. Pure Appl. Logic 131(1-3): 65-102
Gottwald Siegfried (2001) A treatise on many-valued logics, vol. 9 of Studies in Logic and Computation. Research Studies Press Ltd., Baldock
Hájek Petr (1998) Metamathematics of fuzzy logic, vol. 4 of Trends in Logic-Studia Logica Library. Kluwer Academic Publishers, Dordrecht
Hansoul G. (1983) 'A duality for Boolean algebras with operators', Algebra Universalis 17(1): 34-49
Hansoul, G., and B. Teheux, 'Completeness results for many-valued Łukasiewicz modal systems and relational semantics', arXiv:math.LO/ 0612542, 2006.
Jónsson Bjarni, Alfred Tarski (1951) 'Boolean algebras with operators. I', Amer. J. Math. 73: 891-939
Jónsson Bjarni, Alfred Tarski (1952) 'Boolean algebras with operators. II', Amer. J. Math. 74: 127-162
Kheltent, M., and G. Hansoul, 'Stone-C̃ech compactifications of topological structures', manuscript.
Kripke Saul A. (1963) 'Semantical analysis of modal logic. I. Normal modal propositional calculi', Z. Math. Logik Grundlagen Math. 9: 67-96
Kupke, Clemens, Alexander Kurz, and Dirk Pattinson, 'Algebraic semantics for coalgebraic logics', in Proceedings of the Workshop on Coalgebraic Methods in Computer Science, vol. 106 of Electron. Notes Theor. Comput. Sci., Elsevier, Amsterdam, 2004, pp. 219-241 (electronic).
Kupke Clemens, Alexander Kurz, Yde Venema (2004) 'Stone coalgebras', Theoret. Comput. Sci. 327(1-2): 109-134
Łukasiewicz Jan (1920) 'O logice trójwartościowej', Ruch Filozoficzny 5: 170-171
Łukasiewicz, Jan, Selected works, North-Holland Publishing Co., Amsterdam, 1970. Edited by L. Borkowski, Studies in Logic and the Foundations of Mathematics.
Łukasiewicz Jan, Alfred Tarski (1930) 'Untersuchungen über den ausagenkalkül', Compte Rendus Séances Société des Sciences et Lettres Varsovie 23: 30-50
Martínez N.G. (1990) 'The Priestley duality for Wajsberg algebras', Studia Logica 49(1): 31-46
McKinsey J.C.C. (1941) 'A solution of the decision problem for the Lewis systems S2 and S4, with an application to topology', J. Symbolic Logic 6: 117-134
Niederkorn Philippe (2001) 'Natural dualities for varieties of MV-algebras. I', J. Math. Anal. Appl. 255(1): 58-73
Niederkorn, Philippe, Algebraic aspects of fuzzy logic: BL-algebras and their hoop subreducts, Ph.D. thesis, University of Liège, 2002.
Ostermann Pascal (1988) 'Many-valued modal propositional calculi', Z. Math. Logik Grundlag. Math. 34(4): 343-354
Rescher, Nicolas, Many-valued Logic, McGraw-Hill, 1969.
Rosser, J. Barkley, and Atwell R. Turquette, Many-valued logics, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam, 1951.
Sambin Giovanni, Virginia Vaccaro (1988) 'Topology and duality in modal logic', Ann. Pure Appl. Logic, 37(3): 249-296
Venema Yde (2004) 'A dual characterization of subdirectly irreducible BAOs', Studia Logica 77(1): 105-115