A Sahlqvist theorem for distributive modal logic

Annals of Pure and Applied Logic

Volumn 131, Issue 1-3, 2005, Pages 65-102

  Gehrke, Mai ^a   Nagahashi, Hideo ^b   Venema, Yde ^c  

^a NEW MEXICO STATE UNIVERSITY   (United States)

^b University of Arizona   (United States)

^c UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Canonical extensions; Canonical logic; Canonical varieties; Correspondence theory; Distributive modal algebras; Distributive modal logic; Duality; Lattice expansions

Indexed keywords

EID: 7244257540     PISSN: 01680072     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apal.2004.04.007     Document Type: Article

References (28)

1. Balbes R. Dwinger Ph. Distributive Lattices 1974 University of Missouri Press Columbia, MO
2. van Benthem J. Modal Logic and Classical Logic 1983 Bibliopolis Napoli
3. Birkhoff G. Lattice Theory 3rd edition American Mathematical Society Colloquium Publications vol. 25 1967 Amer. Math. Soc. Providence
4. Blackburn P. de Rijke M. Venema Y. Modal Logic 2001 Cambridge University Press Cambridge
5. Burris S. Sankappanavar H.P. A course in universal algebra Graduate Texts in Mathematics vol. 78 1981 Springer-Verlag New York, Berlin
6. Celani S. Jansana R. A new semantics for positive modal logic Notre Dame Journal of Formal Logic 38 1 1997 1-18
7. Celani S. Jansana R. Priestley duality, a Sahlqvist theorem and a Goldblatt-Thomason theorem for positive modal logic Logic Journal of the IGPL 7 6 1999 683-715
8. Chagrov A. Zakharyaschev M. Modal Logic Oxford Logic Guides vol. 35 1997 Oxford Science Publications, The Clarendon Press, Oxford University Press New York
9. Davey B. Priestley H. Introduction to Lattices and Order 1990 Cambridge University Press Cambridge
10. Davey B. Priestley H. Distributive lattices and duality in: Grätzer G. (Ed.)General Lattice Theory 2nd edition 1998 499-517 Birkhäuser Verlag Basel (Appendix B)
11. Dunn J.M. Positive modal logic Studia Logica 55 2 1995 301-317
12. Gehrke M. Harding J. Bounded lattice expansions Journal of Algebra 238 1 2001 345-371
13. Gehrke M. Jónsson B. Bounded distributive lattices with operators Mathematica Japonica 40 2 1994 207-215
14. Gehrke M. Jónsson B. Monotone bounded distributive lattice expansions Mathematica Japonica 52 2 2000 197-213
15. Gehrke M. Jónsson B. Bounded distributive lattice expansions Mathematica Scandinavica 94 1 2004 13-45
16. Ghilardi G. Meloni G. Constructive canonicity in non-classical logics Annals of Pure and Applied Logic 86 1997 1-32
17. Goguadze G. Piazza C. Venema Y. Simulating polyadic modal logics by monadic ones Journal of Symbolic Logic 68 2003 419-462
18. Goldblatt R. Varieties of complex algebras Annals of Pure and Applied Logic 44 3 1989 173-242
19. Harding J. Canonical completions of lattices and ortholattices Tatra Mountains Mathematical Publications 15 1998 85-96
20. Jónsson B. On the canonicity of Sahlqvist identities Studia Logica 53 4 1994 473-491
21. Jónsson B. Tarski A. Boolean algebras with operators I American Journal of Mathematics 73 1951 891-939
22. Jónsson B. Tarski A. Boolean algebras with operators II American Journal of Mathematics 74 1952 127-162
23. Kracht M. Wolter F. Normal modal logics can simulate all others Journal of Symbolic Logic 64 1999 99-138
24. Ribeiro H. A remark on Boolean algebras with operators American Journal of Mathematics 74 1952 163-167
25. Sahlqvist H. Completeness and correspondence in the first and second order semantics for modal logic in: Proceedings of the Third Scandinavian Logic Symposium Univ. Uppsala, Uppsala, 1973 Stud. Logic Found. Math vol. 82 1975 110-143 North-Holland Amsterdam
26. Sambin G. Vaccaro V. A new proof of Sahlqvist's theorem on modal definability and completeness Journal of Symbolic Logic 54 3 1989 992-999
27. Thomason S.K. Categories of frames for modal logics Journal of Symbolic Logic 40 1978 439-442
28. F. Wolter M. Zakharyaschev Intuitionistic modal logics as fragments of classical bimodal logics in: E. Orlowska (Ed.) Logic at Work Physica-Verlag, Heildelberg 1999 168-183