Duality via Truth: Semantic frameworks for lattice-based logics

Logic Journal of the IGPL

Volumn 13, Issue 4, 2005, Pages 467-490

  Orłowska, Ewa ^a   Rewitzky, Ingrid ^b  

^a NATIONAL INSTITUTE OF TELECOMMUNICATIONS   (Poland)

^b STELLENBOSCH UNIVERSITY   (South Africa)

Author keywords

Bounded lattice; Duality; Lattice based logic; Three valued semantics

Indexed keywords

LATTICE THEORY; MANY VALUED LOGICS;

BOUNDED LATTICES; DISTRIBUTIVE LATTICE; DUALITY; KEY ELEMENTS; LATTICE-BASED; LATTICE-BASED LOGIC; REPRESENTATION THEOREM; SEMANTICS FRAMEWORK; THREE-VALUED; THREE-VALUED SEMANTIC;

SEMANTICS;

EID: 33745796252     PISSN: 13670751     EISSN: 13689894     Source Type: Journal    
DOI: 10.1093/jigpal/jzi035     Document Type: Conference Paper

References (15)

1. [AlD93] Allwein, G. and Dunn, M. (1993) Kripke models for linear logic. Journal of Symbolic Logic 58, No 2, 514-545.
2. [AlM01] Allwein, G. and MacCaull, W. (2001) A Kripke semantics for the logic of Gelfand quantales. Studia Logica 68, 173-228.
3. [Bel77] Belnap, N. (1977) A useful four-valued logic. In J. M. Dunn and G. Epstein (eds) Modern Uses of Multiple-Valued Logic, Reidel, Dordrecht, 8-37.
4. [Bim99] Bimbo, K. (1999) Substructural logics, combinatory logic, and λ-calculus. PhD thesis, Indiana University, Bloomington, USA
5. [DeO02] Demri, S. and Onlowska, E. (2002) Incomplete Information: Structure, Inference, Complexity. EATCS Monographs in Theoretical Computer Science. Springer.
6. [Du66] Dunn, M. (1966) The Algebra of Intensional Logics. Doctoral dissertation, University of Pittsburgh, Ann Arbor, USA.
7. [DuH01] Dunn, M. and Hardegree, G. (2001) Algebraic Methods in Philosophical Logic. Oxford Logic Guides vol. 41, Clarendon Press, Oxford.
8. [DuO01] Düntsch, I. and Orłowska, E. (2001) Beyond modalities: sufficiency and mixed algebras. In: E. Orlowska and A. Szalas (eds) Relational Methods for Computer Science Applications, Physica Verlag, Heidelberg, 263-285.
9. [DOR03] Düntsch, I., Onlowska, E., and Radzikowska, A. (2003) Lattice-based relation algebras and their representability. In: H. de Swart, E. Orłowska, G. Schmidt, and M. Roubens (eds) Theory and Applications of Relational Structures as Knowledge Instruments. Lecture Notes in Computer Science 2929, Springer, 231-255.
10. [Har93] Hartonas, C. (1993) Algebraic and Kripke semantics for substructural logics. PhD Thesis, Indiana University, Bloomington, USA.
11. [JaO05] Järvinen, J. and E. Orłowska. (2005) Relational correspondences for lattices with operators. Proceedings of the 8th International Workshop on Relational Methods in Computer Science RelMiCS'8, St Catharines, Ontario, Canada, February 2005, 111-118.
12. [OrV03] Orłowska, E., and Vakarelov, D. (2003) Lattice-based modal algebras and modal logics. In: P. Hajek, L. Valdes and D. Westerstahl (eds) Proceedings of the 12th International Congress of Logic, Methodology and Philosophy of Science, Oviedo, Spain, 2003. Elsevier, to appear. Volume of Abstracts, 22-23.
13. [Pri70] Priestley, H.A. (1970) Representation of distributive lattices by means of ordered Stone spaces. Bulletin of the London Mathematical Society 2, 186-190.
14. [Sto36] Stone, M.H. (1936) The theory of representations for Boolean algebras. Transactions of the American Mathematical Society 40, p 37-111.
15. [Urq78] Urquhart, A. (1978) A topological representation theory for lattices. Algebra Universalis 8, 45-58.