Studia Logica

, 98:429 | Cite as

Paraconsistency in Categories: Case of Relevance Logic

Article

Abstract

Categorical-theoretic semantics for the relevance logic is proposed which is based on the construction of the topos of functors from a relevant algebra (considered as a preorder category endowed with the special endofunctors) in the category of sets Set. The completeness of the relevant system R of entailment is proved in respect to the semantic considered.

Keywords

Toposes relevant algebra RN-categories topos of functors interpretation of the relevance logic in topos completeness of the logic RL 

References

  1. 1.
    Goldblatt, R., Topoi. The categorial analysis of logic, North-Holland, Amsterdam, N.Y., Oxford, 1979.Google Scholar
  2. 2.
    Maksimova L.L.: ‘Structures with implication’. Algebra i Logika 12(4), 445–467 (1973) (in Russian)Google Scholar
  3. 3.
    Mortensen C.: Inconsistent Mathematics. Kluwer Academic Publishers, Dordrecht (1995)Google Scholar
  4. 4.
    Patterson A., Costello T.: ‘Exponentials as Projections from Paraconsistent Logics’. In: Batens, D., Mortensen, C., Priest, G., van Bendegem, J.-P. (eds) Frontiers of Paraconsistent Logic., pp. 209–222. Research Studies Press Ltd., Baldock, Hartfordshire, England (2000)Google Scholar
  5. 5.
    Riscos A., L.M. Laita: ‘N-categories in logic’. Zeitschr. Math. Log. Grundl. Math. 33, 507–516 (1987)CrossRefGoogle Scholar
  6. 6.
    Routley, R., R. K. Meyer, M. Plumwood, and R. Brady, Relevant Logic and Their Rivals, Ridgeway, 1983.Google Scholar
  7. 7.
    Urquhart A.: ‘Duality for Algebras of Relevant Logics’. Studia Logica 56(1-2), 263–276 (1996)CrossRefGoogle Scholar
  8. 8.
    Vasyukov, V. L., ‘RN-categories for Relevance Logics’, Logical Investigations, vol. 1, Moscow, 1993, pp. 124–132 (in Russian).Google Scholar
  9. 9.
    Vasyukov V. L.: ‘Paraconsistency in Categories’. In: Batens, D., Mortensen, C., Priest, G., van Bendegem, J.-P. (eds) Frontiers of Paraconsistent Logic., pp. 263–278. Research Studies Press Ltd., Baldock, Hartfordshire, England (2000)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institute of PhilosophyRussian Academy of ScienceMoscowRussia

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