Completness of relevant modal logics with disjunctive rules

• Autorzy: Seki T.
• Języki publikacji: EN

Abstrakty

EN

Disjunctive rules are known to validate material implication principles, which may not hold in weaker relevant logics. On the other hand, they prevent the oddity of not preserving truth at the base world, from which many weaker relevant logics suffer. The same holds for relevant modal logics. This paper proves completeness of relevant modal logics with disjunctive rules.

Słowa kluczowe

EN

relevant modal logic; disjunctive rules; Routley-Meyer semantics; completeness

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2009
• Tom: Vol. 44
• Strony: 3--18
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Seki T.

• University Evaluation Center Niigata University 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata City, 950-2181, Japan,

Bibliografia

• [1] R.T. Brady (Ed.), Relevant Logics and Their Rivals II, Ashgate Publishing Limited, Aldershot, 2003.
• [2] J.M. Dunn, Relevance logic and entailment, in D.Gabbay and F.Guenthner, editors, Handbook of Philosophical Logic, Vol. III, pp.117–224, D.Reidel Publishing Company, 1986.
• [3] G. Priest and R. Sylvan, Simplified semantics for basic relevant logics, Journal of Philosophical Logic 21 (1992), pp. 217–232.
• [4] G. Restall, Simplified semantics for relevant logics (and some of their rivals), Journal of Philosophical Logic 22 (1993), pp. 481–511.
• [5] R. Routley, V. Plumwood, R.K. Meyer and R.T. Brady, Relevant Logics and Their Rivals I, Ridgeview Publishing Company, Atascadero, 1982.
• [6] T. Seki, A Sahlqvist theorem for relevant modal logics, Studia Logica 73 (2003), pp.383–411.