Abstract
Semantics are given for modal extensions of relevant logics based on the kind of frames introduced in [7]. By means of a simple recipe we may obtain from a class FRM (L) of unreduced frames characterising a (non-modal) logic L, frame-classes FRM □ (L.M) characterising conjunctively regular modal extensions L.M of L. By displaying an incompleteness phenomenon, it is shown how the recipe fails when reduced frames are under consideration.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. R. Anderson and N. D. Belnap, Entailment. The Logic of Relevance and Necessity, vol. 1, Princeton Univ. Press, Princeton and London, 1975.
R. T. Brady, Depth relevance of some paraconsistent logics, Studia, Logica. 43 (1984), pp. 63–73.
A. Fuhrmann, Relevant Logics, Modal Logics and Theory Change, PhD thesis, Australian National University, Canberra, 1988.
S. Kripke, Semantic analysis of modal logic II: non-normal modal calculi, in The Theory of Models, ed. J. W. Addison, L. Henkin and A. Tarski, pp. 206–220, North-Holland, Amsterdam, 1965.
R. Routley and R. K. Meyer, The semantics of entailment II, Journal of Philosophical Logic, 1 (1972), pp. 53–73.
R. Routley and R. K. Meyer, The semantics of entailment, in Truth, Syntax and Modality, ed. H. Leblanc, pp. 194–243, North-Holland, Amsterdam, 1973.
R. Routley, R. K. Meyer, et al., Relevant Logics and Their Rivals, vol. 1, Ridgeview, Atascadero, 1982.
J. K. Slaney, Reduced models for relevant logics without WI, Notre Dame Journal of Formal Logic 28 (1987), pp. 395–407.
R. Sylvan and G. Priest, Much simplified semantics for basic relevant logics, typescript, Canberra, 1989.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fuhrmann, A. Models for relevant modal logics. Studia Logica 49, 501–514 (1990). https://doi.org/10.1007/BF00370161
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00370161