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Analogues of Scott’s isomorphism theorem, Karp’s theorem as well as results on lack of compactness and strong completeness are established for infinitary propositional relevant logics. An “interpolation theorem” (of a particular sort introduced by Barwise and van Benthem) for the infinitary quantificational boolean logic L ω holds. This yields a preservation result characterizing the expressive power of infinitary relevant languages with absurdity using the model-theoretic relation of relevant directed bisimulation as well as a Beth definability property.

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Anderson, A. R. & Belnap, N. D. (1992). Entailment. The Logic of Relevance and Necessity, Vol. II. Princeton, NJ: Princeton University Press.
Badia, G. (2016). The relevant fragment of first order logic. The Review of Symbolic Logic, 9(1), 143166.
Badia, G. (2016). Bi-simulating in bi-intuitionistic logic. Studia Logica, 104(5), 10371050.
Barwise, J. (1974). Axioms for abstract model theory. Annals of Mathematical Logic, 7, 221265.
Barwise, J. & van Benthem, J. (1999). Interpolation, preservation, and pebble games. The Journal of Symbolic Logic, 64(2), 881903.
Barwise, J. & Kunen, K. (1971). Hanf numbers for fragments of L ω . Israel Journal of Mathematics, 10(3), 306320.
van Benthem, J. (1999). Modality, bisimulation and interpolation in infinitary logic. Annals of Pure and Applied Logic, 96(1–3), 2941.
Bergstra, J. & van Benthem, J. (1994). Logic of transition systems. Journal of Logic, Language and Information, 3(4), 247283.
Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal Logic. Cambridge: Cambridge University Press.
Brady, R. T. (2006). Universal Logic. Stanford: CSLI.
Chagrov, A. & Zakharyaschev, M. (1997). Modal Logic. Oxford: Clarendon Press.
Dickmann, M. A. (1975). Large Infinitary Languages. Oxford: North-Holland.
Dunn, M. & Restall, G. (2002). Relevance logic. In Gabbay, D. and Guenthner, F., editors. Handbook of Philosophical Logic. Dordrecht: Springer, pp. 1128.
Ferguson, T. M. (2012). Notes on the model theory of De Morgan logics. Notre Dame Journal of Formal Logic, 53(1), 113132.
Fine, K. (1988). Semantics for quantified relevance logic. Journal of Philosophical Logic, 17, 2759.
Fine, K. (1989). Incompleteness for quantified relevance logics. In Norman, J. and Sylvan, R., editors. Directions in Relevant Logic. Dordrecht: Kluwer, pp. 205212.
Hodges, W. (1993). Model Theory. Cambridge: Cambridge University Press.
Karp, C. (1964). Languages with Expressions of Infinite Length. Amsterdam: North-Holland.
Keisler, H. J. (1971). Model Theory for Infinitary Logic. Amsterdam: North-Holland.
Kurtonina, N. & de Rijke, M. (1997). Simulating without negation. Journal of Logic and Computation, 7(4), 501522.
Mares, E. D. & Goldblatt, R. (2006). An alternative semantics for quantified relevant logic. Journal of Symbolic Logic, 71(1), 163187.
Restall, G. (2000). An Introduction to Substructural Logics. London: Routledge.
Restall, G. (2013). Assertion, denial and non-classical theories. In Tanaka, K., Berto, F., Paoli, F., and Mares, E., editors. Paraconsistency: Logic and Applications. Dordrecht: Springer, pp. 8189.
Robles, G. & Méndez, J. M. (2010). A Routley-Meyer type semantics for relevant logics including Br plus the disjunctive syllogism. Journal of Philosophical Logic, 39, 139158.
Routley, R. (1978). Problems and solutions in the semantics of quantified relevant logics. In Arruda, A. I., Chuaqui, R., and Da costa, N. C. A., editors. Mathematical Logic in Latin America. Proceedings of the IV Latin American Symposium on Mathematical Logic. Amsterdam: North Holland, pp. 305340.
Routley, R., Meyer, R. K., Plumwood, V., & Brady, R. (1983). Relevant Logics and its Rivals, Vol. I. Atascadero, CA: Ridgeview.
Routley, R. & Meyer, R. K. (1973). The semantics of entailment. In Leblanc, H., editor. Truth, Syntax and Modality. Amsterdam: North Holland, pp. 199243.
Routley, R. & Meyer, R. K. (1972). The semantics of entailment II. Journal of Philosophical Logic, 1, 5373.
Routley, R. & Meyer, R. K. (1972). The semantics of entailment III. Journal of Philosophical Logic, 1, 192208.
Thomas, M. (2015). A generalization of the Routley-Meyer semantic framework. Journal of Philosophical Logic, 44(4), 411427.
Yang, E. (2013). R and relevance principle revisited. Journal of Philosophical Logic, 42(5), 767782.
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
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