Humberstone, I. L. The logic of non-contingency. (English) Zbl 0833.03004 Notre Dame J. Formal Logic 36, No. 2, 214-229 (1995). Summary: We consider the modal logic of non-contingency in a general setting, without making special assumptions about the accessibility relation. The basic logic in this setting is axiomatized, and some of its extensions are discussed, with special attention to the expressive weakness of the language whose sole modal primitive is non-contingency (or equivalently, contingency), by comparison with the usual language based on necessity (or equivalently, possibility). Cited in 2 ReviewsCited in 35 Documents MSC: 03B45 Modal logic (including the logic of norms) Keywords:axiomatization; modal logic of non-contingency; expressive weakness × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Chellas, B. F., Modal Logic: An Introduction , Cambridge University Press, Cambridge, 1980. · Zbl 0431.03009 [2] Cresswell, M. J., “Necessity and contingency,” Studia Logica , vol. 47 (1988), pp. 145–149. · Zbl 0666.03015 · doi:10.1007/BF00370288 [3] Hiż, H., “A warning about translating axioms,” American Mathematics Monthly , vol. 65 (1958), pp. 613–614. JSTOR: · Zbl 0082.01504 · doi:10.2307/2309121 [4] Mortensen, C., “A sequence of normal modal systems with non-contingency bases,” Logique et Analyse , vol. 19 (1976), pp. 341–344. · Zbl 0347.02014 [5] Montgomery, H., and R. Routley, “Contingency and non-contingency bases for normal modal logics,” Logique et Analyse , vol. 9 (1966), pp. 318–328. · Zbl 0294.02008 [6] Salomaa, A., “Morphisms on free monoids and language theory,” pp. 141–166 in Formal Language Theory: Perspectives and Open Problems , edited by R. V. Book, Academic Press, New York 1980. [7] Segerberg, K., Classical Propositional Operators , Clarendon Press, Oxford, 1982. · Zbl 0491.03003 [8] Smullyan, R. M., First-Order Logic , Springer-Verlag, Berlin, 1968. · Zbl 0172.28901 [9] van Benthem, J., and I. L. Humberstone, “Halldén-completeness by gluing of Kripke frames,” Notre Dame Journal of Formal Logic , vol. 24 (1983), pp. 426–430. · Zbl 0487.03008 · doi:10.1305/ndjfl/1093870446 [10] von Wright, G. H., “Deontic logic,” pp. 58–74 in Logical Studies , Routledge and Kegan Paul, London, 1957. · Zbl 0081.01001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.