A Non-Standard Kripke Semantics for the Minimal Deontic Logic

Edson Bezerra, Giorgio Venturi

DOI: http://dx.doi.org/10.12775/LLP.2020.016


In this paper we study a new operator of strong modality ⊞, related to the non-contingency operator ∆. We then provide soundness and completeness theorems for the minimal logic of the ⊞-operator.


modal logic; non-normal modal logic; seriality; non-contingency

Full Text:



Boolos, G., 1993, The Logic of Provability, Routledge, Cambridge University Press. DOI: http://dx.doi.org/10.1017/CBO9780511625183

Chellas, B.F., 1980, Modal Logic: An Introduction, Cambridge university press. DOI: http://dx.doi.org/10.1017/CBO9780511621192

Cresswell, M.J., 1988, “Necessity and contingency”, Studia Logica 47 (2): 145–149. DOI: http://dx.doi.org/10.1007/BF00370288

Fan, Jie, Yanjing Wang, and Hans Van Ditmarsch, 2015, “Contingency and knowing whether”, The Review of Symbolic Logic 8 (1): 75–107. DOI: http://dx.doi.org/10.1017/S1755020314000343

Gilbert, David R., and Giorgio Venturi, 2016, “Reflexive-insensitive modal logics”, The Review of Symbolic Logic 9 (1): 167–180. DOI: http://dx.doi.org/10.1017/S175502031500026X

Gilbert, David R., and Giorgio Venturi, 2017, “A neighborhood semantics for the logics of unknown truths and of false beliefs”, Australasian Journal of Logic 14 (1): 246–267. DOI: http://dx.doi.org/10.26686/ajl.v14i1.4033

Gilbert, D., and G. Venturi, 2018, “A note on logics of essence and accident”, Logic Journal of the IGPL, First online. DOI: http://dx.doi.org/10.1093/jigpal/jzy065

Humberstone, L., 1995, “The logic of non-contingency”, Notre Dame Journal of Formal Logic, 36 (2): 214–229. DOI: http://dx.doi.org/10.1305/ndjfl/1040248455

Lemmon, Edward John, 1957, “New foundations for Lewis modal systems”, The Journal of Symbolic Logic 22 (2): 176–186. DOI: http://dx.doi.org/10.2307/2964179

Montgomery, Hugh, and Richard Routley, 1966, “Contingency and non-contingency bases for normal modal logics”, Logique et Analyse 9 (35/36): 318–328.

Steinsvold, Christopher, 2011, “Being wrong: Logics for false belief”, Notre Dame Journal of Formal Logic 52 (3): 245–253. DOI: http://dx.doi.org/10.1215/00294527-1435438

Venturi, Giorgio, and Pedro Teixeira Yago, 2020, “Tableaux for essence and contingency”, Logic Journal of the IGPL, Published: 13 May 2020. DOI: http://dx.doi.org/10.1093/jigpal/jzaa016

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism