-
Views
-
Cite
Cite
Stanislav O Speranski, Negation as a modality in a quantified setting, Journal of Logic and Computation, Volume 31, Issue 5, July 2021, Pages 1330–1355, https://doi.org/10.1093/logcom/exab025
Close - Share Icon Share
Abstract
The idea of treating negation as a modality manifests itself in various logical systems, especially in Došen’s propositional logic |$\textsf {N}$|, whose negation is weaker than that of Johansson’s minimal logic. Among the interesting extensions of |$\textsf {N}$| are the propositional logics |$\textsf {N}^{\ast }$| and |$\textsf {Hype}$|; the former was proposed in Cabalar et al. (2006, Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning, 25–36), while the latter has recently been advocated in Leitgeb (2019, J. Philos. Logic, 48, 305–405), but was first introduced in Moisil (1942, Disquisitiones Math. et Phys., 2, 3–98). I shall develop predicate versions of |$\textsf {N}$| and |$\textsf {N}^{\ast }$| and provide a simple Routley-style semantics for the predicate version of |$\textsf {Hype}$|. The corresponding strong completeness results will be proved by means of a useful general technique. It should be remarked that this work can also be seen as a starting point for the investigation of intuitionistic predicate modal logics.
