Notre Dame Journal of Formal Logic

A New Semantics for Positive Modal Logic

S. Celani and R. Jansana


The paper provides a new semantics for positive modal logic using Kripke frames having a quasi ordering $\leq$ on the set of possible worlds and an accessibility relation $R$ connected to the quasi ordering by the conditions (1) that the composition of $\leq$ with $R$ is included in the composition of $R$ with $\leq$ and (2) the analogous for the inverse of $\leq$ and $R$. This semantics has an advantage over the one used by Dunn in "Positive modal logic," Studia Logica (1995) and works fine for extensions of the minimal system of normal positive modal logic.

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Notre Dame J. Formal Logic, Volume 38, Number 1 (1997), 1-18.

First available in Project Euclid: 12 December 2002

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Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}


Celani, S.; Jansana, R. A New Semantics for Positive Modal Logic. Notre Dame J. Formal Logic 38 (1997), no. 1, 1--18. doi:10.1305/ndjfl/1039700693.

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