## Notre Dame Journal of Formal Logic

### A New Semantics for Positive Modal Logic

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 12 December 2002

https://projecteuclid.org/euclid.ndjfl/1039700693

Digital Object Identifier
doi:10.1305/ndjfl/1039700693

Mathematical Reviews number (MathSciNet)
MR1479365

Zentralblatt MATH identifier
0889.03014

#### Citation

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. https://projecteuclid.org/euclid.ndjfl/1039700693

#### References

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