Notre Dame Journal of Formal Logic

Continuum Many Maximal Consistent Normal Bimodal Logics with Inverses

Timothy Williamson

Abstract

The paper considers extensions of a normal bimodal logic $\textbf{KL}$ in which the two necessity operators are mutual one-sided inverses. A continuum of maximal consistent normal extensions of $\textbf{KL}$ is constructed, each of which has infinitely many quasi-normal Post complete extensions. Some syntactic properties of maximal consistent normal bimodal logics and in particular of such extensions of $\textbf{KL}$ are investigated.

Article information

Source
Notre Dame J. Formal Logic, Volume 39, Number 1 (1998), 128-134.

Dates
First available in Project Euclid: 7 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1039293024

Digital Object Identifier
doi:10.1305/ndjfl/1039293024

Mathematical Reviews number (MathSciNet)
MR1671746

Zentralblatt MATH identifier
0968.03027

Subjects
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}

Citation

Williamson, Timothy. Continuum Many Maximal Consistent Normal Bimodal Logics with Inverses. Notre Dame J. Formal Logic 39 (1998), no. 1, 128--134. doi:10.1305/ndjfl/1039293024. https://projecteuclid.org/euclid.ndjfl/1039293024


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References

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