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A Conservative Negation Extension of Positive Semilattice Logic Without the Finite Model Property

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Abstract

In this article, I present a semantically natural conservative extension of Urquhart’s positive semilattice logic with a sort of constructive negation. A subscripted sequent calculus is given for this logic and proofs of its soundness and completeness are sketched. It is shown that the logic lacks the finite model property. I discuss certain questions Urquhart has raised concerning the decision problem for the positive semilattice logic in the context of this logic and pose some problems for further research.

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Acknowledgements

The author is grateful to Alasdair Urquhart for correspondence concerning the positive semilattice logic, Graham Priest for discussions on related work, and two anonymous referees for comments.

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Correspondence to Yale Weiss.

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Presented by Heinrich Wansing; Received November 8, 2019.

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Weiss, Y. A Conservative Negation Extension of Positive Semilattice Logic Without the Finite Model Property. Stud Logica 109, 125–136 (2021). https://doi.org/10.1007/s11225-020-09903-4

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  • DOI: https://doi.org/10.1007/s11225-020-09903-4

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