Studia Logica 109 (1):125-136 (2021)

Yale Weiss
CUNY Graduate Center
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.
Keywords Semilattice logic  Finite model property  Negation  Sequent calculus  Conservative extension  Decision problem
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DOI 10.1007/s11225-020-09903-4
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References found in this work BETA

Semantics for Relevant Logics.Alasdair Urquhart - 1972 - Journal of Symbolic Logic 37 (1):159-169.
Proofs and Countermodels in Non-Classical Logics.Sara Negri - 2014 - Logica Universalis 8 (1):25-60.
The Undecidability of Entailment and Relevant Implication.Alasdair Urquhart - 1984 - Journal of Symbolic Logic 49 (4):1059-1073.
A Note on the Relevance of Semilattice Relevance Logic.Yale Weiss - 2019 - Australasian Journal of Logic 16 (6):177-185.
Relevance Logic: Problems Open and Closed.Alasdair Urquhart - 2016 - Australasian Journal of Logic 13 (1).

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