State Semantics for Substructural Logics

This paper presents semantics for a wide range of substructural logics and shows soundness and completeness for these systems. The logics characterised by the semantics include both systems that do not contain distribution, such as Full Lambek calculus with negation, Multiplicative–Additive Linear Logic, and Lattice-R, as well as those that are distributive, such as the mainstream relevant logics and R-Mingle. The semantics is an indexical semantics, in which truth is relativised to points. 2020 Mathematics Subject Classification. Primary: 03B47, Secondary: 03B35.

Authors

• Edwin Mares

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