Logic Journal of the IGPL 27 (5):718-742 (2019)

Abstract
We introduce game-theoretic semantics for systems without the conveniences of either a De Morgan negation, or of distribution of conjunction over disjunction and conversely. Much of game playing rests on challenges issued by one player to the other to satisfy, or refute, a sentence, while forcing him/her to move to some other place in the game’s chessboard-like configuration. Correctness of the game-theoretic semantics is proven for both a training game, corresponding to Positive Lattice Logic and for more advanced games for the logics of lattices with weak negation and modal operators.
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DOI 10.1093/jigpal/jzy079
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References found in this work BETA

Semantic Analysis of Orthologic.R. I. Goldblatt - 1974 - Journal of Philosophical Logic 3 (1/2):19 - 35.
Semantic Analysis of Tense Logics.S. K. Thomason - 1972 - Journal of Symbolic Logic 37 (1):150-158.

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