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Order-dual relational semantics for non-distributive propositional logics: a general framework. (English) Zbl 1436.03168

Summary: The contribution of this paper lies with providing a systematically specified and intuitive interpretation pattern and delineating a class of relational structures (frames) and models providing a natural interpretation of logical operators on an underlying propositional calculus of Positive Lattice Logic (the logic of bounded lattices) and subsequently proving a generic completeness theorem for the related class of logics, sometimes collectively referred to as (non-distributive) Generalized Galois Logics (GGL’s).

MSC:

03B60 Other nonclassical logic
03B45 Modal logic (including the logic of norms)
03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
03G10 Logical aspects of lattices and related structures
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