Order-Dual Relational Semantics for Non-distributive Propositional Logics: A General Framework

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...

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Bibliographic Details
Published in:Journal of philosophical logic 2018-02, Vol.47 (1), p.67-94
Main Author: Hartonas, Chrysafis
Format: Article
Language:English
Subjects:
Algebra
Education
Lattice theory
Logic
Philosophy
Semantics
Temporal logic
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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).
ISSN:0022-3611
1573-0433
DOI:10.1007/s10992-016-9417-7