A Characterization of Non-Iterative Normal Modal Logics
Adrian Soncodi
TL;DR
This paper characterizes all non-iterative normal modal logics, defined by degree 1 axioms, by constructing their complete lattice and providing their axiomatic and semantic specifications.
Contribution
It offers a comprehensive classification and description of all non-iterative normal modal logics extending K, using normal form calculations.
Findings
Complete lattice of non-iterative normal modal logics constructed
Axiomatic and semantic specifications provided for these logics
Characterization of modal degree 1 axioms achieved
Abstract
Non-iterative normal modal logics are defined by axioms of modal degree 1. In this paper we use calculations with normal forms to determine the set of all possible non-iterative normal modal logics, unimodal propositional extensions of K. To characterize them, we construct the complete set (lattice) of such logics and we provide the generic specification of their axioms and their semantics.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Advanced Algebra and Logic · Logic, programming, and type systems