On inclusions between quantified provability logics
Taishi Kurahashi
TL;DR
This paper explores the relationships between different quantified provability logics, providing conditions for their inclusion based on arithmetical interpretations, which advances understanding of their logical structure.
Contribution
It offers a necessary and sufficient condition for inclusion relations among quantified provability logics with respect to arithmetical interpretations, clarifying their logical connections.
Findings
Characterizes inclusion relations between quantified provability logics
Provides a criterion for inclusion based on arithmetical interpretations
Enhances understanding of the structure of provability logics
Abstract
We investigate several consequences of inclusion relations between quantified provability logics. Moreover, we give a necessary and sufficient condition for the inclusion relation between quantified provability logics with respect to arithmetical interpretations.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Logic, programming, and type systems · Formal Methods in Verification