On non-self-referential fragments of modal logics

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• 作者：Junhua Yu¹ ; ² ; ^{junhua.yu.5036@outlook.com}
• 关键词：03F07 ; 03B45 ; 03F03 ; 03B60
• 刊名：Annals of Pure and Applied Logic
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：168
• 期：4
• 页码：776-803
• 全文大小：677 K
• 卷排序：168

文摘

Justification logics serve as “explicit” modal logics in a way that, formula ϕ is a modal theorem if and only if there is a justification theorem, called a realization of ϕ, gained by replacing modality occurrences in ϕ by (justification) terms with structures explicitly explaining their evidential contents. In justification logics, terms stand for justifications of (propositions expressed by) formulas, and as a kind of atomic terms, constants stand for that of (justification) axioms. Kuznets has shown that in order to realize (i.e., offer a realization of) some modal theorems, it is necessary to employ a self-referential constant, that is, a constant that stands for a justification of an axiom containing an occurrence of the constant itself. Based on existing works, including some of the author's, this paper treats the collection of modal theorems that are non-self-referentially realizable as a fragment (called non-self-referential fragment) of the modal logic, and verifies: (1) that fragment is not closed in general under modus ponens; and (2) that fragment is not “conservative” in general when going from a smaller modal logic to a larger one.