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NII Technical Report (NII-2004-010E):On the Semantics of Classical First-Order Logic with Constructive Double Negation
https://doi.org/10.20736/0000000398
https://doi.org/10.20736/00000003984accec50-bb00-465a-b6ef-6162611f055a
名前 / ファイル | ライセンス | アクション |
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Item type | レポート / Report(1) | |||||||||
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公開日 | 2004-12-28 | |||||||||
タイトル | ||||||||||
言語 | en | |||||||||
タイトル | NII Technical Report (NII-2004-010E):On the Semantics of Classical First-Order Logic with Constructive Double Negation | |||||||||
言語 | ||||||||||
言語 | eng | |||||||||
キーワード | ||||||||||
言語 | ja | |||||||||
主題Scheme | Other | |||||||||
主題 | テクニカルレポート | |||||||||
キーワード | ||||||||||
言語 | en | |||||||||
主題Scheme | Other | |||||||||
主題 | Technical Report | |||||||||
資源タイプ | ||||||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||||||
タイプ | departmental bulletin paper | |||||||||
ID登録 | ||||||||||
ID登録 | 10.20736/0000000398 | |||||||||
ID登録タイプ | JaLC | |||||||||
著者 |
兼岩, 憲
× 兼岩, 憲
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抄録 | ||||||||||
内容記述タイプ | Abstract | |||||||||
内容記述 | Constructive negation in intuitionistic logic (called strong negation) can be used to directly represent negative assertion, and for which its semantics is defined in Kripke models by two satisfaction relations. However, the interpretation and satisfaction based on the conventional semantics do not fit in with the definition of negation in knowledge representation when considering a double negation of the form $\sim \lnot$, for strong negation $\sim$ and classical negation $\lnot$ (which we call constructive double negation). The problem is caused by the fact that the semantics makes the axiom $\sim \lnot A \leftrightarrow A$ valid. By way of solution, this paper proposes an alternative semantics for constructive double negation $\sim \lnot A$ by capturing the constructive meaning of the combinations of the two negations. In the semantics, we consider the constructive double negation $\sim \lnot A$ as partial to the classical double negation $\lnot \lnot A$ and as exclusive to the classical negation $\lnot A$. Technically, we introduce infinite satisfaction relations to interpret the partiality that is sequentially created by each constructive double negation (of the forms $\sim \lnot A, \sim \lnot \sim \lnot A,\ldots$). | |||||||||
言語 | en | |||||||||
書誌情報 |
ja : NIIテクニカル・レポート en : NII Technical Report p. 1-18, 発行日 2004-12-28 |
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出版者 | ||||||||||
言語 | ja | |||||||||
出版者 | 国立情報学研究所 | |||||||||
ISSN | ||||||||||
収録物識別子タイプ | ISSN | |||||||||
収録物識別子 | 1346-5597 |