On Gödel Algebras of Concepts

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• 关键词：Intended semantics ; Concept lattice ; Many ; valued logic ; FCA ; Formal concept analysis ; Fuzzy logic ; Gödel Logic
• 刊名：Lecture Notes in Computer Science
• 出版年：2017
• 出版时间：2017
• 年：2017
• 卷：10148
• 期：1
• 页码：251-262
• 丛书名：Logic, Language, and Computation
• ISBN：978-3-662-54332-0
• 卷排序：10148

文摘

Beside algebraic and proof-theoretical studies, a number of different approaches have been pursued in order to provide a complete intuitive semantics for many-valued logics. Our intention is to use the powerful tools offered by formal concept analysis (FCA) to obtain further intuition about the intended semantics of a prominent many-valued logic, namely Gödel, or Gödel-Dummett, logic. In this work, we take a first step in this direction. Gödel logic seems particularly suited to the approach we aim to follow, thanks to the properties of its corresponding algebraic variety, the class of Gödel algebras. Furthermore, Gödel algebras are prelinear Heyting algebras. This makes Gödel logic an ideal contact-point between intuitionistic and many-valued logics.