Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics
Recently, algebraic Routley–Meyer-style semantics was introduced for basic substructural logics. This paper extends it to fuzzy logics. First, we recall the basic substructural core fuzzy logic <b>MIAL</b> (Mianorm logic) and its axiomatic extensions, together with their algebraic semant...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/4/273 |
| _version_ | 1797506610627608576 |
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| author | Eunsuk Yang |
| author_facet | Eunsuk Yang |
| author_sort | Eunsuk Yang |
| collection | DOAJ |
| description | Recently, algebraic Routley–Meyer-style semantics was introduced for basic substructural logics. This paper extends it to fuzzy logics. First, we recall the basic substructural core fuzzy logic <b>MIAL</b> (Mianorm logic) and its axiomatic extensions, together with their algebraic semantics. Next, we introduce two kinds of ternary relational semantics, called here linear <i>Urquhart-style</i> and <i>Fine-style</i> Routley–Meyer semantics, for them as <i>algebraic</i> Routley–Meyer-style semantics. |
| first_indexed | 2024-03-10T04:35:59Z |
| format | Article |
| id | doaj.art-b579afa8568c4ffba3c37888ae0191a4 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T04:35:59Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-b579afa8568c4ffba3c37888ae0191a42023-11-23T03:49:20ZengMDPI AGAxioms2075-16802021-10-0110427310.3390/axioms10040273Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style SemanticsEunsuk Yang0Department of Philosophy & Institute of Critical Thinking and Writing, Colleges of Humanities & Social Science Blvd., Jeonbuk National University, Rm 417, Jeonju 54896, KoreaRecently, algebraic Routley–Meyer-style semantics was introduced for basic substructural logics. This paper extends it to fuzzy logics. First, we recall the basic substructural core fuzzy logic <b>MIAL</b> (Mianorm logic) and its axiomatic extensions, together with their algebraic semantics. Next, we introduce two kinds of ternary relational semantics, called here linear <i>Urquhart-style</i> and <i>Fine-style</i> Routley–Meyer semantics, for them as <i>algebraic</i> Routley–Meyer-style semantics.https://www.mdpi.com/2075-1680/10/4/273operational semanticsRoutley–Meyer-style semanticsalgebraic semantics(core) fuzzy logicsimplicational tonoid fuzzy logics |
| spellingShingle | Eunsuk Yang Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics Axioms operational semantics Routley–Meyer-style semantics algebraic semantics (core) fuzzy logics implicational tonoid fuzzy logics |
| title | Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics |
| title_full | Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics |
| title_fullStr | Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics |
| title_full_unstemmed | Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics |
| title_short | Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics |
| title_sort | basic core fuzzy logics and algebraic routley meyer style semantics |
| topic | operational semantics Routley–Meyer-style semantics algebraic semantics (core) fuzzy logics implicational tonoid fuzzy logics |
| url | https://www.mdpi.com/2075-1680/10/4/273 |
| work_keys_str_mv | AT eunsukyang basiccorefuzzylogicsandalgebraicroutleymeyerstylesemantics |