Structural Completeness in Fuzzy Logics

2009/04/01 by Petr Cintula, George Metcalfe · 4 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Algebra over a field #Artificial intelligence #Calculus (dental) #Completeness (order theory) #Computer science #Description logic #Discrete mathematics #Fuzzy logic #Fuzzy number #Fuzzy set #Intermediate logic #Many-valued logic #Mathematics #Multi-Criteria Decision Making #Pure mathematics #Rough Sets and Fuzzy Logic #Substructural logic #T-norm #T-norm fuzzy logics #Łukasiewicz logic

paper · pdf · doi:10.1215/00294527-2009-004

openalex publication_date 2009/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Structural completeness properties are investigated for a range of popular t-norm based fuzzy logics—including Łukasiewicz Logic, Gödel Logic, Product Logic, and Hájek's Basic Logic—and their fragments. General methods are defined and used to establish these properties or exhibit their failure, solving a number of open problems.

Cited by

• Singly generated quasivarieties and residuated structures
• Hereditarily Structurally Complete Superintuitionistic Deductive Systems
• The unification type of Lukasiewicz logic with a bounded number of variables
• Admissible rule [wikipedia]

Related

• On the Undecidability of Fuzzy Description Logics with GCIs with Lukasiewicz t-norm
• The Complexity of Fuzzy Logic
• A tableau for set-satisfiability for extended fuzzy logic BL
• Structural completeness in many-valued logics with rational constants
• On the Failure of the Finite Model Property in some Fuzzy Description Logics