Monadic BL-algebras: the equivalent algebraic semantics of H 'ajek's\n monadic fuzzy logic

2016/09/16 by Diego Castaño, Cecilia Cimadamore, Castaño, Diego +5
Computer Science · Decision Sciences · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Multi-Criteria Decision Making #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.1609.05082

openalex publication_date 2016/09/16 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

In this article we introduce the variety of monadic BL-algebras as\nBL-algebras endowed with two monadic operators \∀ and \∃. After a\nstudy of the basic properties of this variety we show that this class is the\nequivalent algebraic semantics of the monadic fragment of H 'ajek's basic\npredicate logic. In addition, we start a systematic study of the main\nsubvarieties of monadic BL-algebras, some of which constitute the algebraic\nsemantics of well-known monadic logics: monadic G "odel logic and monadic\n Lukasiewicz logic. In the last section we give a complete characterization\nof totally ordered monadic BL-algebras.\n

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