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- Title
Monadic NM-algebras: an algebraic approach to monadic predicate nilpotent minimum logic.
- Authors
Wang, Juntao; He, Pengfei; Yang, Jiang; Wang, Mei; He, Xiaoli
- Abstract
In this paper, we further study the variety of monadic nilpotent minimum (NM)-algebras and their corresponding logic. In order to solve the drawback of monadic NM-algebras, we review some well-known classes of monadic t-norm-based fuzzy logical algebras and then revise the axiomatic system of monadic NM-algebras. Then we show that the variety of monadic NM-algebras is the equivalent algebraic semantics of monadic predicate fuzzy logic |$\textbf {mNM}_{\forall }$| , which is equivalent to the modal fuzzy logic |$\textbf {S5(NM)}$|. Moreover, we show that the propositional case of the modal fuzzy logic |$\textbf {S5(NM)}$| , which is |$\textbf{S5}^{\prime}\textbf{(NM),}$| is also complete with respect to the variety of monadic NM-algebras in the sense of Blok and Pigozzi and obtain a necessary and sufficient condition for this logic to be semilinear. Finally, we give some representations of monadic NM-algebras. In particular, we give some characterizations of representable and directly indecomposable monadic NM-algebras.
- Subjects
MATHEMATICAL logic; CONDITIONALS (Logic); PREDICATE (Logic); MODAL logic; LOGIC; INDECOMPOSABLE modules; MONADS (Mathematics)
- Publication
Journal of Logic & Computation, 2022, Vol 32, Issue 4, p741
- ISSN
0955-792X
- Publication type
Article
- DOI
10.1093/logcom/exab076