摘要: The main goal of this paper is to investigate (strong) monadic NM-algebras and
to prove the (chain) completeness of the monadic NM-logic. In this paper, we
introduce monadic NM-algebras: a variety of NM-algebras equipped with universal
quanti#12;ers. Also, we study some properties of them and obtain some conditions
under which a monadic NM-algebra becomes a monadic Boolean algebra. Besides,
we show that the variety of NM-algebras are the equivalent algebraic semantics of
the monadic fragment of NM predicate logic. Furthermore, we discuss relations
between monadic NM-algebras and some related structures, likeness modal NMalgebras
and rough approximation spaces. In addition, we introduce and investigate
monadic #12;lters in monadic NM-algebras. In particular, by using monadic #12;lters on
monadic NM-algebras, we characterize two kinds of monadic NM-algebras, which
are simple and subdirectly irreducible. Moreover, we focus on a monadic analogous
of representation theorem for NM-algebras and obtain that every strong monadic
NM-algebra can be represented as subalgebras of products of linearly ordered ones.
Then, we present monadic NM-logic, a system of many-valued logic capturing the
tautologies of the predicate logics of nilpotent minimum t-norm and it's residua. As
an application of (strong) monadic NM-algebras, we prove the (chain)completeness
of monadic NM-logic. Our results constitute a crucial #12;rst step for providing a solid
algebraic foundation for the one element fragment of NM predicate logic.