Probability Measures in the Logic of Nilpotent Minimum

STONE DUALITY FOR R0-ALGEBRAS WITH INTERNAL STATES

$Rsb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras and the category of t...

Nilpotent Minimum Fuzzy Description Logics

We define the fuzzy description logic ALCHNM based on the t-norm of Nilpotent Minimum and we prove its reduction to the crisp description logic ALCH. Hence we prove decidability results for ALCHNM.

On Rational Weak Nilpotent Minimum Logics

In this paper we investigate extensions of Gödel and Nilpotent Minimum logics by adding rational truth-values as truth constants in the language and by adding corresponding book-keeping axioms for the truth-constants. We also investigate the rational extensions of some parametric families of Weak Nilpotent Minimum logics, weaker than both Gödel and Nilpotent Minimum logics. Weak and strong stan...

Valuations in Nilpotent Minimum Logic

Joan GISPERT I BRASÓ AXIOMATIC EXTENSIONS OF THE NILPOTENT MINIMUM LOGIC

A b s t r a c t. In this paper we characterize, classify and axiomatize all axiomatic extensions of the Nilpotent Minimum Logic. Every axiomatic extension is complete with respect to a class of NM-chains. Given a family of NM-chains the number of elements of the largest odd finite NM-chain in the family and the number of elements of the largest even finite NM-chain in the family turns out to be...