117 research outputs found
Valuations in Nilpotent Minimum Logic
The Euler characteristic can be defined as a special kind of valuation on
finite distributive lattices. This work begins with some brief consideration on
the role of the Euler characteristic on NM algebras, the algebraic counterpart
of Nilpotent Minimum logic. Then, we introduce a new valuation, a modified
version of the Euler characteristic we call idempotent Euler characteristic. We
show that the new valuation encodes information about the formul{\ae} in NM
propositional logic
Expanding FLew with a Boolean connective
We expand FLew with a unary connective whose algebraic counterpart is the
operation that gives the greatest complemented element below a given argument.
We prove that the expanded logic is conservative and has the Finite Model
Property. We also prove that the corresponding expansion of the class of
residuated lattices is an equational class.Comment: 15 pages, 4 figures in Soft Computing, published online 23 July 201
Interval-valued algebras and fuzzy logics
In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter
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