An algebra M = (M ; ,∨,∧,→, 0, 1) of type 〈2, 2, 2, 2, 0, 0〉 is called a bounded commutative R`-monoid iff (i) (M ; , 1) is a commutative monoid, (ii) (M ;∨,∧, 0, 1) is a bounded lattice, and (iii) x y ≤ z ⇐⇒ x ≤ y → z, (iv) x (x → y) = x ∧ y, for each x, y, z ∈ M . In the sequel, by an R`-monoid we will mean a bounded commutative R`-monoid. (Note that bounded commutative R`-monoids are just bo...

Connections between games and many-valued logic have been shown first by Mundici [M] for the case of the Rényi-Ulam game and à Lukasiewicz logic. Given a finite set Ω of cardinality N (called the search space) and a natural number n, the Rényi-Ulam game G(N,n) is the following: a player, called Responder, chooses an element of Ω called the secret. The other player, called Questioner, has to gue...

Ten questions on fuzzy logic as a formal logic of consequence under vagueness are discussed; a problem of deenability of truth is formulated. Recently I had a very interesting friendly e-mail discussion with Professor Parikh on vagueness and fuzzy logic. Parikh published several papers concerning the notion of vagueness. They contain critical remarks on fuzzy logic and its ability to formalize ...

Mobile robots generally have only incomplete knowledge about their world. This knowledge is augmented through sensing actions. There have been several approaches in reasoning about actions that deal with sensing and knowledge. One important approach, which has been successfully realized on a robotic soccer team, is based on autoepistemic description logics. In this paper, we present a probabili...

By applying the concept of Lukasiewicz fuzzy set to BE-algebras, notions BE-algebra and BE-filter are introduced, their properties investigated. Characterizations discussed, relationship between (resp., BE-filter) is established. The conditions for ∈-set, q-set O-set be BE-subalgebras explored. created by using BE-filter.

in this paper, we study the finitely many constraints of fuzzy relation inequalities problem and optimize the linear objective function on this region which is defined with fuzzy max-lukasiewicz operator. in fact lukasiewicz t-norm is one of the four basic t-norms. a new simplification technique is given to accelerate the resolution of the problem by removing the components having no effect on ...

N.B.: For the references, please see Selected Bibliography on Aristotle's Theory of Categorical Syllogism "When modem logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle’s contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotl...

The main idea motivating the development of fuzzy logic (FL) can be formulated as follows: Fuzzy logic is a special many-valued logic addressing the vagueness phenomenon and developing tools for its modeling via truth degrees taken from an ordered scale. It is expected to preserve as many properties of classical logic as possible. During the past 15 years, the mathematical FL has been developed...