From the viewpoint of Behaviour based Control many control tasks can be divided into separate behaviour components. By defining the relevant behaviour components, the actual control action can be constructed based on the individual control actions of the component behaviours. In this case the control action is either related to an individual behaviour component or to a fusion of behaviour compo...

This material is studying MV-algebras and BL-algebras in terms of applicability in Boole algebra. Boole algebras are expanded use in fuzzy logic.

In [1] the authors considered finitely-valued modal logics with Kripke style semantics where both propositions and the accessibility relation are valued over a finite residuated lattice. Unfortunately, the necessity operator does not satisfy in general the normality axiom (K). In this paper we focus on the case of finite chains, and we consider a different approach based on introducing a multim...

Proof systems based on rules with the property that all formulas contained in the assumptions are contained as subformulas in the conclusion as well, are particularly suitable for automated proof search. Systems of this kind were found for several well-known fuzzy logics. However, for BL (Basic Logic), the logic of continuous t-norms and their residua, the situation is less satisfactory. We con...

Imai and Iséki [1] introduced the concept of BCK-algebra as a generalization of notions of set difference operation and propositional calculus. The notion of pseudo-BCK algebra was introduced by Georgescu and Iorgulescu [2] as generalization of BCK-algebras not assuming commutativity. Hájek [3] introduced the concept of BL-algebras as the general semantics of basic fuzzy logic (BL-logic). Iorgu...

Pseudo-MTL algebras or weak pseudo-BL algebras are non-commutative fuzzy structures which arise from pseudo-t-norms, namely, pseudo-BL algebras without the pseudo-divisibility condition. The aim of this paper is to investigate the properties of pseudo-BL algebras that also hold for pseudoMTL algebras. We will also study some classes of pseudo-MTL algebras such as good, local and Archimedean pse...

We show by standard automated theorem proving methods and freely available automated theorem prover software that axiom (A2), stating that multiplicative conjunction implies its first member, is provable from other axioms in fuzzy logics BL and MTL without using axiom (A3), which is known to be provable from other axioms [1]. We also use freely available automated model generation software to s...

in this paper, we de ne the concepts of general fuzzy recognizer, language recognized by a general fuzzy recognizer, the accessible and the coac- cessible parts of a general fuzzy recognizer and the reversal of a general fuzzy recognizer. then we obtain the relationships between them and construct a topology and some hypergroups on a general fuzzy recognizer.