In this paper, we introduce the notion of fuzzy C-matroids, a new class of fuzzy matroids. We study properties of this class and define several new types of fuzzy maps between fuzzy matroids. In addition, we define fuzzy C-inner and fuzzy C-closure operators in this class and characterize fuzzy C-matroids and fuzzy maps between matroids in terms of these notions.

In [3] Daigneault and Monk proved that the class of (ω dimensional) representable polyadic algebras (RPAω for short) is axiomatizable by finitely many equationschemas. However, this result does not imply that the equational theory of RPAω would be recursively enumerable; one simple reason is that the language of RPAω contains a continuum of operation symbols. Here we prove the following. Roughl...

This paper presents new classes of tree automata combining automata with equality test and automata modulo equational theories. We believe that this class has a good potential for application in e.g. software verification. These tree automata are obtained by extending the standard Horn clause representations with equational conditions and rewrite systems. We show in particular that a generalize...

This paper provides a sound, complete and decidable equational theory for the terms of the (I; ;?;!)-fragment of intuitionistic linear logic with respect to the class of models known as linear categories. This work uses the natural deduction style presentation of the !-type constructor in DILL so as to be able to apply the ideas of adjoint rewriting. We obtain an expansionary-rewrite rule and c...

All applications of equational uniication in the area of term rewriting and theorem proving require algorithms for general E-uniica-tion, i.e., E-uniication with free function symbols. On this background, the complexity of general E-uniication algorithms has been investigated for a large number of equational theories. For most of the relevant cases, the problem of deciding solvability of genera...

Kleene algebra (KA) is the algebra of regular events. Familiar examples of Kleene algebras include regular sets, relational algebras, and trace algebras. A Kleene algebra with tests (KAT) is a Kleene algebra with an embedded Boolean subalgebra. The addition of tests allows one to encode while programs as KAT terms, thus the equational theory of KAT can express (propositional) program equivalenc...

In the paper, fuzzy fisherface is extended to image matrix, namely, the fuzzy 2DLDA (F2DLDA). In the proposed method, we calculate the membership degree matrix by fuzzy K-nearest neighbor (FKNN), and then incorporate the membership degree into the definition of the between-class scatter matrix and the within-class scatter matrix. Finally, we get the fuzzy between-class scatter matrix and fuzzy ...

An equational theory E is permutative if for all terms s, t : s =E t implies that the terms s and t contain the same symbols with the same number of occurrences. The class of permutative equational theories includes the theory of AC (associativity and commutativity). It is shown in this research note that there is no algorithm that decides E-unifiability of terms for all permutative theories. T...

The equational theory generated by all algebras of binary relations with operations of union, composition, converse and reflexive transitive closure was studied by Bernátsky, Bloom, Ésik, and Stefanescu in 1995. We reformulate some of their proofs in syntactic and elementary terms, and we provide a new algorithm to decide the corresponding theory. This algorithm is both simpler and more efficie...

Security protocols employing cryptographic primitives with algebraic properties are conveniently modeled using Horn clauses modulo equational theories. We consider clauses corresponding to the class H3 of Nielson, Nielson and Seidl. We show that modulo the theory ACU of an associative-commutative symbol with unit, as well as its variants like the theory XOR and the theory AG of Abelian groups, ...