It is proved that every involutive equivalential equality algebra (E, ∧, ∼, 1), an residualted lattice EQ-algebra, which operation ⊗ defined by x y = (x → 0 ) . Moreover, it showen EQ-algebra we have

Abstract An E -fuzzy group is a lattice-valued algebraic structure, defined on a crisp algebra which is not necessarily a group. The crisp equality is replaced by a particular fuzzy one denoted by E . Classical group-like properties are formulated as appropriate fuzzy identities special lattice theoretic formulas. We prove basic features of E -fuzzy groups: properties of the unit and inverses, ...

We consider algebraic speciications with observational features. Axioms as well as observations are formulae of full (Many-Sorted) First Order Logic with Equality. The associated semantics is based on a non standard interpretation of equality called observational equality. We study the adequacy of this semantics for software specii-cation and the relationship with behavioural equivalence of alg...

One can attempt to solve the problem of establishing the correctness of some software w.r.t. a formal speciication at the semantical level. For this purpose, the semantics of an algebraic speciication should be the class of all algebras which correspond to the correct realizations of the speciication. We approach this goal by deening an observational satisfaction relation which is less restrict...

We consider algebraic speciications with observational features. Axioms as well as observations are formulae of full (Many-Sorted) First Order Logic with Equality. The associated semantics is based on a non standard interpretation of equality called observational equality. We study the adequacy of this semantics for software speciication and the relationship with behavioural equivalence of alge...

We introduce an intersection typing system for combinatory logic, such that a term of combinatory logic is typeable ii it is sn. We then prove the soundness and completeness for the class of partial com-binatory algebras. Let F be the class of non-empty lters which consist of types. Then F is an extensional non-total partial combinatory algebra. Furthermore, it validates the strongest consisten...

To establish the correctness of some software w.r.t. its formal speciication is widely recognized as a diicult task. A rst simpliication is obtained when the semantics of an algebraic speciication is deened as the class of all algebras which correspond to the correct realizations of the speciication. A software is then declared correct if it corresponds to some algebra of this class. We approac...

Hirsch and Hodkinson proved, for 3 ≤ m < ω and any k < ω, that the class SNrmCAm+k+1 is strictly contained in SNrmCAm+k and if k ≥ 1 then the former class cannot be defined by any finite set of first order formulas, within the latter class. We generalise this result to the following algebras of m-ary relations for which the neat reduct operator Nrm is meaningful: polyadic algebras with or witho...