Order-sorted type systems supporting inheritance hierarchies and subtype polymorphism are used in theorem proving, AI, and declarative programming. The satisfiability problems for the theories of: (i) order-sorted uninterpreted function symbols, and (ii) of such symbols modulo a subset Δ of associative-commutative ones are reduced to the unsorted versions of such problems at no extra computatio...

We prove some results about the limitations of the expressive power of quantiiers on nite structures. We deene the concept of a bounded quantiier and prove that every relativizing quantiier which is bounded is already rst-order deenable (Theorem 3.8). We weaken the concept of congruence closed (see 6]) to weakly congruence closed by restricting to congruence relations where all classes have the...

By using a special t-level relation U(μ, t) = {(x, y) ∈ S × S|(μ(x) ∧ μ(y)) ∨ IdS(x, y) ≥ t} based on a fuzzy ideal μ of a semigroup S, which is a congruence relation, we study the roughness of soft semigroups under this special ideal of S, such as rough soft subsemigroups, rough soft ideals and rough soft prime ideals.

in this paper, a fuzzy version of the analytic form of hahn-banachextension theorem is given. as application, the hahn-banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

Today most research related to manufacturing strategy development concentrates on descriptive processes and conceptual models, and therefore lacks the capability of assessing the supportive degree of manufacturing strategy to competitive priorities, and is also difficult to assess the congruence among various decisions of the manufacturing strategy. This paper proposes an approach for manufactu...

An important concept in the theory of residuated lattices and other algebraic structures used for formal fuzzy logic, is that of a filter. Filters can be used, amongst others, to define congruence relations. Specific kinds of filters include Boolean filters and prime filters. In this paper, we define several different filters of residuated lattices and triangle algebras and examine their mutual...