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Algebras
Published in Janet Woodcock, Software Engineering Mathematics, 1988
The underlying logical system we are going to use for the theory presentations in this chapter makes use of universally quantified equations. There are no predicates other than equality, and the semantics we will give to equations is slightly different from that introduced earlier in the book. The substitution rule will be interpreted in contexts outside of propositions, allowing us to discuss values of objects rather than just the truth of statements. We will say that the substitution of equal terms into an expression allows the expression to be rewritten to an equivalent expression. Consequently the axioms of such a system are sometimes referred to as rewrite rules. If we wish to state that an expression, A, can be rewritten to another expression, B, by the application of one or more of the rewrite rules given as axioms of the system, we will write
Sociological Issues in HCI Design
Published in Constantine Stephanidis, User Interfaces for All, 2000
This relationship follows the mathematical principle of transitivity determining that, when two entities are equal to a third one, they are equal to each other; or, vice versa, when one of two entities is not equal to a third one, to which the other is equal, they are not equal to each other.
Equations and calculations
Published in Michael Drury, Electrical Inspection, Testing and Certification, 2019
Take the simple equation 2 + 4 = 6. The equal sign (=) merely states that the left-hand side of the equation is equal to the right-hand side. Consequently, if 2 is subtracted from 6, on the right-hand side of the equation, will it remain equal?
Fifty years of similarity relations: a survey of foundations and applications
Published in International Journal of General Systems, 2022
Let us consider the reflexive and symmetric relation R on with matrix A fuzzy relation S on X with matrix is a fuzzy equivalence relation smaller than or equal to R if and only if If is the Łukasiewicz t-norm and we are looking for transitive openings, we can consider only solution with a 3 on the denominator (see Boixader and Recasens (2011)), then there are 8 possible solutions in : Among them, there are 2 Ł-transitive openings of R. Namely
Research on parallel nonlinear control system of PD and RBF neural network based on U model
Published in Automatika, 2020
Fengxia Xu, Deqiang Tang, Shanshan Wang
The selection of radial basis function plays an important role in the design of RBF neural network. Generally, there are several options as follows: Gaussian function: Inversion sigmoid function Quasi-multiple quadratic function where represents the extended constant or width of the basis function. These frequently used radial basis functions are monotonically decreasing as the Euclidean distance between the variable and the 0 point increases. When the variable is equal to 0, the value of the function is the maximum. From the radial basis function, it can be seen that the radial basis neural network has good local characteristics. Gaussian functions are widely used in radial basis neural networks because of their simple expression, good symmetry and the existence of arbitrary derivatives. Therefore, Gaussian function is adopted as the radial basis function of neurons in the hidden layer in this paper.
Domain-specific requirements analysis framework: ontology-driven approach
Published in International Journal of Computers and Applications, 2019
Shreya Banerjee, Anirban Sarkar
Table 2 specifies Goals and corresponding Roles existing in the running example based on Is_assigned_to relationships. The formalization of Is_assigned_to relationship is as Explanation: In this axiom, Is_assigned_to relationship specifies relationships between Goal and Role. Further, range() is a predicate that specifies the range of the relationship. Here, domain() is a predicate that specifies the domain of the relationship in a specific time t1 or t2. Besides these, NotEqual() predicate implies that arguments of this predicate are not equal.