In the spirit of Chang and Shelah’s presentation results (from [Cha68] and [Sh88], respectively), we prove a presentation theorem for classes of continuous structures, both those axiomatized by first-order and beyond, in terms of a class of discrete structures. The thrust of this presentation theorem is the basic analytic fact that the behavior of continuous functions is determined by their val...

Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic properties of the action. In classical logic there is a strong dichotomy: while over finitely many propositional variables everything is trivial, the study of t...

in last decades, the skillful planning of land resources has become a major issue for rural development. the development of cultivated areas becomes gradually impossible due to ever increasing population growth and urban development. fuzzy logic is preferred to boolean logic for land evaluation, because fuzzy techniques lead to estimate for land use suitability on a continuous scale and can the...

Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic properties of the action. In classical logic there is a strong dichotomy: while over finitely many propositional variables everything is trivial, the study of t...

Default reasoning can provide a means of deriving plausible semantic conclusion under imprecise and contradictory information in forensic visual surveillance. In such reasoning under uncertainty, proper uncertainty handling formalism is required. A discrete species of Bilattice for multivalued default logic demonstrated default reasoning in visual surveillance. In this article, the authors pres...

of the Dissertation Inference and Learning in Probabilistic Logic Programs with Continuous Random Variables

a generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by m. h. faroughi and r. ahmadi, is presented in this study. continuous resolution of the identity (cri) is introduced, a new family of cri is constructed, and a number of reconstruction formulas are obtained. also, new results are given on the duality of continuous fusion fram...

Continuous random variables are widely used to mathematically describe random phenomenon in engineering and physical sciences. In this paper, we present a higher-order logic formalization of the Standard Uniform random variable. We show the correctness of this specification by proving the corresponding probability distribution properties within the HOL theorem prover and the proof steps have be...

This paper is about a generalization of Scott’s domain theory in such a way that its definitions and theorems become meaningful in quasimetric spaces. The generalization is achieved by a change of logic: the fundamental concepts of original domain theory (order, way-below relation, Scott-open sets, continuous maps, etc.) are interpreted as predicates that are valued in an arbitrary completely d...

Continuous random variables are widely used to mathematically describe random phenomenon in engineering and physical sciences. In this paper, we present a higherorder logic formalization of the Standard Uniform random variable as the limit value of the sequence of its discrete approximations. We then show the correctness of this specification by proving the corresponding probability distributio...