We exhibit Pontryagin duality as a special case of Stone in continuous logic setting. More specifically, given an abelian topological group A, and F the family (group) homomorphisms from A to circle T, then, viewing (A,+) equipped with collection structure M, we show that local type space SF(M) is precisely dual where latter considered discrete group. conclude, using (between compact groups), B...

this paper introduces an indirect adaptive fuzzy sliding mode controller as a power system stabilizer for damping local and inter-area modes of oscillations of multi-machine power systems. this controller is designed based on the combination of sliding mode controller and the fuzzy logic systems. the fuzzy systems are used to approximate the unknown functions of power system model. generator sp...

We present some model theoretic results for {L}ukasiewiczpredicate logic by using the methods of continuous model theorydeveloped by Chang and Keisler.We prove compactness theorem with respect to the class of allstructures taking values in the {L}ukasiewicz $texttt{BL}$-algebra.We also prove some appropriate preservation theorems concerning universal and inductive theories.Finally, Skolemizatio...

We investigate the continuous model theory of ultrametric spaces of diameter ≤ 1. There is no universal Polish ultrametric space of diameter 1; but there is a Polish ultrametric space, Umax, taking distances in Q∩[0, 1], which is universal for all such Polish ultrametric spaces. We show that in the continuous theory of Umax, nonforking is characterized by a stable independence relation, which i...

In this paper we present Minimal Polynomial Logic (MPL), a generalisation of classical propositional logic which allows truth values in the continuous interval 0; 1] and in which propositions are represented by multi-variate polynomials with integer coeecients. The truth values in MPL are suited to represent the probability of an assertion being true, as in Nilsson's Probabilistic Logic, but ca...