Formal System

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Formal System

 

an uninterpreted calculus such that (1) the class of its expressions, or formulas, is usually defined inductively through the specification of primitive (elementary, atomic) formulas and rules for the formation (construction) of formulas and (2) the subclass of provable formulas (theorems) is defined through the specification of a system of axioms and of rules for the derivation of theorems from axioms and already proved theorems (seeRULE OF INFERENCE).

The term “formal system” has many synonyms, which, however, are sometimes used to refer to concepts related to, but not identical with, formal systems. Examples of these synonyms are “formal theory,” “formal mathematics,” “formalism,” “formal calculus,” “abstract calculus,” “syntactic system,” “axiomatic system,” “logistic system,” “formal language,” “formal logic,” “codification,” and “deductive system.”

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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The BS regularly monitors the network status and decides how many nodes are to be selected for re-encryption based on three parameters (the r emaining energy of the nodes on the routing path (REL), hop count distance between two current executive re-encryption nodes (HC), and false positive rate (FPR)) using a fuzzy logic system, as shown in Fig.
This paper is organized as follows: Section 2 describes concepts of fuzzy logic systems, Section 3 describes the concepts of fuzzy logic controllers, Section 4 describes the original harmony search method, Section 5 describes the proposed method, Section 6 shows the description of the ball and beam controller, Section 7 presents experiments and results, Section 8 presents a statistical comparison, and finally Section 9 offers the conclusions.
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