# Formal System

(redirected from Logic 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 It might be outdated or ideologically biased.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.”

References in periodicals archive ?
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.
In above literature, fuzzy logic systems were employed to approximate the uncertain functions.
The adopted approach to conceive the controllers which are dedicated for the reactive method is Type-2 Fuzzy Logic System (Type-2 FLS).
Model of Fuzzy Logic System. In the fuzzy logic system, the input and output variables and their membership functions have to be first decided upon based on the expert's knowledge and experimental studies and a rue base is formed to represent the expert's knowledge.
This method is effective and superior for handling parametric and structure uncertainties, external disturbances in integer-order nonlinear systems [28, 29], where tracking error is developed to update adjusted parameters and fuzzy logic systems or neural networks are introduced to model unknown physical systems as well as to approximate unknown nonlinear functions.
If the safety logic system detects a conflict like an aircraft in LUAW with an aircraft on short final, the triggered alarm startles everyone in the tower.
[6] Valarmathi and Ayesh has presented paper on Prediction of risk in breast cancer using fuzzy logic tool box in mat lab environment this paper describes about the fuzzy logic system to predict the breast cancer using ID3 algorithm, Association rule and fuzzy logic system.
For any given positive constant [epsilon], there always exists a fuzzy logic system y(X) in theform of(7) such that
Their topics include using a geographical information system to assess hydropower potential within the Upper Indus Basin in Pakistan, predicting flood-vulnerability of areas using satellite remote-sensing images in Japan's Kumamoto City, monitoring soil moisture deficit using satellite data from the Soil Moisture and Ocean Salinity mission: correspondence through rainfall-runoff model, predicting Caspian Sea level fluctuation using artificial intelligence, and soil moisture retrieval from bistatic scatterometer measurement using fuzzy logic system. ([umlaut] Ringgold, Inc., Portland, OR)

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