# Formal System

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## 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 ?
In the father's opinion, paying through the formal system did nothing to improve their child's well-being.
With regard to system, there are two possibilities: (1) the hospital is located in a community with a formal, publicly administered system, or (2) the hospital is in a community without a formal system.
A formal system consists of primitives, formation rules, formulae, axioms, and rules of inference.
In contrast, a formal system produces "heads up" cockpit displays.
Built into the college system are internal structures to ensure that the formal system is functional and effective.
The number of schools and enrollment during the years 2001 to 2004 of the formal system for primary, middle and high level was considered and enrollment during the year 198-1999 and 2004 for Secondary School Certificate to Ph.
A more formal system of credits, merits and prizes can also be used to recognise and congratulate pupils when they set a good example or show improvement in their behaviour.
The introduction of a formal system for sharing tax losses and other tax attributes among groups of related corporations would bring the Canadian tax system in line with that of most other developed countries in the world.
For years, we'd done some marketing, but it wasn't a formal system of well-thought-out tactics.
In fact, many administrators believe that training at the police academy level remains sufficient for the agency workforce and that a formal system of continuing education and training for sworn officers is unnecessary or too expensive.
The Alliance last week unveiled proposals for a formal system of sharing top seats on committee chairmanships.
We are thinking about a more formal system of performance appraisal.

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