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 It might be outdated or ideologically biased.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.
References in periodicals archive ?
joining formal system of education so I###2.181###.030* .275###.126
This issue aside, neo-formalism still faces Godelian worries, which is to say: so long as theoremhood in the relevant formal systems is recursively enumerable, mathematical truth will outstrip formal proof.
A superb logician, Godel improved the standing of logic within mathematics and was the first mathematician to prove a number theoretical truth, not by deducing it formally from the axioms and rules of a formal system, but through meta-mathematical argument (Godel, 1931; Nagel & Newman, 2001; Feferman, 2006c).
This change has been brought about by the use of distance education to complement the formal system of education (Brown and Constantin, 1992).
Think of the letters and words of a language, together with its rules, as a formal system. Although the words have arbitrary meanings assigned to them by minds, and there may be a "deep structure" of syntax that conforms to logic, the words themselves have no reality apart from a culture.
'Reliance on lisan [traditional] procedures became even more important during the Indonesian occupation because the formal system of justice was perceived as an instrument of selective oppression rather than a means of protection of the rights of people' (Commission for Reception, Truth and Reconciliation in East Timor, 2005, p.
Such management is based on a formal system of allocation of individual fishing rights to fishermen, fishing vessels, enterprises, cooperatives or fishing communities.
An ancient system that actually predates banking, it works in an analogous manner to a more formal system of "wiring" money.
Similarly, we urge the Standing Committee to recommend that a formal system be introduced to permit the sharing and utilization of tax losses and other tax attributes among groups of related corporations.
Eric Keller, Movaris' CEO, says that most companies seem to piece together a close in a non-automated fashion that includes Excel spreadsheets, emails and voice-mails and has "no formal system of records." Mara adds that regulators, investors and others outside the companies want to see the close as more science than art, and for it "to be a reproducible process."
Somewhat surprisingly, less than 20 percent of the respondents felt a formal system is in place to deal with changes in risks or controls in response to changes in the business, its structures, systems or processes; this contrasts with the 83 percent who thought that this area was a medium to high priority for their organization.
Hilliard's mistake was not having a formal system for documenting change orders.

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