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 It might be outdated or ideologically biased.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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Length of stay of trauma patients in Level I trauma centers in formal systems are similar to Level I centers not in formal systems.
Despite their inadequacies, formal systems are powerful tools of (partial) understanding.
Informal or alternative electoral dispute resolution mechanisms are not meant to replace formal systems, but to play a supportive role, especially when the later face credibility, financial or time constraints.
Formal systems based on text mimics how natural language is generated and semantically regulated by grammar.
the study material in AIOU has built in activities whereas in the formal systems built in activities are not included in their material.
Fast, a consultant who has worked as a senior manager in the wire and cable industry, provides leaders of manufacturing organizations with 12 principles of manufacturing excellence that focus on Lean thinking and continuous improvement: safety, good housekeeping and organization, authorized formal systems, preventive/predictive maintenance, process capability, product quality, delivery performance, visual management, continuous improvement, communication, training, and operator-led process control.
In his budget speech delivered on February 28, the finance minister had said that while are were 5.77 crore small businesses in India, mostly individual proprietorships, these bottom-of-the-pyramid entrepreneurs found it difficult, if not impossible, to access formal systems of credit.
It also has a revised and updated list of online databases; case studies in their use; more exercises on online searching; clarification of basic research concepts for making judgments about the quality of research methods; explanation of the major available formal systems for evaluating transparency and quality; more qualitative examples and guidelines and checklists for evaluating their quality; discussion and examples of mixed-methods research; and more examples of writing up reviews.
Estyn said providers are only just beginning to implement formal systems to record and recognise outcomes for learners.
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.

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