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Topic: Formal system

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  Formal system - Open Encyclopedia   (Site not responding. Last check: 2007-10-07)
In logic, mathematics, and computer science, a formal system is a formal grammar used for modelling purposes.
Formalization is the act of creating a formal system, in an attempt to capture the essential features of a real-world or conceptual system in formal language.
On the other hand, David Hilbert founded metamathematics as a discipline designed for discussing formal systems; it is not assumed that the metalanguage in which proofs are studied is itself less informal than the usual habits of mathematicians suggest.
open-encyclopedia.com /Formal_system   (360 words)

 Logical Consequence, Philosophical Considerations [Internet Encyclopedia of Philosophy]
Hence, (2) is a formal consequence of (1) and on each interpretation of S, M, and P the resulting (2') is a formal consequence of the sentence that results from (1') (e.g., Some clowns are sad is a formal consequence of Some clowns are both lonely and sad).
This mechanism is a deductive system (also known as a formal system or as a formal proof calculus).
Hence, a proof in a deductive system of the former sentence from the latter two is evidence that the deductive system is incorrect.
www.iep.utm.edu /l/logcon.htm   (6498 words)

 non-formal education @ the encyclopedia of informal education
The conclusion was that formal educational systems had adapted too slowly to the socio-economic changes around them and that they were held back not only by their own conservatism, but also by the inertia of societies themselves.
Formal education: the hierarchically structured, chronologically graded 'education system', running from primary school through the university and including, in addition to general academic studies, a variety of specialised programmes and institutions for full-time technical and professional training.
In this way formal education would broadly approximate to top-down curriculum formation (c); non-formal to bottom-up or negotiated curriculum formation (b); and informal education would arguably be a non-curriculum or conversational form (a).
www.infed.org /biblio/b-nonfor.htm   (2928 words)

 formal system --  Britannica Concise Encyclopedia - Your gateway to all Britannica has to offer!
Each formal system has a formal language composed of primitive symbols that figure in certain rules of formation (statements concerning the expressions allowable in the system) and a set of theorems developed by inference from a set of axioms.
A theorem within such a system is a formula capable of proof through a finite sequence of well-formed formulas, each of which either is an axiom or is validly inferred from earlier formulas.
All structural openings have evolved from this system, which is seen in pure form only in colonnades and in framed structures, because the posts of doors, windows, ceilings, and roofs normally form part of the wall.
concise.britannica.com /ebc/article?eu=390016   (861 words)

 Formal system - Encyclopedia.WorldSearch   (Site not responding. Last check: 2007-10-07)
Unlike the grammar for wffs, there is no guarantee that there will be a decision procedure for deciding whether a given wff is a theorem or not.
Formal Techniques for Networked and Distributed Systems - FORTE 2004
Formal Ontology In Information Systems: SProceedings of the Third International Conference (FOIS-2004) (Frontiers in Artificial Intelligence and Applications)
encyclopedia.worldsearch.com /formal_systems.htm   (487 words)

 101 Taxonomy - www.101science.com
Modern taxonomic classification, based on the natural concepts and system of the Swedish botanist Carolus Linnaeus, has progressed steadily since the 18th century, modified by advances in knowledge of morphology, evolution, and genetics.
Classification, in biology, identification, naming, and grouping of organisms into a formal system based on similarities such as internal and external anatomy, physiological functions, genetic makeup, or evolutionary history.
Darwin argued that classification systems should reflect the history of life—that is, species should be related based on their shared ancestry.
www.101science.com /Taxonomy.htm   (3454 words)

 Interpretations of Probability
Normally, we speak of interpreting a formal system, that is, attaching familiar meanings to the primitive terms in its axioms and theorems, usually with an eye to turning them into true statements about some subject of interest.
However, there is no single formal system that is ‘probability’, but rather a host of such systems.
We say that an interpretation of a formal system is admissible if the meanings assigned to the primitive terms in the interpretation transform the formal axioms, and consequently all the theorems, into true statements.
plato.stanford.edu /entries/probability-interpret   (15179 words)

 Foundations of Mathematics
Formal Languages and Systems - by Heinrich Herre and Peter Schroeder-Heister
Background, formal systems and semantics for intuitionistic logic, intuitionistic logic in mathematics
Constructive and predicative redevelopments of mathematics, formal systems for Bishop constructive mathematics and for predicativity
sakharov.net /foundation_rt.html   (2708 words)

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