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- Formal_system abstract "A formal system is broadly defined as any well-defined system of abstract thought based on the model of mathematics. Euclid's Elements is often held to be the first formal system and displays the characteristic of a formal system. The entailment of the system by its logical foundation is what distinguishes a formal system from others which may have some basis in an abstract model. Often the formal system will be the basis for or even identified with a larger theory or field (e.g. Euclidean geometry) consistent with the usage in modern mathematics such as model theory. A formal system need not be mathematical as such, Spinoza's Ethics for example imitates the form of Euclid's Elements.Each formal system has a formal language, which is composed by primitive symbols. These symbols act on certain rules of formation and are developed by inference from a set of axioms. The system thus consists of any number of formulas built up through finite combinations of the primitive symbols—combinations that are formed from the axioms in accordance with the stated rules.Formal systems in mathematics consist of the following elements: A finite set of symbols (i.e. the alphabet), that can be used for constructing formulas (i.e. finite strings of symbols). A grammar, which tells how well-formed formulas (abbreviated wff) are constructed out of the symbols in the alphabet. It is usually required that there be a decision procedure for deciding whether a formula is well formed or not. A set of axioms or axiom schemata: each axiom must be a wff. A set of inference rules.A formal system is said to be recursive (i.e. effective) if the set of axioms and the set of inference rules are decidable sets or semidecidable sets, according to context.Some theorists use the term formalism as a rough synonym for formal system, but the term is also used to refer to a particular style of notation, for example, Paul Dirac's bra–ket notation.".
- Formal_system wikiPageExternalLink inform.htm.
- Formal_system wikiPageExternalLink RoutledgeFLS1995.pdf.
- Formal_system wikiPageExternalLink formal-system.
- Formal_system wikiPageExternalLink formal.sys.haug.html.
- Formal_system wikiPageExternalLink machines.htm.
- Formal_system wikiPageID "396102".
- Formal_system wikiPageRevisionID "599761042".
- Formal_system hasPhotoCollection Formal_system.
- Formal_system subject Category:Formal_languages.
- Formal_system subject Category:Formal_systems.
- Formal_system subject Category:Metalogic.
- Formal_system subject Category:Syntax_(logic).
- Formal_system type Ability105616246.
- Formal_system type Abstraction100002137.
- Formal_system type Cognition100023271.
- Formal_system type Communication100033020.
- Formal_system type FormalLanguages.
- Formal_system type FormalMethods.
- Formal_system type Know-how105616786.
- Formal_system type Language106282651.
- Formal_system type Method105660268.
- Formal_system type PsychologicalFeature100023100.
- Formal_system comment "A formal system is broadly defined as any well-defined system of abstract thought based on the model of mathematics. Euclid's Elements is often held to be the first formal system and displays the characteristic of a formal system. The entailment of the system by its logical foundation is what distinguishes a formal system from others which may have some basis in an abstract model. Often the formal system will be the basis for or even identified with a larger theory or field (e.g.".
- Formal_system label "Formal system".
- Formal_system label "Formales System".
- Formal_system label "Formeel systeem".
- Formal_system label "Sistema formal".
- Formal_system label "Sistema formal".
- Formal_system label "Sistema formale".
- Formal_system label "System formalny".
- Formal_system label "Système formel".
- Formal_system label "Формальная система".
- Formal_system label "نظام شكلي".
- Formal_system label "形式体系".
- Formal_system label "形式系統".
- Formal_system sameAs Formales_System.
- Formal_system sameAs Τυπικό_σύστημα.
- Formal_system sameAs Sistema_formal.
- Formal_system sameAs Système_formel.
- Formal_system sameAs Sistema_formale.
- Formal_system sameAs 形式体系.
- Formal_system sameAs Formeel_systeem.
- Formal_system sameAs System_formalny.
- Formal_system sameAs Sistema_formal.
- Formal_system sameAs m.0239v0.
- Formal_system sameAs Q649732.
- Formal_system sameAs Q649732.
- Formal_system sameAs Formal_system.
- Formal_system wasDerivedFrom Formal_system?oldid=599761042.
- Formal_system isPrimaryTopicOf Formal_system.