Editing Formal system (section)

=== Formal language ===
{{Formal languages}}
{{Main|Formal language|Formal grammar|Syntax (logic)|Logical form}}

A [[formal language]] is a language that is defined by a formal system. Like languages in [[linguistics]], formal languages generally have two aspects:
* the [[Syntax (logic)|syntax]] is what the language looks like (more formally: the set of possible expressions that are valid utterances in the language)
* the [[Semantics of logic|semantics]] are what the utterances of the language mean (which is formalized in various ways, depending on the type of language in question)

Usually only the [[Syntax (logic)|syntax]] of a formal language is considered via the notion of a [[formal grammar]]. The two main categories of formal grammar are that of [[generative grammar]]s, which are sets of rules for how strings in a language can be written, and that of [[analytic grammar]]s (or reductive grammar<ref>{{cite dictionary |dictionary=Dictionary of Scientific and Technical Terms |url=http://encyclopedia2.thefreedictionary.com/reductive+grammar |title=Reductive grammar |publisher=McGraw-Hill |edition=6th |quote=Reductive grammar:  (''computer science'') A set of syntactic rules for the analysis of strings to determine whether the strings exist in a language.}}</ref>{{unreliable source?|date=February 2015}}<ref>{{cite web|url=http://bitsavers.informatik.uni-stuttgart.de/pdf/sri/arc/rulifson/A_Tree_Meta_For_The_XDS_940_Appendix_D_Apr68.pdf|title=A Tree Meta for the XDS 940 | publisher=[[Augmentation Research Center]] |date=April 1968 |last=Rulifson |first=Johns F. |author-link=Jeff Rulifson |access-date=30 November 2024 |quote="There are two classes of formal-language definition compiler-writing schemes. The productive [[formal grammar|grammar]] approach is the most common. A productive grammar consists primarrly of a set of rules that describe a method of generating all possible strings of the language. The reductive or [[formal grammar#Analytic grammars|analytical grammar]] technique states a set of rules that describe a method of analyzing any string of characters and deciding whether that string is in the language."}}</ref>), which are sets of rules for how a string can be analyzed to determine whether it is a member of the language.