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Topic: Formal grammars

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  Grammar - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-11-07)
A descriptive grammar is a grammar that describes the language as it is actually used by people, regardless of whether prescriptive grammars would consider a construction correct or not.
Formal grammars are codifications of usage that are developed by observation.
The formal study of grammar is an important part of education from a young age through advanced learning, though the rules taught in schools are not a "grammar" in the sense most linguists use the term, as they are often prescriptive rather than descriptive.
www.secaucus.us /project/wikipedia/index.php/Grammar   (859 words)

 Formal grammar - Wikipedia, the free encyclopedia
In computer science a formal grammar is an abstract structure that describes a formal language precisely, i.e., a set of rules that mathematically delineates a (usually infinite) set of finite-length strings over a (usually finite) alphabet.
An analytic grammar, in contrast, is a set of rules that assume an arbitrary string to be given as input, and which successively reduce or analyze that input string yielding a final boolean, "yes/no" result indicating whether or not the input string is a member of the language described by the grammar.
Generative formal grammars are identical to Lindenmayer systems (L-systems), except that L-systems are not affected by a distinction between terminals and nonterminals, L-systems have restrictions on the order in which the rules are applied, and L-systems can run forever, generating an infinite sequence of strings.
en.wikipedia.org /wiki/Formal_grammar   (1527 words)

 Chomsky hierarchy - Wikipedia, the free encyclopedia
The Chomsky hierarchy is a containment hierarchy of classes of formal grammars that generate formal languages.
A formal grammar consists of a finite set of terminal symbols (the letters of the words in the formal language), a finite set of nonterminal symbols, a finite set of production rules with a left- and a right-hand side consisting of a word of these symbols, and a start symbol.
Such a grammar restricts its rules to a single nonterminal on the left-hand side and a right-hand side consisting of a single terminal, possibly followed (or preceded, but not both in the same grammar) by a single nonterminal.
en.wikipedia.org /wiki/Chomsky_hierarchy   (707 words)

 Context-sensitive grammar - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-11-07)
This is different from a context-free grammar where the context of a nonterminal is not taken into consideration.
The concept of context-sensitive grammar was introduced by Noam Chomsky in the 1950s as a way to describe the syntax of natural language where it is indeed often the case that a word may or may not be appropriate in a certain place depending upon the context.
Such a grammar is also called a monotonic or noncontracting grammar because none of the rules decreases the size of the string that is being rewritten.
www.peekskill.us /project/wikipedia/index.php/Context-sensitive_grammar   (556 words)

 Grammar   (Site not responding. Last check: 2007-11-07)
The subfields of grammar are phonetics, phonology, morphology, syntax, and semantics.
Descriptive grammar -- the method of describing the language as it is being used, regardless whether it is considered correct or not.
A generative grammar for a particular language specifies, for each string of words, whether or not that string constitutes a grammatical sentence in that language.
www.theezine.net /g/grammar.html   (670 words)

A Language L (spoken or written) formally given, is a set S(A*) of finite length strings A* formed from some primary finite set A usually called the alphabet possessed of a syntactical (grammatical) and a semantical structure.
Operations On and Between formal languages The only fundamental characteristic of a language generated by an alphabet A is that it is a subset of A*, therefore, Let L1 and L2 be languages over a common alphabet A, then: The set theoretic union of L1 and L2 is a language.
While in formal set theory, the membership relation x is a member of X is a logical proposition with truth values in the diploid set {0, 1}, in fuzzy set theory, the truth values lie in the real interval [0, 1] which is then associated with a probability measure.
graham.main.nc.us /~bhammel/MATH/autom.html   (3721 words)

 Formal Grammars   (Site not responding. Last check: 2007-11-07)
Whatever one's stand on this issue, grammar complexity is defined by constraints on types of strings; these constraints are the rules of formal grammars.
A formal grammar is generally described as a structure containing a vocabulary and a set of rules for defining strings on the basis of the vocabulary.
Formal grammars and languages are ordered with in a subset or implication relationship along a scale of restrictiveness:
coral.lili.uni-bielefeld.de /Classes/Winter97/IntroCompPhon/compphon/node65.html   (197 words)

 CS 434 Lecture Notes -- Informal Formal Grammars   (Site not responding. Last check: 2007-11-07)
A grammar is a specification for a language that is composed of rules like the following which (informally) says that anything composed of an expression followed by an assignment operator and a variable is a valid statement.
This symbols in angle brackets denote classes of syntactic phrases.
The syntactic phrases in most interesting grammars are frequently defined recursively (either directly or indirectly).
www.cs.williams.edu /~tom/courses/434/outlines/lect6_3.html   (137 words)

 Formal methods in interface specification
Grammars are primarily rules (e.g., for sequences of actions) which combine with syntax, vocabulary, and semantics to comprise languages.
Grammars for textual interfaces (e.g., command line interfaces) are fairly common, formalized grammars (e.g., a set of linguistic rules for the formulation of command syntax) for textual interfaces are somewhat less common; formalized grammars for GUIs are fairly rare...as are formal languages for user interface specification.
It is a partially annotated bibliographic listing of publications, some of which are quite germane to the topic of grammars and formal languages applicable to user interface specification and some of which are only tangentially related to that topic.
www.otal.umd.edu /guse/formal.html   (2301 words)

 CMSC 451 Lecture 13, Formal Grammars, CFG   (Site not responding. Last check: 2007-11-07)
Grammars that have the same languages as DFA's A grammar is defined as G = (V, T, P, S) where V is a set of variables.
A grammar for matching parenthesis might be G = (V, T, P, S) V = { S } T = { (,) } P = S -> epsilon
"Generating" the strings in a language defined by a grammar is also called "derivation" of the strings in a language.
www.cs.umbc.edu /~squire/s01-451/cs451_l13.html   (640 words)

 The Chomsky Hierarchy of formal grammars
The languages defined by Type 1 grammars are accepted by linear bounded automata; the syntax of some natural languages (including Dutch, Swiss German and Bambara), but not all, is generally held in computational linguistics to have structures of this type.
The languages defined by Type 2 grammars are accepted by push-down automata; the syntax of natural languages is definable almost entirely in terms of context-free languages and the tree structures generated by them.
The languages defined by Type 3 grammars are accepted by finite state automata; morphological structure and perhaps all the syntax of informal spoken dialogue is describable by regular grammars.
coral.lili.uni-bielefeld.de /Classes/Winter97/IntroCompPhon/compphon/node66.html   (207 words)

 HANDBOOK OF LOGIC AND LANGUAGE, Elsevier Science, 1996, Introduction Chapter 12   (Site not responding. Last check: 2007-11-07)
Ironically, the combinatorial apparatus of Generative Grammar with its focusing on derivations of syntactic structures on the basis of grammatical rules was methodologically closer to logical deductive systems than the descriptive approach of Montague Grammar.
According to this view, formal languages of mathematical logic are the only correct representations of meaning structures, hence semantic description of natural language reduces to an interpretation of linguistic expressions within some (flexible enough) standard logical formalism, as, e.g., the theory of types.
Grammars are represented by Prolog programs, and grammatical derivations are simulated by executions of these programs, that means, logical proofs employing resolution and unification (see Pereira and Shieber, 1987; Gazdar and Mellish, 1989).
www.elsevier.com /homepage/sac/hll/prefch12.htm   (1501 words)

 CS 434 Lecture Notes -- Formal Grammars   (Site not responding. Last check: 2007-11-07)
Context free grammars are a notation for describing sets of strings (each phrase type is really just the name of a set of strings).
The association between a context free grammar and the language it describes is formalized through the notion of a derivation:
The language defined by a grammar G is the set of all sentences.
www.cs.williams.edu /~tom/courses/434/outlines/lect6_4.html   (591 words)

 Chomsky hierarchy   (Site not responding. Last check: 2007-11-07)
A formal grammar consists of a finite set of terminal symbols (the letters of the words in the formal language), a finite set of nonterminal symbols, a set of production rules with a left- and a right-hand side consisting of a word of these symbols, and a start symbol.
These grammars have rules of the form αAβ -> αγβ with A a nonterminal and α, β and γ strings of terminals and nonterminals.
Such a grammar restricts its rules to a single nonterminal on the left-hand side and a right-hand side consisting of a single terminal, possibly followed by a single nonterminal.
www.enlightenweb.net /c/ch/chomsky_hierarchy.html   (641 words)

 No Title
We may be able to describe music with grammars but that is not the same as saying that music is syntactically constructed.
Formally, a grammar is a Quadruple/Quartet of elements
A grammar is a way of describing the structure of a sequence of things.
www.csis.ul.ie /ccmcm/cs5632/cs5632_lect02_grammar1.htm   (1169 words)

 CMSC 451 Lecture 13, Formal Grammars, CFG   (Site not responding. Last check: 2007-11-07)
Grammars can be more powerful (read accept a larger class of languages) than finite state machines (DFA's NFA's NFA-epsilon regular expressions).
0S1 Note that this grammar violates the restriction needed to make the grammars language a regular language, i.e.
More examples of constructing grammars from language descriptions: Construct a CFG for non empty Palindromes over T = { 0, 1 } The strings in this language read the same forward and backward.
www.cs.umbc.edu /~squire/s04-451/cs451_l13.html   (640 words)

 Formal Language Grammars - Section 2
Here, for instance, is the grammar from the first section represented as a sequence of syntax diagrams.
Start from the word on the left that you are trying to define, work along in the direction of the arrows and don't stop until you reach the end of the line on the right.
This grammar rule could generate the strings X, Y, XY or an empty string (where both X and Y had been skipped).
richardbowles.tripod.com /durham/grammars/gram2.htm   (479 words)

 Using XML as an Intermediate Form for Compiler Development
A grammar is a notation for describing the syntax of a language.
The grammar given earlier for infix multiplication and division is a typical LR grammar.
The direct translation of a grammar to an implementation is a tremendous advantage of LL grammar parsing via recursive descent.
www.idealliance.org /papers/xml2001/papers/html/03-05-04.html   (2436 words)

 Lambek calculus papers in Russian by Mati Pentus
We prove that the class of languages recognized by Lambek categorial grammars coincides with the class of all context-free languages.
It is proved that the class of languages recognized by categorial grammars based on the Lambek calculus coincides with the class of all context-free languages.
Similar results are obtained also for the Lambek calculus allowing empty premises, the Lambek calculus with the unit, the multiplicative fragment of the cyclic linear logic.
lpcs.math.msu.su /~pentus/abrus.htm   (234 words)

 Conference on Automated Learning and Discovery
The simplest grammars are regular grammars, which become Markov chains when fitted with a probability distribution.
More general and more powerful are the context-free grammars, the probabilistic versions of which are equivalent to branching processes.
There is no general theory for how to put probability distributions on context-sensitive grammars, yet it is increasingly apparent that successful applications require a probabilistic framework, with its associated statistical theory and theory of inference.
www.cs.cmu.edu /People/caldcon/plenary_2.shtml   (257 words)

 CS 451
The relationship between grammars and machines with emphasis on regular expressions and context-free languages.
To study the fundamental concepts of the theory of computation including finite state machines, formal grammars and languages, Turing machines and recursive functions.
To become familiar with the relationships between grammars and machines, and the general properties of formal languages with emphasis on regular expressions and context free languages.
www.cs.siu.edu /courses/cs451.html   (118 words)

 Titivillus: Projects
Artificial Languages: A Study of Formal Grammars, November 17th, 2003.
An Introduction to the theory of Formal Languages and Parsing, October 9th, 2003.
Abstract The notion of Formal Languages and their grammars will be introduced and defined and their relevance Mathematics and other fields explained.
tos.maintree.com /titivillus/thesis/index.asp   (716 words)

 TMs can be made into "language recognition machines":
It was proved in the 1970 time frame that the Chomskean transformational grammars of the time could generate any RE set of strings, and therefore were equivalent to TMs.
To Type 3 grammars, there corresponds the notion of "a finite state automata"…sometimes called Markov machines (which is a particular way of conceptualizing them).
Therefore there is a sense in which the Type 0 grammars are "stronger" than the Type 1 grammars, which are "stronger" than the Type 2 grammars, which in turn are "stronger" than the Type 3 grammars.
www.cs.ualberta.ca /~jeffp/phil417/FormalSystems3.html   (1882 words)

 LREC 2000 - Papers   (Site not responding. Last check: 2007-11-07)
In this paper, we present a methodological formal approach to evaluate grammars based on a unified representation.
The first one considers a grammar as a resource enabling the representation of particular aspects of a given language.
The second is interested in using grammars in the development of lingware.
www.lrec-conf.org /lrec2000/www.xanthi.ilsp.gr/lrec/conference/papers-239.htm   (153 words)

 Information and Computation Bibliography   (Site not responding. Last check: 2007-11-07)
The clearness and uniformity of the derivation process for SR grammars allow the extension of well-established techniques for syntactic and semantic analysis to the case of SR grammars.
The most meaningful features of SR grammars as well as their generative power are compared with those of well-known graph grammar families.
In spite of their structural simplicity, variations of SR grammars have a generative power comparable with that of expressive classes of graph grammars, such as the edNCE and the N-edNCE classes.
theory.lcs.mit.edu /~iandc/References/ferruccipssttv1996:1.html   (287 words)

Relevant classes of grammars for natural language syntax, the so-called mildly context sensitive languages, are just a bit beyond context-free languages, and they hare parsable in polynomial time as well.
Edward Stabler introduced Minimalist Grammars (MGs) as a formalization of the most recent model of the Chomskian or generative tradition and they are quite appealing to us.
Indeed, a strong reason for using categorial grammars, [63] despite their poor computational properties, and poor linguistic coverage, is that they provide a correspondence bewteeen syntactic analyses and semantic representations.
www.inria.fr /rapportsactivite/RA2004/signes/uid23.html   (459 words)

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