§-Calculus
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§-Calculus
An adaptive grammar is a formal grammar that explicitly provides mechanisms within the formalism to allow its own production rules to be manipulated. Overview John N. Shutt defines adaptive grammar as a grammatical formalism that allows rule sets (aka sets of production rules) to be explicitly manipulated within a grammar. Types of manipulation include rule addition, deletion, and modification. Early history The first description of grammar adaptivity (though not under that name) in the literature is generallyChristiansen, Henning, "Survey of Adaptable Grammars" ''ACM SIGPLAN Notices'', Vol. 25 No. 11, pp. 35-44, Nov. 1990.Shutt, John N., Recursive Adaptable Grammars', Master’s Thesis, Worcester Polytechnic Institute, 1993. (16 December 2003 emended revision.)Jackson, Quinn Tyler, Adapting to Babel: Adaptivity and Context-Sensitivity in Parsing', Ibis Publications, Plymouth, Massachusetts, March 2006. taken to be in a paper by Alfonso Caracciolo di Forino published in 1963.Car ...
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Syntactic Predicate
A syntactic predicate specifies the syntactic validity of applying a production in a formal grammar and is analogous to a semantic predicate that specifies the semantic validity of applying a production. It is a simple and effective means of dramatically improving the recognition strength of an LL parser by providing arbitrary lookahead. In their original implementation, syntactic predicates had the form “( α )?” and could only appear on the left edge of a production. The required syntactic condition α could be any valid context-free grammar fragment. More formally, a syntactic predicate is a form of production intersection, used in parser specifications or in formal grammars. In this sense, the term ''predicate'' has the meaning of a mathematical indicator function. If ''p1'' and ''p2,'' are production rules, the language generated by ''both'' ''p1'' ''and'' ''p2'' is their set intersection. As typically defined or implemented, syntactic predicates implicitly order the p ...
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Formal Grammar
A formal grammar is a set of Terminal and nonterminal symbols, symbols and the Production (computer science), production rules for rewriting some of them into every possible string of a formal language over an Alphabet (formal languages), alphabet. A grammar does not describe the semantics, meaning of the strings — only their form. In applied mathematics, formal language theory is the discipline that studies formal grammars and languages. Its applications are found in theoretical computer science, theoretical linguistics, Formal semantics (logic), formal semantics, mathematical logic, and other areas. A formal grammar is a Set_(mathematics), set of rules for rewriting strings, along with a "start symbol" from which rewriting starts. Therefore, a grammar is usually thought of as a language generator. However, it can also sometimes be used as the basis for a "recognizer"—a function in computing that determines whether a given string belongs to the language or is grammatical ...
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Turing Completeness
In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine (devised by English mathematician and computer scientist Alan Turing). This means that this system is able to recognize or decode other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete. A related concept is that of Turing equivalence two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can simulate a Turing machine, it is Turing equivalent to a Turing m ...
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Grammar Induction
Grammar induction (or grammatical inference) is the process in machine learning of learning a formal grammar (usually as a collection of ''re-write rules'' or '' productions'' or alternatively as a finite-state machine or automaton of some kind) from a set of observations, thus constructing a model which accounts for the characteristics of the observed objects. More generally, grammatical inference is that branch of machine learning where the instance space consists of discrete combinatorial objects such as strings, trees and graphs. Grammar classes Grammatical inference has often been very focused on the problem of learning finite-state machines of various types (see the article Induction of regular languages for details on these approaches), since there have been efficient algorithms for this problem since the 1980s. Since the beginning of the century, these approaches have been extended to the problem of inference of context-free grammars and richer formalisms, such as mult ...
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Artificial Grammar Learning
Artificial grammar learning (AGL) is a paradigm of study within cognitive psychology and linguistics. Its goal is to investigate the processes that underlie human language learning Language acquisition is the process by which humans acquire the capacity to perceive and comprehend language. In other words, it is how human beings gain the ability to be aware of language, to understand it, and to produce and use words and ... by testing subjects' ability to learn a made-up grammar in a laboratory setting. It was developed to evaluate the processes of human language learning but has also been utilized to study implicit learning in a more general sense. The area of interest is typically the subjects' ability to detect patterns and statistical regularities during a training phase and then use their new knowledge of those patterns in a testing phase. The testing phase can either use the symbols or sounds used in the training phase or transfer the patterns to another set of symbols o ...
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