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Linear Context-free Rewriting Language
Generalized context-free grammar (GCFG) is a grammar formalism that expands on Context-free grammar, context-free grammars by adding potentially non-context-free composition functions to rewrite rules. Head grammar (and its weak equivalents) is an instance of such a GCFG which is known to be especially adept at handling a wide variety of non-CF properties of natural language. Description A GCFG consists of two components: a set of composition functions that combine string tuples, and a set of rewrite rules. The composition functions all have the form f(\langle x_1, ..., x_m \rangle, \langle y_1, ..., y_n \rangle, ...) = \gamma, where \gamma is either a single string tuple, or some use of a (potentially different) composition function which reduces to a string tuple. Rewrite rules look like X \to f(Y, Z, ...), where Y, Z, ... are string tuples or non-terminal symbols. The rewrite semantics of GCFGs is fairly straightforward. An occurrence of a non-terminal symbol is rewritten usin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Context-free Grammar
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form : A\ \to\ \alpha with A a ''single'' nonterminal symbol, and \alpha a string of terminals and/or nonterminals (\alpha can be empty). Regardless of which symbols surround it, the single nonterminal A on the left hand side can always be replaced by \alpha on the right hand side. This distinguishes it from a context-sensitive grammar, which can have production rules in the form \alpha A \beta \rightarrow \alpha \gamma \beta with A a nonterminal symbol and \alpha, \beta, and \gamma strings of terminal and/or nonterminal symbols. A formal grammar is essentially a set of production rules that describe all possible strings in a given formal language. Production rules are simple replacements. For example, the first rule in the picture, : \lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Head Grammar
Head grammar (HG) is a grammar formalism introduced in Carl Pollard (1984) Pollard, C. 1984. ''Generalized Phrase Structure Grammars, Head Grammars, and Natural Language''. Ph.D. thesis, Stanford University, CA. as an extension of the context-free grammar class of grammars. Head grammar is therefore a type of phrase structure grammar, as opposed to a dependency grammar. The class of head grammars is a subset of the linear context-free rewriting systems. One typical way of defining head grammars is to replace the terminal strings of CFGs with indexed terminal strings, where the index denotes the "head" word of the string. Thus, for example, a CF rule such as A \to abc might instead be A \to (abc, 0), where the 0th terminal, the ''a'', is the head of the resulting terminal string. For convenience of notation, such a rule could be written as just the terminal string, with the head terminal denoted by some sort of mark, as in A \to \widehatbc. Two fundamental operations are then a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Proper Subclass
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. Classes act as a way to have set-like collections while differing from sets so as to avoid paradoxes, especially Russell's paradox (see '). The precise definition of "class" depends on foundational context. In work on Zermelo–Fraenkel set theory, the notion of class is informal, whereas other set theories, such as von Neumann–Bernays–Gödel set theory, axiomatize the notion of "proper class", e.g., as entities that are not members of another entity. A class that is not a set (informally in Zermelo–Fraenkel) is called a proper class, and a class that is a set is sometimes called a small class. For instance, the class of all ordinal numbers, and the class of all sets, are proper classes in many formal systems. In Quine's set-theoretical writing, the phrase "ultimate cla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Linear-indexed Grammar
Indexed grammars are a generalization of context-free grammars in that nonterminals are equipped with lists of ''flags'', or ''index symbols''. The language produced by an indexed grammar is called an indexed language. Definition Modern definition by Hopcroft and Ullman In contemporary publications following Hopcroft and Ullman (1979), an indexed grammar is formally defined a 5-tuple ''G'' = ⟨''N'',''T'',''F'',''P'',''S''⟩ where * ''N'' is a set of variables or nonterminal symbols, * ''T'' is a set ("alphabet") of terminal symbols, * ''F'' is a set of so-called ''index symbols'', or ''indices'', * ''S'' ∈ ''N'' is the '' start symbol'', and * ''P'' is a finite set of '' productions''. In productions as well as in derivations of indexed grammars, a string ("stack") ''σ'' ∈ ''F'' * of index symbols is attached to every nonterminal symbol ''A'' ∈ ''N'', denoted by ''A'' 'σ''" and " are meta symbols to indicate the stack. Terminal symbols may not be followed by index ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
