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Categorial Grammar
Categorial grammar is a family of formalisms in natural language syntax that share the central assumption that syntactic constituents combine as functions and arguments. Categorial grammar posits a close relationship between the syntax and semantic composition, since it typically treats syntactic categories as corresponding to semantic types. Categorial grammars were developed in the 1930s by Kazimierz Ajdukiewicz and in the 1950s by Yehoshua Bar-Hillel and Joachim Lambek. It saw a surge of interest in the 1970s following the work of Richard Montague, whose Montague grammar assumed a similar view of syntax. It continues to be a major paradigm, particularly within formal semantics. Basics A categorial grammar consists of two parts: a lexicon, which assigns a set of types (also called categories) to each basic symbol, and some type inference rules, which determine how the type of a string of symbols follows from the types of the constituent symbols. It has the advantage that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Language
In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages can take different forms, such as speech or signing. They are distinguished from constructed and formal languages such as those used to program computers or to study logic. Defining natural language Natural language can be broadly defined as different from * artificial and constructed languages, e.g. computer programming languages * constructed international auxiliary languages * non-human communication systems in nature such as whale and other marine mammal vocalizations or honey bees' waggle dance. All varieties of world languages are natural languages, including those that are associated with linguistic prescriptivism or language regulation. ( Nonstandard dialects can be viewed as a wild type in comparison with stan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ajdukiewicz
Kazimierz Ajdukiewicz (12 December 1890 – 12 April 1963) was a Polish philosopher and logician, a prominent figure in the Lwów–Warsaw school of logic. He originated many novel ideas in semantics. Among these was categorial grammar, a highly flexible framework for the analysis of natural language syntax and (indirectly) semantics that remains a major influence on work in formal linguistics. Ajdukiewicz's fields of research were model theory and the philosophy of science. Biography Ajdukiewicz was born in 1890 in Tarnopol in Galicia, which at that time, due to Partitions of Poland, was annexed by Austria-Hungary ( The Austrian Partition). His father was a senior civil servant. Ajdukiewicz studied at the University of Lwów, and lectured there, as well as in Warsaw and in Poznań. He received his PhD degree with the thesis on Kant's philosophy of space. He was Rector of the University of Poznań from 1948 to 1952. He was one of the founders of the journal '' Studia Logica'' i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greibach Normal Form
In formal language theory, a context-free grammar is in Greibach normal form (GNF) if the right-hand sides of all production rules start with a terminal symbol, optionally followed by some variables. A non-strict form allows one exception to this format restriction for allowing the empty word (epsilon, ε) to be a member of the described language. The normal form was established by Sheila Greibach and it bears her name. More precisely, a context-free grammar is in Greibach normal form, if all production rules are of the form: :A \to a A_1 A_2 \cdots A_n where A is a nonterminal symbol, a is a terminal symbol, A_1 A_2 \ldots A_n is a (possibly empty) sequence of nonterminal symbols not including the start symbol and S is the start symbol. Observe that the grammar does not have left recursions. Every context-free grammar can be transformed into an equivalent grammar in Greibach normal form. Various constructions exist. Some do not permit the second form of rule and cannot transfo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Production Rule (formal Languages)
A production or production rule in computer science is a ''rewrite rule'' specifying a symbol substitution that can be recursively performed to generate new symbol sequences. A finite set of productions P is the main component in the specification of a formal grammar (specifically a generative grammar). The other components are a finite set N of nonterminal symbols, a finite set (known as an alphabet) \Sigma of terminal symbols that is disjoint from N and a distinguished symbol S \in N that is the ''start symbol''. In an unrestricted grammar, a production is of the form u \to v, where u and v are arbitrary strings of terminals and nonterminals, and u may not be the empty string. If v is the empty string, this is denoted by the symbol \epsilon, or \lambda (rather than leave the right-hand side blank). So productions are members of the cartesian product :V^*NV^* \times V^* = (V^*\setminus\Sigma^*) \times V^*, where V := N \cup \Sigma is the ''vocabulary'', ^ is the Kleene star ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantification (linguistics)
In formal semantics, a generalized quantifier (GQ) is an expression that denotes a set of sets. This is the standard semantics assigned to quantified noun phrases. For example, the generalized quantifier ''every boy'' denotes the set of sets of which every boy is a member: \ This treatment of quantifiers has been essential in achieving a compositional semantics for sentences containing quantifiers. Type theory A version of type theory is often used to make the semantics of different kinds of expressions explicit. The standard construction defines the set of types recursively as follows: #''e'' and ''t'' are types. #If ''a'' and ''b'' are both types, then so is \langle a,b\rangle #Nothing is a type, except what can be constructed on the basis of lines 1 and 2 above. Given this definition, we have the simple types ''e'' and ''t'', but also a countable infinity of complex types, some of which include: \langle e,t\rangle;\qquad \langle t,t\rangle;\qquad \langle\langle e,t\rangle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intensionality
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — an intension is any Property (philosophy), property or Quality (philosophy), quality Connotation#Logic, connoted by a word, phrase, or another symbol. In the case of a word, the word's definition often implies an intension. For instance, the intensions of the word ''plant'' include properties such as "being composed of cellulose", "alive", and "organism", among others. A ''comprehension (logic), comprehension'' is the collection of all such intensions. Overview The meaning of a word can be thought of as the bond between the ''idea the word means'' and the ''physical form of the word''. Swiss linguist Ferdinand de Saussure (1857–1913) contrasts three concepts: # the ''signifier'' – the "sound image" or the string of Letter (alphabet), letters on a page that one recognizes as the form of a Sign (linguistics), si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derived Category
In mathematics, the derived category ''D''(''A'') of an abelian category ''A'' is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on ''A''. The construction proceeds on the basis that the objects of ''D''(''A'') should be chain complexes in ''A'', with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism on the level of homology of the chain complexes. Derived functors can then be defined for chain complexes, refining the concept of hypercohomology. The definitions lead to a significant simplification of formulas otherwise described (not completely faithfully) by complicated spectral sequences. The development of the derived category, by Alexander Grothendieck and his student Jean-Louis Verdier shortly after 1960, now appears as one terminal point in the explosive development of homological algebra in the 1950s, a decade in which it had made r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpretation Type
Interpretation may refer to: Culture * Aesthetic interpretation, an explanation of the meaning of a work of art * Allegorical interpretation, an approach that assumes a text should not be interpreted literally * Dramatic Interpretation, an event in speech and forensics competitions in which participants perform excerpts from plays * Heritage interpretation, communication about the nature and purpose of historical, natural, or cultural phenomena * Interpretation (music), the process of a performer deciding how to perform music that has been previously composed * Language interpretation, the facilitation of dialogue between parties using different languages * Literary theory, methods for interpreting literature, including historicism, feminism, structuralism, deconstruction * Oral interpretation, a dramatic art Law * Authentic interpretation, the official interpretation of a statute issued by the statute's legislator * Financial Accounting Standards Board Interpretations, part ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lexicalized
In linguistics, lexicalization is the process of adding words, set phrases, or word patterns to a language's lexicon. Whether '' word formation'' and ''lexicalization'' refer to the same process is controversial within the field of linguistics. Most linguists agree that there is a distinction, but there are many ideas of what the distinction is. Lexicalization may be simple, for example borrowing a word from another language, or more involved, as in calque or loan translation, wherein a foreign phrase is translated literally, as in ''marché aux puces'', or in English, flea market. Other mechanisms include compounding, abbreviation, and blending. Particularly interesting from the perspective of historical linguistics is the process by which ''ad hoc'' phrases become set in the language, and eventually become new words (see lexicon). Lexicalization contrasts with grammaticalization, and the relationship between the two processes is subject to some debate. In psycholinguistics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context-free Grammar
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules are 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). A formal grammar is "context-free" if its production rules can be applied regardless of the context of a nonterminal. No matter which symbols surround it, the single nonterminal on the left hand side can always be replaced by the right hand side. This is what distinguishes it from a context-sensitive grammar. 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, :\langle\text\rangle \to \langle\text\rangle = \langle\text\rangle ; replaces \langle\text\rangle with \langle\text\rangle = \langle\text\rangle ;. There can be multiple replacement rules for a given nonterminal symbol. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inference Rule
In the philosophy of logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of inference called ''modus ponens'' takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics), in the sense that if the premises are true (under an interpretation), then so is the conclusion. Typically, a rule of inference preserves truth, a semantic property. In many-valued logic, it preserves a general designation. But a rule of inference's action is purely syntactic, and does not need to preserve any semantic property: any function from sets of formulae to formulae counts as a rule of inference. Usually only rules that are recursive are important; i.e. rule ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Verb
A verb () is a word ( part of speech) that in syntax generally conveys an action (''bring'', ''read'', ''walk'', ''run'', ''learn''), an occurrence (''happen'', ''become''), or a state of being (''be'', ''exist'', ''stand''). In the usual description of English, the basic form, with or without the particle ''to'', is the infinitive. In many languages, verbs are inflected (modified in form) to encode tense, aspect, mood, and voice. A verb may also agree with the person, gender or number of some of its arguments, such as its subject, or object. Verbs have tenses: present, to indicate that an action is being carried out; past, to indicate that an action has been done; future, to indicate that an action will be done. For some examples: * I ''washed'' the car yesterday. * The dog ''ate'' my homework. * John ''studies'' English and French. * Lucy ''enjoys'' listening to music. *Barack Obama ''became'' the President of the United States in 2009. ''(occurrence)'' * Mike T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
