|
Type Shifter
In formal semantics, a type shifter is an interpretation rule that changes an expression's semantic type. For instance, the English expression "John" might ordinarily denote John himself, but a type shifting rule called can raise its denotation to a function which takes a property and returns "true" if John himself has that property. Lift can be seen as mapping an individual onto the principal ultrafilter that it generates. # Without type shifting: \, \, ohn.html" ;"title="![John">![John!= j # Type shifting with : ohn.html" ;"title="![John">![John!= \lambda P_ . P(j) Type shifters were proposed by Barbara Partee and Mats Rooth in 1983 to allow for systematic type ambiguity. Work of the period assumed that syntactic category, syntactic categories corresponded directly with semantic types, and researchers thus had to "generalize to the worst case" when particular uses of particular expressions from a given category required an especially high type. Moreover, Partee argued ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
 |
Formal Semantics (natural Language)
Formal semantics is the scientific study of linguistic meaning through formal tools from logic and mathematics. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy of language. Formal semanticists rely on diverse methods to analyze natural language. Many examine the meaning of a sentence by studying the circumstances in which it would be true. They describe these circumstances using abstract mathematical models to represent entities and their features. The principle of compositionality helps them link the meaning of expressions to abstract objects in these models. This principle asserts that the meaning of a compound expression is determined by the meanings of its parts. Propositional and predicate logic are formal systems used to analyze the semantic structure of sentences. They introduce concepts like singular terms, predicates, quantifiers, and logical connectives to represent the logical form of natural language expres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
 |
Scope (formal Semantics)
In formal semantics (linguistics), formal semantics, the scope of a semantic operator is the semantic object to which it applies. For instance, in the sentence "''Paulina doesn't drink beer but she does drink wine''," the proposition that Paulina drinks beer occurs within the scope of negation, but the proposition that Paulina drinks wine does not. Scope can be thought of as the semantic order of operations. One of the major concerns of research in formal semantics is the relationship between operators' syntax, syntactic positions and their semantic scope. This relationship is not transparent, since the scope of an operator need not directly correspond to its Deep structure and surface structure, surface position and a single surface form can be semantic ambiguity, semantically ambiguous between different scope construals. Some theories of scope posit a level of syntactic structure called Logical form (linguistics), logical form, in which an item's syntactic position corresponds t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
Type Theory
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system. Type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that have been proposed as foundations are: * Typed λ-calculus of Alonzo Church * Intuitionistic type theory of Per Martin-Löf Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid paradoxes in naive set theory and formal logic, such as Russell's paradox which demonstrates that, without proper axioms, it is possible to define the set of all sets that are not members of themselves; this set both contains itself and does not contain itself. Between 1902 and 1908, Bertrand Russell proposed various solutions to this problem. By 1908, Russell arrive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
Type Conversion
In computer science, type conversion, type casting, type coercion, and type juggling are different ways of changing an expression from one data type to another. An example would be the conversion of an integer value into a floating point value or its textual representation as a string, and vice versa. Type conversions can take advantage of certain features of type hierarchies or data representations. Two important aspects of a type conversion are whether it happens ''implicitly'' (automatically) or ''explicitly'', and whether the underlying data representation is converted from one representation into another, or a given representation is merely ''reinterpreted'' as the representation of another data type. In general, both primitive and compound data types can be converted. Each programming language has its own rules on how types can be converted. Languages with strong typing typically do little implicit conversion and discourage the reinterpretation of representations, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
Alternative Semantics
Alternative semantics (or Hamblin semantics) is a framework in formal semantics and logic. In alternative semantics, expressions denote ''alternative sets'', understood as sets of objects of the same semantic type. For instance, while the word "Lena" might denote Lena herself in a classical semantics, it would denote the singleton set containing Lena in alternative semantics. The framework was introduced by Charles Leonard Hamblin in 1973 as a way of extending Montague grammar to provide an analysis for questions. In this framework, a question denotes the set of its possible answers. Thus, if P and Q are propositions, then \ is the denotation of the question whether P or Q is true. Since the 1970s, it has been extended and adapted to analyze phenomena including focus, scope, disjunction In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as \lor and read aloud as "o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
 |
Generative Grammar
Generative grammar is a research tradition in linguistics that aims to explain the cognitive basis of language by formulating and testing explicit models of humans' subconscious grammatical knowledge. Generative linguists, or generativists (), tend to share certain working assumptions such as the competence–performance distinction and the notion that some domain-specific aspects of grammar are partly innate in humans. These assumptions are rejected in non-generative approaches such as usage-based models of language. Generative linguistics includes work in core areas such as syntax, semantics, phonology, psycholinguistics, and language acquisition, with additional extensions to topics including biolinguistics and music cognition. Generative grammar began in the late 1950s with the work of Noam Chomsky, having roots in earlier approaches such as structural linguistics. The earliest version of Chomsky's model was called Transformational grammar, with subsequent itera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
Quantifier Raising
In generative grammar, the technical term operator denotes a type of expression that enters into an a-bar movement dependency.Chomsky, Noam. (1981) Lectures on Government and Binding, Foris, Dordrecht.Haegeman, Liliane (1994) Introduction to Government and Binding Theory. Blackwell.Koopman, H., & Sportiche, D. (1982). Variables and the Bijection Principle. ''The Linguistic Review, 2'', 139-60. One often says that the operator "binds a variable". Cinque, Guglielmo (1991) Types of A-Bar Dependencies. MIT Press. Operators are often determiners, such as interrogatives ('which', 'who', 'when', etc.), or quantifiers ('every', 'some', 'most', 'no'), but adverbs such as sentential negation ('not') have also been treated as operators.Zanuttini, R. (1997) Negation and Clausal Structure: A Comparative Study of Romance Languages, Oxford University Press. It is also common within generative grammar to hypothesise phonetically empty operators whenever a clause type or construction exhibits s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
|
|
Compositionality
In semantics, mathematical logic and related disciplines, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. The principle is also called Frege's principle, because Gottlob Frege is widely credited for the first modern formulation of it. However, the principle has never been explicitly stated by Frege, and arguably it was already assumed by George Boole decades before Frege's work. The principle of compositionality (also known as semantic compositionalism) is highly debated in linguistics. Among its most challenging problems there are the issues of contextuality, the non-compositionality of idiomatic expressions, and the non-compositionality of quotations. History Discussion of compositionality started to appear at the beginning of the 19th century, during which it was debated whether what was most fundamental in language was compositionalit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |