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Reification (linguistics)
Reification in natural language processing refers to where a natural language statement is transformed so actions and events in it become quantifiable variables. For example "John chased the duck furiously" can be transformed into something like :(Exists e)(chasing(e) & past_tense(e) & actor(e,John) & furiously(e) & patient(e,duck)). Another example would be "Sally said John is mean", which could be expressed as something like :(Exists u,v)(saying(u) & past_tense(u) & actor(u,Sally) & that(u,v) & is(v) & actor(v,John) & mean(v)). Such representations allow one to use the tools of classical first-order predicate calculus even for statements which, due to their use of tense, modality, adverbial constructions, propositional arguments (''e.g.'' "Sally said that X"), etc., would have seemed intractable. This is an advantage because predicate calculus is better understood and simpler than the more complex alternatives (higher-order logics, modal logics, temporal logics, etc.), and ther ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Language Processing
Natural language processing (NLP) is an interdisciplinary subfield of linguistics, computer science, and artificial intelligence concerned with the interactions between computers and human language, in particular how to program computers to process and analyze large amounts of natural language data. The goal is a computer capable of "understanding" the contents of documents, including the contextual nuances of the language within them. The technology can then accurately extract information and insights contained in the documents as well as categorize and organize the documents themselves. Challenges in natural language processing frequently involve speech recognition, natural-language understanding, and natural-language generation. History Natural language processing has its roots in the 1950s. Already in 1950, Alan Turing published an article titled "Computing Machinery and Intelligence" which proposed what is now called the Turing test as a criterion of intelligence, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantification (logic)
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier \forall in the first order logic, first order formula \forall x P(x) expresses that everything in the domain satisfies the property denoted by P. On the other hand, the existential quantifier \exists in the formula \exists x P(x) expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope (logic), scope is called a quantified formula. A quantified formula must contain a Free variables and bound variables, bound variable and a subformula specifying a property of the referent of that variable. The mostly commonly used quantifiers are \forall and \exists. These quantifiers are standardly defined as Dual (mathematics), duals; in classical logic, they are interdefinable using negation. They can also be used to define more complex quantifiers, as i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists''"'' is a quantifier, while ''x'' is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic. A theory about a topic is usually a first-order logic together with a specified domain of discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of ax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automated Theorem Prover
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science. Logical foundations While the roots of formalised logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalised mathematics. Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional calculus and what is essentially modern predicate logic. His ''Foundations of Arithmetic'', published 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Russell and Whitehead in their influential ''Principia Mathematica'', first published 1910–1913, and with a revised second edition in 1927. Russell and Whitehead thought they could derive all mathematical truth using axioms and inference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Checker
In computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness). This is typically associated with hardware or software systems, where the specification contains liveness requirements (such as avoidance of livelock) as well as safety requirements (such as avoidance of states representing a system crash). In order to solve such a problem algorithmically, both the model of the system and its specification are formulated in some precise mathematical language. To this end, the problem is formulated as a task in logic, namely to check whether a structure satisfies a given logical formula. This general concept applies to many kinds of logic and many kinds of structures. A simple model-checking problem consists of verifying whether a formula in the propositional logic is satisfied by a given structure. Overview Property checking is used for verification when two de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skolem Constant
In mathematical logic, a formula of first-order logic is in Skolem normal form if it is in prenex normal form with only universal first-order quantifiers. Every first-order formula may be converted into Skolem normal form while not changing its satisfiability via a process called Skolemization (sometimes spelled Skolemnization). The resulting formula is not necessarily equivalent to the original one, but is equisatisfiable with it: it is satisfiable if and only if the original one is satisfiable. Reduction to Skolem normal form is a method for removing existential quantifiers from formal logic statements, often performed as the first step in an automated theorem prover. Examples The simplest form of Skolemization is for existentially quantified variables that are not inside the scope of a universal quantifier. These may be replaced simply by creating new constants. For example, \exists x P(x) may be changed to P(c), where c is a new constant (does not occur anywhere else i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donkey Sentence
Donkey sentences are sentences that contain a pronoun with clear meaning (it is bound semantically) but whose syntactical role in the sentence poses challenges to grammarians. Such sentences defy straightforward attempts to generate their formal language equivalents. The difficulty is with understanding how English speakers parse such sentences. Barker and Shan define a donkey pronoun as "a pronoun that lies outside the restrictor of a quantifier or the if-clause of a conditional, yet covaries with some quantificational element inside it, usually an indefinite." The pronoun in question is sometimes termed a donkey pronoun or donkey anaphora. The following sentences are examples of donkey sentences. *"" ("Every man who owns a donkey sees it") — Walter Burley (1328), *"Every farmer who owns a donkey beats it." *"Every police officer who arrested a murderer insulted him." History Walter Burley, a medieval scholastic philosopher, introduced donkey sentences in the context ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Drinker Paradox
The drinker paradox (also known as the drinker's theorem, the drinker's principle, or the drinking principle) is a theorem of classical predicate logic that can be stated as "There is someone in the pub such that, if he or she is drinking, then everyone in the pub is drinking." It was popularised by the mathematical logician Raymond Smullyan, who called it the "drinking principle" in his 1978 book ''What Is the Name of this Book?'' The apparently paradoxical nature of the statement comes from the way it is usually stated in natural language. It seems counterintuitive both that there could be a person who is ''causing'' the others to drink, or that there could be a person such that all through the night that one person were always the ''last'' to drink. The first objection comes from confusing formal "if then" statements with causation (see Correlation does not imply causation or Relevance logic for logics that demand relevant relationships between premise and consequent, unlik ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonfirstorderizability
In formal logic, nonfirstorderizability is the inability of a natural-language statement to be adequately captured by a formula of first-order logic. Specifically, a statement is nonfirstorderizable if there is no formula of first-order logic which is true in a model if and only if the statement holds in that model. Nonfirstorderizable statements are sometimes presented as evidence that first-order logic is not adequate to capture the nuances of meaning in natural language. The term was coined by George Boolos in his paper "To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables)". Reprinted in Quine argued that such sentences call for second-order symbolization, which can be interpreted as plural quantification over the same domain as first-order quantifiers use, without postulation of distinct "second-order objects" (properties, sets, etc.). Examples Geach-Kaplan sentence A standard example is the '' Geach– Kaplan sentence'': "Some critics admire only ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reification (computer Science)
Reification is the process by which an abstract idea about a computer program is turned into an explicit data model or other object created in a programming language. A computable/addressable object—a resource—is created in a system as a proxy for a non computable/addressable object. By means of reification, something that was previously implicit, unexpressed, and possibly inexpressible is explicitly formulated and made available to conceptual (logical or computational) manipulation. Informally, reification is often referred to as "making something a first-class citizen" within the scope of a particular system. Some aspect of a system can be reified at ''language design time'', which is related to reflection in programming languages. It can be applied as a stepwise refinement at ''system design time''. Reification is one of the most frequently used techniques of conceptual analysis and knowledge representation. Reflective programming languages In the context of programming ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reification (fallacy)
Reification (also known as concretism, hypostatization, or the fallacy of misplaced concreteness) is a fallacy of ambiguity, when an abstraction (abstract belief or hypothetical construct) is treated as if it were a concrete real event or physical entity. In other words, it is the error of treating something that is not concrete, such as an idea, as a concrete thing. A common case of reification is the confusion of a model with reality: " the map is not the territory". Reification is part of normal usage of natural language (just like metonymy for instance), as well as of literature, where a reified abstraction is intended as a figure of speech, and actually understood as such. But the use of reification in logical reasoning or rhetoric is misleading and usually regarded as a fallacy. Etymology From Latin ''res'' ("thing") and -''fication'', a suffix related to ''facere'' ("to make"). Thus ''reification'' can be loosely translated as "thing-making"; the turning of something abstra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reification (knowledge Representation)
Reification in knowledge representation is the process of turning a predicate or statement into an addressable object. Reification allows the representation of assertions so that they can be referred to or qualified by ''other'' assertions, i.e., meta-knowledge. The message "John is six feet tall" is an assertion involving truth that commits the speaker to its factuality, whereas the reified statement "Mary reports that John is six feet tall" defers such commitment to Mary. In this way, the statements can be incompatible without creating contradictions in reasoning. For example, the statements "John is six feet tall" and "John is five feet tall" are mutually exclusive (and thus incompatible), but the statements "Mary reports that John is six feet tall" and "Paul reports that John is five feet tall" are not incompatible, as they are both governed by a conclusive rationale that either Mary or Paul is (or both are), in fact, incorrect. In linguistics, reporting, telling, and saying a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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