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Completeness (knowledge Bases)
The term completeness as applied to knowledge bases refers to two different concepts. Formal logic In formal logic, a knowledge base KB is complete ''if'' there is no formula α such that KB ⊭ α and KB ⊭ ¬α. Example of knowledge base with incomplete knowledge: KB := Then we have KB ⊭ A and KB ⊭ ¬A. In some cases, a consistent knowledge base can be made complete with the closed world assumption—that is, adding all not-entailed literals as negations to the knowledge base. In the above example though, this would not work because it would make the knowledge base inconsistent: KB' = In the case where KB := , KB ⊭ P(b) and KB ⊭ ¬P(b), so, with the closed world assumption, KB' = , where KB' ⊨ ¬P(b). Data management In data management, completeness is metaknowledge Metaknowledge or meta-knowledge is knowledge about knowledge. Some authors divide meta-knowledge into orders: * ''zero order meta-knowledge'' is knowledge whose domain is not knowledge (and he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knowledge Base
In computer science, a knowledge base (KB) is a set of sentences, each sentence given in a knowledge representation language, with interfaces to tell new sentences and to ask questions about what is known, where either of these interfaces might use inference. It is a technology used to store complex structured data used by a computer system. The initial use of the term was in connection with expert systems, which were the first knowledge-based systems. Original usage of the term The original use of the term knowledge base was to describe one of the two sub-systems of an expert system. A knowledge-based system consists of a knowledge-base representing facts about the world and ways of reasoning about those facts to deduce new facts or highlight inconsistencies. Properties The term "knowledge-base" was coined to distinguish this form of knowledge store from the more common and widely used term ''database''. During the 1970s, virtually all large management information sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consistency (knowledge Bases)
In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T is consistent if there is no formula \varphi such that both \varphi and its negation \lnot\varphi are elements of the set of consequences of T. Let A be a set of closed sentences (informally "axioms") and \langle A\rangle the set of closed sentences provable from A under some (specified, possibly implicitly) formal deductive system. The set of axioms A is consistent when there is no formula \varphi such that \varphi \in \langle A \rangle and \lnot \varphi \in \langle A \rangle. A ''trivial'' theory (i.e., one which proves every sentence in the language of the theory) is clearly inconsistent. Conversely, in an explosive formal system (e.g., classical or intuitionistic propositional or first-order logics) every inconsistent theory is trivial. Consistency of a theory is a syntactic notion, whose semantic counterpart is satisfiability. A theory is satisfiable if it has a model, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed World Assumption
The closed-world assumption (CWA), in a formal system of logic used for knowledge representation, is the presumption that a statement that is true is also known to be true. Therefore, conversely, what is not currently known to be true, is false. The same name also refers to a logical formalization of this assumption by Raymond Reiter. The opposite of the closed-world assumption is the open-world assumption (OWA), stating that lack of knowledge does not imply falsity. Decisions on CWA vs. OWA determine the understanding of the actual semantics of a conceptual expression with the same notations of concepts. A successful formalization of natural language semantics usually cannot avoid an explicit revelation of whether the implicit logical backgrounds are based on CWA or OWA. Negation as failure is related to the closed-world assumption, as it amounts to believing false every predicate that cannot be proved to be true. Example In the context of knowledge management, the closed- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linguistic Entailment
Linguistic entailments are entailments which arise in natural language. If a sentence ''A'' entails a sentence ''B'', sentence ''A'' cannot be true without ''B'' being true as well. For instance, the English sentence "Pat is a fluffy cat" entails the sentence "Pat is a cat" since one cannot be a fluffy cat without being a cat. On the other hand, this sentence does not entail "Pat chases mice" since it is possible (if unlikely) for a cat to not chase mice. Entailments arise from the semantics of linguistic expressions. Entailment contrasts with the pragmatic notion of implicature. While implicatures are fallible inferences, entailments are enforced by lexical meanings plus the laws of logic. Entailments also differ from presuppositions, whose truth is taken for granted. The classic example of a presupposition is the existence presupposition which arises from definite descriptions. For example, the sentence "The king of France is bald" presupposes that there is a king of France. Unl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metaknowledge
Metaknowledge or meta-knowledge is knowledge about knowledge. Some authors divide meta-knowledge into orders: * ''zero order meta-knowledge'' is knowledge whose domain is not knowledge (and hence zero order meta-knowledge is not meta-knowledge ''per se'') * ''first order meta-knowledge'' is knowledge whose domain is zero order meta-knowledge * ''second order meta-knowledge'' is knowledge whose domain is first order meta-knowledge * most generally, n + 1 order meta-knowledge is knowledge whose domain is n order meta-knowledge. Other authors call zero order meta-knowledge ''first order knowledge'', and call first order meta-knowledge ''second order knowledge''; meta-knowledge is also known as higher order knowledge.Pedersen, Nikolaj Jl Linding, and Christoph Kelp. "Second-Order Knowledge." ''The Routledge Companion to Epistemology''. Routledge, 2010. 586-596. Meta-knowledge is a fundamental conceptual instrument in such research and scientific domains as, knowledge engineering, knowl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predicate (mathematical Logic)
In logic, a predicate is a symbol that represents a property or a relation. For instance, in the first-order formula P(a), the symbol P is a predicate that applies to the individual constant a. Similarly, in the formula R(a,b), the symbol R is a predicate that applies to the individual constants a and b. According to Gottlob Frege, the meaning of a predicate is exactly a function from the domain of objects to the truth values "true" and "false". In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula R(a,b) would be true on an interpretation if the entities denoted by a and b stand in the relation denoted by R. Since predicates are non-logical symbols, they can denote different relations depending on the interpretation given to them. While first-order logic only includes predicates that apply to individual objects, other logics may allow predicates that apply to collections of objects defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Logic
First-order logic, also called predicate logic, predicate calculus, or quantificational logic, 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. Rather than propositions such as "all humans are mortal", in first-order logic one can have expressions in the form "for all ''x'', if ''x'' is a human, then ''x'' is mortal", where "for all ''x"'' is a quantifier, ''x'' is a variable, and "... ''is a human''" and "... ''is mortal''" are predicates. 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, such as set theory, a theory for groups,A. Tarski, ''Undecidable Theories'' (1953), p. 77. Studies in Logic and the Foundation of Mathematics, North-Holland or a formal theory o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Certain Answer
In database theory and knowledge representation, the certain answers is the set of answers to a given query consisting of the intersection of all the complete databases that are consistent with a given knowledge base. The notion of certain answer, investigated in database theory since the 1970s, is indeed defined in the context of open world assumption, where the given knowledge base is assumed to be incomplete. Intuitively, certain answers are the answers that are always returned when querying a given knowledge base, considering both the extensional knowledge that the possible implications inferred by automatic reasoning, regardless of the specific interpretation. Definition In literature, the set of certain answers is usually defined as follows:. :cert_\cap(Q,D) = \bigcap \left\ where: * Q is a query * D is an incomplete database * D' is any complete database consistent with D * is the semantics of D In description logics">D_">![_D_<_a>!.html" ;"title="D_.html ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vivid Knowledge
Vivid may refer to: Music * Vivid (band), a Japanese rock band * "Vivid" (song), by Electronic, 1999 *"ViViD", a 2016 song by Loona from ''HeeJin'' Albums * ''Vivid'' (Vivian Green album), 2015 * ''Vivid'' (Crystal Kay album), 2012 * ''Vivid'' (Living Colour album), 1988 * ''Vivid'' (Ailee album), 2015 * ''Vivid'' (KM-MARKIT album), 2005 * '' Vivid: Kissing You, Sparkling, Joyful Smile'', a 2008 mini-album by BoA * ''Vivid'' (EP), 2020 EP by AB6IX Organizations * Vivid Entertainment, a company that produces and distributes adult media * Vivid Image, a defunct UK video game developer * Vivid Imaginations, a UK toy company * Vivid Seats, a ticket exchange company Technology * HTC Vivid, a mobile phone * Vivid Vervet, the code name for version 15.04 of the Ubuntu Linux distribution Festivals and arts * Vivid (arts centre), a media art centre in Birmingham, England * Vivid Sydney, an outdoor festival in Sydney, Australia * Vivid Live, a contemporary music festival held by Sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
