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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 that can be asserted for parts of the KB via completeness assertions. As example, a knowledge base may contain complete information for predicates R and S, while nothing is asserted for predica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knowledge Base
A knowledge base (KB) is a technology used to store complex structured and unstructured information 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 systems stored their data in some type of hierarchical or relational database. At this point in the history of information technology, the distinction between a database and a knowledge-base was clear and unambiguous. A databas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consistency (knowledge Bases)
A knowledge base KB is consistent ''iff'' its negation is not a Tautology (logic), tautology. I.e., a knowledge base KB is inconsistent (not consistent) iff there is no Interpretation (logic), interpretation which entailment, entails KB. Example of an inconsistent knowledge base: KB := Consistency in terms of knowledge bases is mostly the same as the natural understanding of consistency. Knowledge representation {{database-stub ... [...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-worl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entailment (linguistics)
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 instance, 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
Meta-knowledge or metaknowledge 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. Note that 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 engineer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predicate (mathematical Logic)
In logic, a predicate is a symbol which represents a property or a relation. For instance, in the first order formula P(a), the symbol P is a predicate which applies to the individual constant a. Similarly, in the formula R(a,b), R is a predicate which applies to the individual constants a and b. 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 used to interpret them. While first-order logic only includes predicates which apply to individual constants, other logics may allow predicates which apply to other predicates. Predicates in different systems * In propositional logic, atomic formulas are sometimes regarded as zero-place predicates In a sense, these are nullar ... [...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] |
Certain Answer
In database theory and knowledge representation, the one of 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 quering 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 * D_.html"_;"title="![_D_">![_D_!/math>_is_the_semantics_of_D In_![_D_!.html"_;"title="D_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vivid Knowledge
Vivid knowledge refers to a specific kind of knowledge representation. The idea of a vivid knowledge base is to get an interpretation mostly straightforward out of it – it implies the interpretation. Thus, any query to such a knowledge base can be reduced to a database-like query. Propositional knowledge base A propositional knowledge base KB is vivid ''iff'' KB is a complete and consistent set of literals (over some vocabulary). Such a knowledge base has the property that it as exactly one interpretation, i.e. the interpretation is unique. A check for entailment of a sentence can simply be broken down into its literals and those can be answered by a simple database-like check of KB. First-order knowledge base A first-order knowledge base KB is vivid ''iff'' for some finite set of positive function-free ground literals KB+, : KB = KB+ ∪ Negations ∪ DomainClosure ∪ UniqueNames, whereby : Negations ≔ , : DomainClosure ≔ , : UniqueNames ≔ . All interpre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
