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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] |
Database Theory
Database theory encapsulates a broad range of topics related to the study and research of the theoretical realm of databases and database management systems. Theoretical aspects of data management include, among other areas, the foundations of query languages, computational complexity and expressive power of queries, finite model theory, database design theory, dependency theory, foundations of concurrency control and database recovery, deductive databases, temporal and spatial databases, real-time databases, managing uncertain data and probabilistic databases, and Web data. Most research work has traditionally been based on the relational model, since this model is usually considered the simplest and most foundational model of interest. Corresponding results for other data models, such as object-oriented or semi-structured models, or, more recently, graph data models and XML, are often derivable from those for the relational model. A central focus of database theory is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open World Assumption
In a formal system of logic used for knowledge representation, the open-world assumption is the assumption that the truth value of a statement may be true irrespective of whether or not it is ''known'' to be true. It is the opposite of the closed-world assumption, which holds that any statement that is true is also known to be true. Origin An open-world assumption was first developed by Ancient Greek philosophers as a means to explain varying degrees of validity amongst mathematical and philosophical concepts proposed at the time of inception. Logical implication The open-world assumption (OWA) codifies the informal notion that in general no single agent or observer has complete knowledge, and therefore cannot make the closed-world assumption. The OWA limits the kinds of inference and deductions an agent can make to those that follow from statements that are known to the agent to be true. In contrast, the closed world assumption allows an agent to infer from the lack of knowledg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Variables
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol. In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context. A bound variable, in contrast, is a variable that has been ''bound'' to a specific value or range of values in the domain of discourse or universe. This may be achieved through the use of logical quantifie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Constant
In logic, a logical constant of a language \mathcal is a symbol that has the same semantic value under every interpretation of \mathcal. Two important types of logical constants are logical connectives and quantifiers. The equality predicate (usually written '=') is also treated as a logical constant in many systems of logic. One of the fundamental questions in the philosophy of logic is "What is a logical constant?"; that is, what special feature of certain constants makes them ''logical'' in nature? Some symbols that are commonly treated as logical constants are: Many of these logical constants are sometimes denoted by alternate symbols (''e.g.'', the use of the symbol "&" rather than "∧" to denote the logical and). Defining logical constants is a major part of the work of Gottlob Frege and Bertrand Russell. Russell returned to the subject of logical constants in the preface to the second edition (1937) of ''The Principles of Mathematics'' noting that logic becomes lingu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abox
In computer science, the terms TBox and ABox are used to describe two different types of statements in knowledge bases. TBox statements are the "terminology component", and describe a domain of interest by defining classes and properties as a domain vocabulary. ABox statements are the "assertion component" — facts associated with the TBox's conceptual model or ontologies. Together ABox and TBox statements make up a knowledge base or a knowledge graph. ABox statements must be TBox-compliant: they are assertions that use the vocabulary defined by the TBox. TBox statements are sometimes associated with object-oriented classes and ABox statements associated with instances of those classes. Examples of ABox and TBox statements ABox statements typically deal with concrete entities. They specify what category an entity belongs to, or what relation one entity has to another entity. * Item A is-an-instance-of Category C * Item A has-this-relation-to Item B Examples: * Niger is-a co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tbox
In computer science, the terms TBox and ABox are used to describe two different types of statements in knowledge bases. TBox statements are the "terminology component", and describe a domain of interest by defining classes and properties as a domain vocabulary. ABox statements are the "assertion component" — facts associated with the TBox's conceptual model or ontologies. Together ABox and TBox statements make up a knowledge base or a knowledge graph. ABox statements must be TBox-compliant: they are assertions that use the vocabulary defined by the TBox. TBox statements are sometimes associated with object-oriented classes and ABox statements associated with instances of those classes. Examples of ABox and TBox statements ABox statements typically deal with concrete entities. They specify what category an entity belongs to, or what relation one entity has to another entity. * Item A is-an-instance-of Category C * Item A has-this-relation-to Item B Examples: * Niger is-a co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model (mathematical Logic)
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols. Model theory has a different scope that encompasses more arbitrary theories, including foundational structures such as models of set theory. From the model-theoretic point of view, structures are the objects used to define the semantics of first-order logic. For a given theory in model theory, a structure is called a model if it satisfies the defining axioms of that theory, although it is sometimes disambiguated as a ''semantic model'' when one discusses the notion in the more general setting of mathematical models. Logicians sometimes refer to structures as " interpretations", whereas the term "interpretation" generally has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ontology (information Science)
In computer science and information science, an ontology encompasses a representation, formal naming, and definition of the categories, properties, and relations between the concepts, data, and entities that substantiate one, many, or all domains of discourse. More simply, an ontology is a way of showing the properties of a subject area and how they are related, by defining a set of concepts and categories that represent the subject. Every academic discipline or field creates ontologies to limit complexity and organize data into information and knowledge. Each uses ontological assumptions to frame explicit theories, research and applications. New ontologies may improve problem solving within that domain. Translating research papers within every field is a problem made easier when experts from different countries maintain a controlled vocabulary of jargon between each of their languages. For instance, the definition and ontology of economics is a primary concern in Marxist econo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpretation (logic)
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways of presenting an interpretation. In these contexts an interpretation is a function that provides the extension of symbols and strings of symbols of an object language. For example, an interpretation function could take the predicate ''T'' (for "tall") and assign it the extension (for "Abraham Lincoln"). Note that all our interpretation does is assign the extension to the non-logical constant ''T'', and does not make a claim about whether ''T'' is to stand for tall and 'a' f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knowledge Representation
Knowledge representation and reasoning (KRR, KR&R, KR²) is the field of artificial intelligence (AI) dedicated to representing information about the world in a form that a computer system can use to solve complex tasks such as diagnosing a medical condition or having a dialog in a natural language. Knowledge representation incorporates findings from psychology about how humans solve problems and represent knowledge in order to design formalisms that will make complex systems easier to design and build. Knowledge representation and reasoning also incorporates findings from logic to automate various kinds of ''reasoning'', such as the application of rules or the relations of sets and subsets. Examples of knowledge representation formalisms include semantic nets, systems architecture, frames, rules, and ontologies. Examples of automated reasoning engines include inference engines, theorem provers, and classifiers. History The earliest work in computerized knowledge represe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automatic Reasoning
In computer science, in particular in knowledge representation and reasoning and metalogic, the area of automated reasoning is dedicated to understanding different aspects of reasoning. The study of automated reasoning helps produce computer programs that allow computers to reason completely, or nearly completely, automatically. Although automated reasoning is considered a sub-field of artificial intelligence, it also has connections with theoretical computer science and philosophy. The most developed subareas of automated reasoning are automated theorem proving (and the less automated but more pragmatic subfield of interactive theorem proving) and automated proof checking (viewed as guaranteed correct reasoning under fixed assumptions). Extensive work has also been done in reasoning by analogy using induction and abduction. Other important topics include reasoning under uncertainty and non-monotonic reasoning. An important part of the uncertainty field is that of argumentat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
