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Partial-closed 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] |
Mathematical Logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonicity Of Entailment
Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions. In sequent calculi this property can be captured by an inference rule called weakening, or sometimes thinning, and in such systems one may say that entailment is monotone if and only if the rule is admissible. Logical systems with this property are occasionally called ''monotonic logics'' in order to differentiate them from non-monotonic logics. Weakening rule To illustrate, consider the natural deduction sequent: Γ \vdash C That is, on the basis of a list of assumptions Γ, one can prove C. Weakening, by adding an assumption A, allows one to conclude: Γ, A \vdash C For example, the syllogism "All men are mortal. Socrates is a man. Therefore Socrates is mortal." can be weakened by adding a premise: "All men are mortal. Socrates is a man. Cows produce milk. Therefore Socrates is mortal." The validity of th ... [...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] |
Unique Name Assumption
The unique name assumption is a simplifying assumption made in some ontology languages and description logics. In logics with the unique name assumption, different names always refer to different entities in the world. It was included in Ray Reiter's discussion of the closed-world assumption often tacitly included in Database Management Systems (e.g. SQL) in his 1984 article "Towards a logical reconstruction of relational database theory" (in M. L. Brodie, J. Mylopoulos, J. W. Schmidt (editors), Data Modelling in Artificial Intelligence, Database and Programming Languages, Springer, 1984, pages 191–233). The standard ontology language OWL does not make this assumption, but provides explicit constructs to express whether two names denote the same or distinct entities. * owl:sameAs is the OWL property that asserts that two given names or identifiers (e.g., URIs) refer to the same individual or entity. * owl:differentFrom is the OWL property that asserts that two given names or ide ... [...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] |
A Modern Approach
A, or a, is the first letter and the first vowel of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''a'' (pronounced ), plural ''aes''. It is similar in shape to the Ancient Greek letter alpha, from which it derives. The uppercase version consists of the two slanting sides of a triangle, crossed in the middle by a horizontal bar. The lowercase version can be written in two forms: the double-storey a and single-storey ɑ. The latter is commonly used in handwriting and fonts based on it, especially fonts intended to be read by children, and is also found in italic type. In English grammar, " a", and its variant " an", are indefinite articles. History The earliest certain ancestor of "A" is aleph (also written 'aleph), the first letter of the Phoenician alphabet, which consisted entirely of consonants (for that reason, it is also called an abjad to distinguis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stable Model Semantics
The concept of a stable model, or answer set, is used to define a declarative semantics for logic programs with negation as failure. This is one of several standard approaches to the meaning of negation in logic programming, along with program completion and the well-founded semantics. The stable model semantics is the basis of answer set programming. Motivation Research on the declarative semantics of negation in logic programming was motivated by the fact that the behavior of SLDNF resolution — the generalization of SLD resolution used by Prolog in the presence of negation in the bodies of rules — does not fully match the truth tables familiar from classical propositional logic. Consider, for instance, the program :p\ :r \leftarrow p,\ q :s \leftarrow p,\ \operatorname q. Given this program, the query will succeed, because the program includes as a fact; the query will fail, because it does not occur in the head of any of the rules. The query will fail also ... [...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] |
Database Transaction
A database transaction symbolizes a unit of work, performed within a database management system (or similar system) against a database, that is treated in a coherent and reliable way independent of other transactions. A transaction generally represents any change in a database. Transactions in a database environment have two main purposes: # To provide reliable units of work that allow correct recovery from failures and keep a database consistent even in cases of system failure. For example: when execution prematurely and unexpectedly stops (completely or partially) in which case many operations upon a database remain uncompleted, with unclear status. # To provide isolation between programs accessing a database concurrently. If this isolation is not provided, the programs' outcomes are possibly erroneous. In a database management system, a transaction is a single unit of logic or work, sometimes made up of multiple operations. Any logical calculation done in a consistent mode in ... [...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] |
Database
In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spans formal techniques and practical considerations, including data modeling, efficient data representation and storage, query languages, security and privacy of sensitive data, and distributed computing issues, including supporting concurrent access and fault tolerance. A database management system (DBMS) is the software that interacts with end users, applications, and the database itself to capture and analyze the data. The DBMS software additionally encompasses the core facilities provided to administer the database. The sum total of the database, the DBMS and the associated applications can be referred to as a database system. Often the term "database" is also used loosely to refer to any of the DBMS, the database system or an appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Procedural Programming Language
Procedural programming is a programming paradigm, derived from imperative programming, based on the concept of the ''procedure call''. Procedures (a type of routine or subroutine) simply contain a series of computational steps to be carried out. Any given procedure might be called at any point during a program's execution, including by other procedures or itself. The first major procedural programming languages appeared circa 1957–1964, including Fortran, ALGOL, COBOL, PL/I and BASIC. Pascal and C were published circa 1970–1972. Computer processors provide hardware support for procedural programming through a stack register and instructions for calling procedures and returning from them. Hardware support for other types of programming is possible, but no attempt was commercially successful (for example Lisp machines or Java processors). Procedures and modularity Modularity is generally desirable, especially in large, complicated programs. Inputs are usua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
