|
DLV
The DLV (DataLog with Disjunction, where the logical disjunction symbol V is used) system is a disjunctive logic programming system, implementing the stable model semantics under the answer set programming paradigm. It extends the Datalog language to allow the use of OR in the heads of rules. Briefly, disjunctive Datalog is a variant of Datalog where disjunctions may appear in the rule heads; advanced versions also allow for negation in the bodies, which can be handled according to a semantics for negation in disjunctive logic programming. Programming example The following is a program in Datalog extended with negation as failure Negation as failure (NAF, for short) is a non-monotonic inference rule in logic programming, used to derive \mathrm~p (i.e. that ~p is assumed not to hold) from failure to derive ~p. Note that \mathrm ~p can be different from the statement \neg p ...: smoker(john). smoker(jack). jogger(jill). jogger(john). healthy(X) :- jogger(X), \+ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Datalog
Datalog is a declarative logic programming language. While it is syntactically a subset of Prolog, Datalog generally uses a bottom-up rather than top-down evaluation model. This difference yields significantly different behavior and properties from Prolog. It is often used as a query language for deductive databases. In recent years, Datalog has found new application in data integration, information extraction, networking, program analysis, security, cloud computing and machine learning. Its origins date back to the beginning of logic programming, but it became prominent as a separate area around 1977 when Hervé Gallaire and Jack Minker organized a workshop on logic and databases. David Maier is credited with coining the term Datalog. Features, limitations and extensions Unlike in Prolog, statements of a Datalog program can be stated in any order. Furthermore, Datalog queries on finite sets are guaranteed to terminate, so Datalog does not have Prolog's cut operator. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Answer Set Programming
Answer set programming (ASP) is a form of declarative programming oriented towards difficult (primarily NP-hard) search problems. It is based on the stable model (answer set) semantics of logic programming. In ASP, search problems are reduced to computing stable models, and ''answer set solvers''—programs for generating stable models—are used to perform search. The computational process employed in the design of many answer set solvers is an enhancement of the DPLL algorithm and, in principle, it always terminates (unlike Prolog query evaluation, which may lead to an infinite loop). In a more general sense, ASP includes all applications of answer sets to knowledge representation and the use of Prolog-style query evaluation for solving problems arising in these applications. History An early example of answer set programming was the planning method proposed in 1997 by Dimopoulos, Nebel and Köhler. Their approach is based on the relationship between plans and stable model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disjunctive Datalog
Disjunctive Datalog is an extension of the logic programming language Datalog that allows disjunctions in the heads of rules. This extension enables disjunctive Datalog to express several NP-hard problems that are not known to be expressable in plain Datalog. Disjunctive Datalog has been applied in the context of reasoning about ontologies in the semantic web. DLV is an implementation of disjunctive Datalog. Syntax A disjunctive Datalog program is a collection of rules. A is a clause of the form: :a_1 \vee \dots \vee a_n \leftarrow b_1 \wedge \dots \wedge b_m \quad 1 \leq n, 0 \leq m where b_1, ..., b_m may be negated, and may include (in)equality constraints. Semantics There are at least three ways to define the semantics of disjunctive Datalog: * Minimal model semantics * Perfect model semantics * Disjunctive stable model semantics, which generalizes the stable model semantics Expressivity Disjunctive Datalog can express several NP-complete and NP-hard pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Disjunction
In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor S , assuming that R abbreviates "it is raining" and S abbreviates "it is snowing". In classical logic, disjunction is given a truth functional semantics according to which a formula \phi \lor \psi is true unless both \phi and \psi are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an ''inclusive'' interpretation of disjunction, in contrast with exclusive disjunction. Classical proof theoretical treatments are often given in terms of rules such as disjunction introduction and disjunction elimination. Disjunction has also been given numerous non-classical treatments, motivated by problems including Aristotle's sea battle argument, Heisenberg's uncertainty principle, as well ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic Programming
Logic programming is a programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. Major logic programming language families include Prolog, answer set programming (ASP) and Datalog. In all of these languages, rules are written in the form of ''clauses'': :H :- B1, …, Bn. and are read declaratively as logical implications: :H if B1 and … and Bn. H is called the ''head'' of the rule and B1, ..., Bn is called the ''body''. Facts are rules that have no body, and are written in the simplified form: :H. In the simplest case in which H, B1, ..., Bn are all atomic formulae, these clauses are called definite clauses or Horn clauses. However, there are many extensions of this simple case, the most important one being the case in which conditions in the body of a clause can also be negations of atomic formulas. Logic programming languag ... [...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] |
Negation As Failure
Negation as failure (NAF, for short) is a non-monotonic inference rule in logic programming, used to derive \mathrm~p (i.e. that ~p is assumed not to hold) from failure to derive ~p. Note that \mathrm ~p can be different from the statement \neg p of the logical negation of ~p, depending on the completeness of the inference algorithm and thus also on the formal logic system. Negation as failure has been an important feature of logic programming since the earliest days of both Planner and Prolog. In Prolog, it is usually implemented using Prolog's extralogical constructs. More generally, this kind of negation is known as weak negation, in contrast with the strong (i.e. explicit, provable) negation. Planner semantics In Planner, negation as failure could be implemented as follows: :''if'' (''not'' (''goal'' p)), ''then'' (''assert'' ¬p) which says that if an exhaustive search to prove p fails, then assert ¬p. This states that proposition p shall be assumed as "not true" in any ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Query Languages
Query languages, data query languages or database query languages (DQL) are computer languages used to make queries in databases and information systems. A well known example is the Structured Query Language (SQL). Types Broadly, query languages can be classified according to whether they are database query languages or information retrieval query languages. The difference is that a database query language attempts to give factual answers to factual questions, while an information retrieval query language attempts to find documents containing information that is relevant to an area of inquiry. Other types of query languages include: * Full-text. The simplest query language is treating all terms as bag of words that are to be matched with the postings in the inverted index and where subsequently ranking models are applied to retrieve the most relevant documents. Only tokens are defined in the CFG. Web search engines often use this approach. * Boolean. A query language that also s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
