Negation as failureNegation as failure (NAF, for short) is a non-monotonic inference rule in logic programming, used to derive (i.e. that is assumed not to hold) from failure to derive . Note that can be different from the statement of the logical negation of , 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.
Stable model semanticsThe 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.
Unification (computer science)In logic and computer science, unification is an algorithmic process of solving equations between symbolic expressions. For example, using x,y,z as variables, the singleton equation set { cons(x,cons(x,nil)) = cons(2,y) } is a syntactic first-order unification problem that has the substitution { x ↦ 2, y ↦ cons(2,nil) } as its only solution.
Oz (programming language)Oz is a multiparadigm programming language, developed in the Programming Systems Lab at Université catholique de Louvain, for programming language education. It has a canonical textbook: Concepts, Techniques, and Models of Computer Programming. Oz was first designed by Gert Smolka and his students in 1991. In 1996, development of Oz continued in cooperation with the research group of Seif Haridi and Peter Van Roy at the Swedish Institute of Computer Science.
Constraint logic programmingConstraint logic programming is a form of constraint programming, in which logic programming is extended to include concepts from constraint satisfaction. A constraint logic program is a logic program that contains constraints in the body of clauses. An example of a clause including a constraint is . In this clause, is a constraint; A(X,Y), B(X), and C(Y) are literals as in regular logic programming. This clause states one condition under which the statement A(X,Y) holds: X+Y is greater than zero and both B(X) and C(Y) are true.
Planner (programming language)Planner (often seen in publications as "PLANNER" although it is not an acronym) is a programming language designed by Carl Hewitt at MIT, and first published in 1969. First, subsets such as Micro-Planner and Pico-Planner were implemented, and then essentially the whole language was implemented as Popler by Julian Davies at the University of Edinburgh in the POP-2 programming language.
Inductive logic programmingInductive logic programming (ILP) is a subfield of symbolic artificial intelligence which uses logic programming as a uniform representation for examples, background knowledge and hypotheses. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesised logic program which entails all the positive and none of the negative examples. Schema: positive examples + negative examples + background knowledge ⇒ hypothesis.
Non-monotonic logicA non-monotonic logic is a formal logic whose conclusion relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences (cf. defeasible reasoning), i.e., a kind of inference in which reasoners draw tentative conclusions, enabling reasoners to retract their conclusion(s) based on further evidence. Most studied formal logics have a monotonic entailment relation, meaning that adding a formula to a theory never produces a pruning of its set of conclusions.
Wolfram LanguageThe Wolfram Language (ˈwʊlfrəm ) is a proprietary, general high-level multi-paradigm programming language developed by Wolfram Research. It emphasizes symbolic computation, functional programming, and rule-based programming and can employ arbitrary structures and data. It is the programming language of the mathematical symbolic computation program Mathematica. The Wolfram Language was a part of the initial version of Mathematica in 1988. Symbolic aspects of the engine make it a computer algebra system.
Backward chainingBackward chaining (or backward reasoning) is an inference method described colloquially as working backward from the goal. It is used in automated theorem provers, inference engines, proof assistants, and other artificial intelligence applications. In game theory, researchers apply it to (simpler) subgames to find a solution to the game, in a process called backward induction. In chess, it is called retrograde analysis, and it is used to generate table bases for chess endgames for computer chess.
