Concepts inOpen answer set programming with guarded programs
Answer set programming
Answer set programming (ASP) is a form of declarative programming oriented towards difficult 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.
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In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is impossible to construct a single algorithm that always leads to a correct yes-or-no answer. A decision problem is any arbitrary yes-or-no question on an infinite set of inputs. Because of this, it is traditional to define the decision problem equivalently as the set of inputs for which the problem returns yes.
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Datalog
Datalog is a query and rule language for deductive databases that syntactically is a subset of Prolog. 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.
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Computation tree logic
Computation tree logic (CTL) is a branching-time logic, meaning that its model of time is a tree-like structure in which the future is not determined; there are different paths in the future, any one of which might be an actual path that is realised. It is used in formal verification of software or hardware artifacts, typically by software applications known as model checkers which determine if a given artifact possesses safety or liveness properties.
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Axiom
An axiom is a premise or starting point of reasoning. As classically conceived, an axiom is a premise so evident as to be accepted as true without controversy. The word comes from the Greek ¿¿¿¿¿¿ 'that which is thought worthy or fit,' or 'that which commends itself as evident. ' As used in modern logic, an axiom is simply a premise or starting point for reasoning, and equivalent to what Aristotle calls a definition. Axioms define and delimit the realm of analysis.
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Open set
In topology, a set is called an open set if it is a neighborhood of every point . When dealing with metric spaces, this can be intuitively interpreted as saying that every can be "moved" some non-zero distance, in any direction, and it will still lie within . The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined.
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Model theory
In mathematics, model theory is the study of (classes of) mathematical structures using tools from mathematical logic. It has close ties to abstract algebra, particularly universal algebra. Objects of study in model theory are models for formal languages which are structures that give meaning to the sentences of these formal languages.
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