A metatheory or meta-theory is a theory whose subject matter is some other theory. In other words it is a theory about a theory. Statements made in the metatheory about the theory are called metatheorems. The following is an example of a meta-theoretical statement: ¿ Any physical theory is always provisional, in the sense that it is only a hypothesis; you can never prove it.
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Model checking
In computer science, model checking refers to the following problem: Given a model of a system, test automatically whether this model meets a given specification. Typically, the systems one has in mind are hardware or software systems, and the specification contains safety requirements such as the absence of deadlocks and similar critical states that can cause the system to crash. Model checking is a technique for automatically verifying correctness properties of finite-state systems.
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Negation as failure
Negation 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.
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Negation
In logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. In classical logic negation is normally identified with the truth function that takes truth to falsity and vice versa.
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Formal system
A formal system is loosely speaking, any well defined system of abstract thought, on the model of mathematics. Technically, Euclid's elements, with a model consisting of 23 definitions and 10 postulates/axioms followed by 13 books of theorems with proof, is often held to be the first formal system and displays the characteristic of a formal system.
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Operational semantics
In computer science, operational semantics is a way to give meaning to computer programs in a mathematically rigorous way. Operational semantics are classified into two categories: structural operational semantics (or small-step semantics) formally describe how the individual steps of a computation take place in a computer-based system. By opposition natural semantics (or big-step semantics) describe how the overall results of the executions are obtained.
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Counterexample
In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule. For example, consider the proposition "all students are lazy". Because this statement makes the claim that a certain property (laziness) holds for all students, even a single example of a diligent student will prove it false. Thus, any hard-working student is a counterexample to "all students are lazy".
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Type system
A type system associates a type with each computed value. By examining the flow of these values, a type system attempts to ensure or prove that no type errors can occur. The particular type system in question determines exactly what constitutes a type error, but in general the aim is to prevent operations expecting a certain kind of value being used with values for which that operation does not make sense; memory errors will also be prevented.
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