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The extension of a predicate – a truth-valued function – is the set of tuples of values that, used as arguments, satisfy the predicate. Such a set of tuples is a relation . Examples
Prolog is a logic programming language that has its origins in artificial intelligence, automated theorem proving and computational linguistics. [1] [2] [3]Prolog has its roots in first-order logic, a formal logic, and unlike many other programming languages, Prolog is intended primarily as a declarative programming language: the program is a set of facts and rules, which define relations.
Let be a theory obtained from by extending its language with a new functional symbol (of arity ) and adding a new axiom ((),). Then T 1 {\displaystyle T_{1}} is a conservative extension of T {\displaystyle T} , i.e. the theories T {\displaystyle T} and T 1 {\displaystyle T_{1}} prove the same theorems not involving the functional symbol f ...
The core of the language fits on two printed pages. The Scheme implementation of miniKanren is designed to be easily understood, modified, and extended. αleanTAP is a program written in αKanren, an extension of miniKanren for nominal logic. Given a theorem, it can find a proof, making it a theorem-prover. Given a proof, it can find the ...
The language that Lparse accepts is now commonly called AnsProlog, [9] short for Answer Set Programming in Logic. [10] It is now used in the same way in many other answer set solvers, including assat, clasp, cmodels, gNt, nomore++ and pbmodels. (dlv is an exception; the syntax of ASP programs written for dlv is somewhat different.)
Some of these languages, such as miniKanren [28] and relational linear programming [30] are logic programming languages in the sense of this article. However, the relational language RML is an imperative programming language [ 31 ] whose core construct is a relational expression, which is similar to an expression in first-order predicate logic.
A definite clause grammar (DCG) is a way of expressing grammar, either for natural or formal languages, in a logic programming language such as Prolog. It is closely related to the concept of attribute grammars / affix grammars. DCGs are usually associated with Prolog, but similar languages such as Mercury also include DCGs.
However, TLA + specifications are written in a formal language of logic and mathematics, and the precision of specifications written in this language is intended to uncover design flaws before system implementation is underway. [6] Since TLA + specifications are written in a formal language, they are amenable to finite model checking.