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While the name "logic programming" is used to refer to the entire paradigm of programming languages including Datalog and Prolog, when discussing formal semantics, it generally refers to an extension of Datalog with function symbols. Logic programs are also called Horn clause programs.
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.
An explicit listing of the extension, which is only possible for finite sets and only practical for relatively small sets, is a type of enumerative definition. Extensional definitions are used when listing examples would give more applicable information than other types of definition, and where listing the members of a set tells the questioner ...
λProlog, also written lambda Prolog, is a logic programming language featuring polymorphic typing, modular programming, and higher-order programming.These extensions to Prolog are derived from the higher-order hereditary Harrop formulas used to justify the foundations of λProlog.
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.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
(That set might be empty, currently.) For example, the extension of a function is a set of ordered pairs that pair up the arguments and values of the function; in other words, the function's graph. The extension of an object in abstract algebra, such as a group, is the underlying set of the object. The extension of a set is the set itself.
In mathematical logic, a conservative extension is a supertheory of a theory which is often convenient for proving theorems, but proves no new theorems about the language of the original theory. Similarly, a non-conservative extension is a supertheory which is not conservative, and can prove more theorems than the original.