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First-order logic also satisfies several metalogical theorems that make it amenable to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem. First-order logic is the standard for the formalization of mathematics into axioms, and is studied in the foundations of mathematics.
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.
In artificial intelligence, a fluent is a condition that can change over time. In logical approaches to reasoning about actions, fluents can be represented in first-order logic by predicates having an argument that depends on time.
The logical semantics of NAF was unresolved until Keith Clark [35] showed that, under certain natural conditions, NAF is an efficient, correct (and sometimes complete) way of reasoning with the logical consequence semantics using the completion of a logic program in first-order logic.
Horn clause logic is more restricted than first-order logic and is used in logic programming languages such as Prolog. Extensions to first-order logic include temporal logic , to handle time; epistemic logic , to reason about agent knowledge; modal logic , to handle possibility and necessity; and probabilistic logics to handle logic and ...
In artificial intelligence, with implications for cognitive science, the frame problem describes an issue with using first-order logic to express facts about a robot in the world. Representing the state of a robot with traditional first-order logic requires the use of many axioms that simply imply that things in the environment do not change ...
The first reasoning systems were theorem provers, systems that represent axioms and statements in First Order Logic and then use rules of logic such as modus ponens to infer new statements. Another early type of reasoning system were general problem solvers.
There are three common ways of handling this in first-order logic: Use first-order logic with two types. Use ordinary first-order logic, but add a new unary predicate "Set", where "Set(t)" means informally "t is a set". Use ordinary first-order logic, and instead of adding a new predicate to the language, treat "Set(t)" as an abbreviation for ...