FO(.)

In computer science, FO(.) (a.k.a. FO-dot) is a knowledge representation language based on first-order logic (FO). ^[1]

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Table of Contents

1. 13 relations: Axiom, Boolean, Computer science, First-order logic, Function (mathematics), Integer, Knowledge representation and reasoning, Logical consequence, Material conditional, Model theory, Negation, Satisfiability, Type theory.

2. Knowledge representation languages

Axiom

An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

See FO(.) and Axiom

Boolean

Any kind of logic, function, expression, or theory based on the work of George Boole is considered Boolean.

See FO(.) and Boolean

Computer science

Computer science is the study of computation, information, and automation.

See FO(.) and Computer science

First-order logic

First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

See FO(.) and First-order logic

Function (mathematics)

In mathematics, a function from a set to a set assigns to each element of exactly one element of.

See FO(.) and Function (mathematics)

Integer

An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.

See FO(.) and Integer

Knowledge representation and reasoning

Knowledge representation and reasoning (KRR, KR&R, KR²) is the field of artificial intelligence (AI) dedicated to representing information about the world in a form that a computer system can use to solve complex tasks such as diagnosing a medical condition or having a dialog in a natural language.

See FO(.) and Knowledge representation and reasoning

Logical consequence

Logical consequence (also entailment) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically follows from one or more statements.

See FO(.) and Logical consequence

Material conditional

The material conditional (also known as material implication) is an operation commonly used in logic.

See FO(.) and Material conditional

Model theory

In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold).

See FO(.) and Model theory

Negation

In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P to another proposition "not P", standing for "P is not true", written \neg P, \mathord P or \overline.

See FO(.) and Negation

Satisfiability

In mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables.

See FO(.) and Satisfiability

Type theory

In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system.

See FO(.) and Type theory

See also

Knowledge representation languages

• Attempto Controlled English
• CIDOC Conceptual Reference Model
• CLIPS
• ClearTalk
• Common Logic
• Contextual Query Language
• CosmicOS
• CycL
• DARPA Agent Markup Language
• Description logic
• FO(.)
• Jess (programming language)
• KRL (programming language)
• Knowledge Interchange Format
• Knowledge Query and Manipulation Language
• LOOM (ontology)
• Lincos language
• Ontology Inference Layer
• Production Rule Representation
• R2ML
• RDF Schema
• Resource Description Framework
• Rule Interchange Format
• RuleML
• Semantic Web Rule Language
• Topic map
• Universal Networking Language

References

[1] https://en.wikipedia.org/wiki/FO(.)

Also known as FO-dot.

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