First-order logic

First-order logic is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. It is also known as first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic. First-order logic uses quantified variables over (non-logical) objects. This distinguishes it from propositional logic, which does not use quantifiers.

A theory about some topic is usually a first-order logic together with a specified domain of discourse over which the quantified variables range, finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of axioms believed to hold for those things. Sometimes "theory" is understood in a more formal sense, which is just a set of sentences in first-order logic.

The adjective "first-order" distinguishes first-order logic from higher-order logic in which there are predicates having predicates or functions as arguments, or in which one or both of predicate quantifiers or function quantifiers are permitted. In first-order theories, predicates are often associated with sets. In interpreted higher-order theories, predicates may be interpreted as sets of sets.

First-order

In mathematics and other formal sciences, first-order or first order most often means either:

In detail, it may refer to:

Mathematics

Differential equations

Friar

A friar is a member of one of the mendicant orders founded since the twelfth or thirteenth century; the term distinguishes the mendicants' itinerant apostolic character, exercised broadly under the jurisdiction of a superior general, from the older monastic orders' allegiance to a single monastery formalized by their vow of stability. The most significant orders of friars are the Dominicans, Franciscans, Augustinians and Carmelites.

Definition

Friars are different from monks in that they are called to live the evangelical counsels (vows of poverty, chastity and obedience) in service to society, rather than through cloistered asceticism and devotion. Whereas monks live in a self-sufficient community, friars work among laypeople and are supported by donations or other charitable support. A monk or nun makes their vows and commits to a particular community in a particular place. Friars commit to a community spread across a wider geographical area known as a province, and so they will typically move around, spending time in different houses of the community within their province.

Artificial intelligence

Artificial intelligence (AI) is the intelligence exhibited by machines or software. It is also the name of the academic field of study which studies how to create computers and computer software that are capable of intelligent behavior. Major AI researchers and textbooks define this field as "the study and design of intelligent agents", in which an intelligent agent is a system that perceives its environment and takes actions that maximize its chances of success.John McCarthy, who coined the term in 1955, defines it as "the science and engineering of making intelligent machines".

AI research is highly technical and specialized, and is deeply divided into subfields that often fail to communicate with each other. Some of the division is due to social and cultural factors: subfields have grown up around particular institutions and the work of individual researchers. AI research is also divided by several technical issues. Some subfields focus on the solution of specific problems. Others focus on one of several possible approaches or on the use of a particular tool or towards the accomplishment of particular applications.