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• First-order_logic abstract "First-order logic is a formal system 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 is distinguished from propositional logic by its use of quantified variables.A theory about some topic is usually first-order logic together with a specified domain of discourse over which the quantified variables range, finitely many functions which map from that domain into it, finitely many predicates defined on that domain, and a recursive set of axioms which are 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.There are many deductive systems for first-order logic that are sound (all provable statements are true in all models) and complete (all statements which are true in all models are provable). Although the logical consequence relation is only semidecidable, much progress has been made in automated theorem proving in first-order logic. 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. Mathematical theories, such as number theory and set theory, have been formalized into first-order axiom schemata such as Peano arithmetic and Zermelo–Fraenkel set theory (ZF) respectively.No first-order theory, however, has the strength to describe fully and categorically structures with an infinite domain, such as the natural numbers or the real line. Categorical axiom systems for these structures can be obtained in stronger logics such as second-order logic.For a history of first-order logic and how it came to dominate formal logic, see José Ferreirós (2001).".
• First-order_logic wikiPageExternalLink index.html.
• First-order_logic wikiPageExternalLink 2687794.
• First-order_logic wikiPageExternalLink sici?sici=1079-8986%28200112%297%3A4%3C441%3ATRTMLI%3E2.0.CO%3B2-O.
• First-order_logic wikiPageExternalLink logic-classical.
• First-order_logic wikiPageExternalLink index.html.
• First-order_logic wikiPageExternalLink logic.
• First-order_logic wikiPageExternalLink ~podnieks.
• First-order_logic wikiPageExternalLink 978-1-4419-1220-6.
• First-order_logic wikiPageID "10983".
• First-order_logic wikiPageRevisionID "606428761".
• First-order_logic date "June 2013".
• First-order_logic hasPhotoCollection First-order_logic.
• First-order_logic id "p/p074360".
• First-order_logic reason "delocalize "citation needed" tag; the entire second paragraph is what is challenged".
• First-order_logic title "Predicate calculus".
• First-order_logic subject Category:Model_theory.
• First-order_logic subject Category:Predicate_logic.
• First-order_logic subject Category:Systems_of_formal_logic.
• First-order_logic type Ability105616246.
• First-order_logic type Abstraction100002137.
• First-order_logic type Cognition100023271.
• First-order_logic type Know-how105616786.
• First-order_logic type Logic105664069.
• First-order_logic type Method105660268.
• First-order_logic type PsychologicalFeature100023100.
• First-order_logic type System105661996.
• First-order_logic type SystemsOfFormalLogic.
• First-order_logic comment "First-order logic is a formal system 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 label "First-order logic".
• First-order_logic label "Lógica de primeira ordem".
• First-order_logic label "Lógica de primer orden".
• First-order_logic label "Prädikatenlogik erster Stufe".
• First-order_logic label "Rachunek predykatów pierwszego rzędu".
• First-order_logic label "Teoria del primo ordine".
• First-order_logic label "Логика первого порядка".
• First-order_logic label "منطق الرتبة الأولى".
• First-order_logic label "一阶逻辑".
• First-order_logic label "一階述語論理".
• First-order_logic sameAs Predikátová_logika_prvního_řádu.
• First-order_logic sameAs Prädikatenlogik_erster_Stufe.
• First-order_logic sameAs Λογική_πρώτου_βαθμού.
• First-order_logic sameAs Lógica_de_primer_orden.
• First-order_logic sameAs Logika_predikat_tingkat_pertama.
• First-order_logic sameAs Teoria_del_primo_ordine.
• First-order_logic sameAs 一階述語論理.
• First-order_logic sameAs 1차_논리.
• First-order_logic sameAs Rachunek_predykatów_pierwszego_rzędu.
• First-order_logic sameAs Lógica_de_primeira_ordem.
• First-order_logic sameAs m.02yz4.
• First-order_logic sameAs Q4055684.
• First-order_logic sameAs Q4055684.
• First-order_logic sameAs First-order_logic.
• First-order_logic wasDerivedFrom First-order_logic?oldid=606428761.
• First-order_logic isPrimaryTopicOf First-order_logic.