Article should clarify syntactic-semantic distinction here, e.g. second-order logic can be interpreted as a many-sorted first-order logic, so syntactically it could be argued that it's not more expressive, and it admits categorical axiomatizations only using full semantics, but using Henkin semantics it is a conservative extension of the typical semantics for first-order logic. So really the article needs to clarify whether it is discussing FOL exclusively as a syntactic system, or as a syntactic and semantic system, and in either case clarify in which senses "extensions" of first-order logic are being assumed to extend it .
Predicate logic
koleksi sistem formal yang digunakan dalam bidang matematika, linguistik dan ilmu komputer
Lógica de primeira ordem
一阶逻辑
First-order logic
Logika predikat tingkat pertama
Rachunek predykatów pierwszego rzędu
使用於數學、哲學、語言學及電腦科學中的一種形式系統
January 2023
Λογική πρώτου βαθμού
Predikátová logika prvního řádu
Predicate calculus
Första ordningens logik
méthode formelle, utilise des variables sur des objets non logiques et permet l'usage de phrases qui contiennent des variables; seules les variables sont quantifiées
sistema formale usato in matematica, filosofia, linguistica e informatica
一階述語論理
Teilgebiet der mathematischen Logik: Familie logischer Systeme
Lògica de primer ordre
1차 논리
引数として変数を取る関数や述語の量化は許さず、個体のみの量化を許す述語論理のこと
در منطق مرتبه اول جملاتی وجود دارد که از «متغیرهای سور داده شده» روی اشیای غیر منطقی استفاده می‌کند.
منطق الرتبة الأولى
Predikatkalkulo
collection of formal systems used in mathematics, philosophy, linguistics, and computer science
Teoria del primo ordine
Логика первого порядка
Логіка першого порядку
Prädikatenlogik erster Stufe
Lehen mailako logika
Lógica de primer orden
sistema lógico que estende a lógica proposicional
sistema formal diseñado para estudiar la inferencia en los lenguajes de primer orden
Calcul des prédicats