Linked from

The 75 pages that link to First-order logic, each with the reason it gives.

• Higher-order logicCompared with: It provides the baseline that higher-order quantifiers extend.

• Prenex normal formNarrower topic: Prenex form is a normal form for formulas in this logic.

• Symbolic logicBroader topic: It extends propositional logic by representing objects, properties, and quantified claims.

• Von Neumann–Bernays–Gödel set theoryNarrower topic: NBG’s axioms are expressed in a first-order language with class and set variables.

• Paris–Harrington theoremRelated: The theorem’s arithmetic formulation is expressed in first-order logic.

• Axiom schema of replacementNarrower topic: Each instance of replacement is expressed as a first-order axiom in the language of set theory.

• Description logicNarrower topic: Description logics draw on predicate logic while restricting syntax to preserve useful reasoning properties.

• Tarski's axiomsNarrower topic: Tarski's axioms quantify over points and state properties of their betweenness and congruence.

• Atomic formulaNarrower topic: Atomic formulas are the quantifier-free base cases in first-order formula construction.

• Automated reasoningRelated: It expresses general claims about objects and relations that reasoning systems can process.

• Herbrand's theoremNarrower topic: Herbrand's theorem links its quantified formulas to propositional reasoning.

• Skolem normal formNarrower topic: Skolem normal form is defined for formulas in this logic.

• Willard Van Orman QuineRelated: Quine used first-order logic to clarify ontological commitment and formal theory.

• Axiom of Empty SetRelated: The axiom is commonly expressed as a sentence in first-order logic.

• Courcelle's theoremCompared with: It is weaker than the monadic second-order language used to express the theorem's properties.

• Law of identityRelated: Its identity symbol lets the law be stated for objects within a formal language.

• Lindenbaum's lemmaNarrower topic: In first-order logic, the lemma extends consistent theories in a language with quantifiers.

• Löb's theoremNarrower topic: Löb’s theorem is formulated within formal systems whose reasoning can be represented logically.

• Skolem's paradoxRelated: Its quantifiers range over the model's domain, not over external collections of subsets.

• Craig interpolationRelated: Craig interpolation applies to first-order logical consequence as well as other formal systems.

• Jaakko HintikkaNarrower topic: Hintikka’s work on quantification and its limits begins from this central logical system.

• Knowledge (artificial intelligence)Related: Its variables and predicates express relationships among entities.

• Lindström's theoremBroader topic: It is the logic characterized by the theorem.

• Trakhtenbrot's theoremNarrower topic: The theorem identifies a boundary between finite and unrestricted models of this logic.

• Universe (mathematics and logic)Narrower topic: Its quantifiers range over a specified domain rather than over arbitrary properties.