Independence-Friendly (IF) logic extends first-order logic, enabling richer expressions of quantifier scope and dependence. It's particularly useful in game-theoretical semantics…
Inclusive first-order logic is a flexible variant that permits empty domains, unlike standard first-order logic which mandates at least one…
Higher-order logic extends first-order logic by enabling quantification over predicates and other higher-order entities. It offers greater expressive power for…
Henkin semantics offers a flexible alternative to standard first-order semantics, allowing quantifiers to range over restricted domains within models. This…
Gödel's First Incompleteness Theorem states that any consistent formal system capable of basic arithmetic contains true statements that are unprovable…
First-order variables are placeholders for individuals within a specific domain in first-order logic. They are fundamental to expressing general statements…
A first-order theory formalizes mathematical reasoning using first-order logic. It defines relationships between individuals, properties, and relations, forming the foundation…
First-order logic (FOL) is a formal system using quantifiers like 'for all' and 'there exists' to reason about individuals. It's…
FDE is a logical system that allows propositions to be both true and false, or neither, rejecting the law of…
A fundamental theorem in mathematical logic asserting that if every finite subset of a set of sentences is satisfiable, then…