first-order logic

Monadic Predicate Logic

Monadic predicate logic, a subset of first-order logic, focuses on predicates with a single argument. It's used to express properties…

4 days ago

Monadic First-Order Logic

Monadic first-order logic simplifies first-order logic by using only predicates with a single argument. This focuses on the properties of…

4 days ago

Matrix in Logic

The matrix is the quantifier-free part of a formula after it's converted to prenex normal form. It's the core propositional…

4 days ago

Many-Sorted Logic

Many-sorted logic enhances first-order logic by introducing multiple domains. Variables and quantifiers are typed, specifying the sort of objects they…

4 days ago

Löwenheim–Skolem Theorem

A fundamental theorem in mathematical logic stating that any countable theory with an infinite model has models of all infinite…

4 days ago

Independence-Friendly Logic

Independence-Friendly (IF) logic extends first-order logic, enabling richer expressions of quantifier scope and dependence. It's particularly useful in game-theoretical semantics…

4 days ago

Inclusive First-Order Logic Explained

Inclusive first-order logic is a flexible variant that permits empty domains, unlike standard first-order logic which mandates at least one…

4 days ago

Higher-Order Logic

Higher-order logic extends first-order logic by enabling quantification over predicates and other higher-order entities. It offers greater expressive power for…

4 days ago

Henkin Semantics

Henkin semantics offers a flexible alternative to standard first-order semantics, allowing quantifiers to range over restricted domains within models. This…

4 days ago

Understanding Formulas in Formal Languages

A formula is a true or false expression in a formal language. It uses variables and logical connectives to construct…

4 days ago