Knowra Predicate logic Predicate logic Predicate logic is a formal system for representing objects, their properties, and relations using predicates, variables, and quantifiers. It extends propositional logic by expressing how claims apply to individuals and groups.
First-order logic : A logic whose quantifiers range over individual objects, with predicates expressing their properties and relations. It is the most widely used form of predicate logic, quantifying over objects in a domain.
Propositional logic : A formal system that combines whole propositions using connectives such as and, or, and not. Predicate logic extends it by analyzing the internal structure of propositions.
Second-order logic : A logic that permits quantification over predicates, relations, or other properties as well as objects. It expands first-order predicate logic by quantifying over properties and relations.
Automated theorem proving : The use of computer programs to derive conclusions from formal axioms and inference rules. Proof systems mechanize reasoning from predicate-logic formulas.
Quantifier : An operator that specifies how many elements in a domain satisfy a formula. Quantifiers such as ∀ and ∃ determine how broadly a predicate claim applies.
Logical connective : An operator such as negation, conjunction, or implication that combines or modifies formulas. Connectives combine quantified statements into more complex predicate-logic formulas.
Higher-order logic : A family of formal systems that allow quantification over entities such as predicates or functions. Predicate logic is commonly contrasted with these systems because its quantifiers range over objects.
Model theory : The mathematical study of the relationships between formal languages and the structures that interpret them. It studies which structures make predicate-logic sentences true.
Predicate : An expression that assigns truth values to objects or tuples of objects. Predicates supply the properties and relations that predicate logic represents.
Term (logic) : An expression that denotes an object, formed from variables, constants, and sometimes function symbols. Terms provide the object arguments to which predicates are applied.
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