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Science Mathematics Foundations Mathematical logic

Mathematical logic

Analytical hierarchy

Concept in mathematical logic and set theory

Arithmetical hierarchy

Hierarchy of complexity classes for formulas defining sets

Mathematical logic concept

Statement that is taken to be true

A formula in the metalanguage of an axiomatic system in which one or more schematic variables appear

Boolean algebra

Manipulation of variables taking only "true" and "false" as values

Inference that says that a conditional statement is logically equivalent to its contrapositive

Existential quantification

Logical quantification stating that a statement holds for at least one object

First-order logic

Type of logical system

Free variables and bound variables

Classification of variables in a logic formula based on whether or not they are inside the scope of a quantifier

Higher-order logic

Form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics

Logical connective

Intuitionistic logic

Various systems of symbolic logic

Graphical method to simplify Boolean expressions

Logical connective

Symbol connecting sentential formulas in logic

Material conditional

Logical connective

Mathematical logic

Subfield of mathematics

Rule of logical inference

Rule of logical inference

Theorem in computability theory

Prenex normal form

First-order formula consisting of a string of quantifiers and bound variables followed by a quantifier-free part

Principle of explosion

Theorem which states that any statement can be proven from a contradiction

Proof by contradiction

Form of indirect proof that establishes the truth or validity of a proposition

Propositional calculus

Logical study of propositions (whether they are true or false) that are formed by other propositions with the use of logical connectives

Quantifier (logic)

Mathematical use of "for all" and "there exists"

Rule of inference

Method of deriving conclusions

Logical operation

Skolem normal form

Formalism of first-order logic

Mathematical table used in logic

Concept in mathematical logic

Universal quantification

Mathematical use of "for all"

Well-formed formula

Finite sequence of symbols from a given alphabet that is part of a formal language