Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...

In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence...

In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first...

relational databases, in the form of relational models. In the context of mathematical logic, the term "model" was first applied in 1940 by the philosopher Willard...

In mathematical logic, independence is the unprovability of some specific sentence from some specific set of other sentences. The sentences in this set...

Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had...

foundation of mathematics has been eventually resolved with the rise of mathematical logic as a new area of mathematics. In this framework, a mathematical or logical...

portal Glossary of logic Józef Maria Bocheński List of notation used in Principia Mathematica List of mathematical symbols Logic alphabet, a suggested...

In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in a metalanguage. For example, typical judgments in first-order...

what consistent meant in traditional Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead. In a sound formal...

important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasoning about them...

the theorems are logical consequences. Mathematical logic, a subfield of mathematics and logic, uses mathematical methods and frameworks to study rules...

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence...

Igor Andreevich; Maksimova, Larisa (2003). Problems in Set Theory, Mathematical Logic, and the Theory of Algorithms. New York: Springer. p. 52. ISBN 0306477122...

identical at first, but fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance. A basic...

proof used in mathematics, a hearkening back to the Greek tradition. The development of the modern "symbolic" or "mathematical" logic during this period...

In mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic. For example, the modal logic S4...

First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy...

is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and...

the framework of classical logic. However, within that system 'true' and 'false' essentially function more like mathematical states such as binary 1s and...

This is a list of mathematical logic topics. For traditional syllogistic logic, see the list of topics in logic. See also the list of computability and...

list of mathematical terms; just a selection of typical terms of art that may be encountered. Logic – Study of correct reasoning Modal logic – Type of...

In logic, mathematics and linguistics, and ( ∧ {\displaystyle \wedge } ) is the truth-functional operator of conjunction or logical conjunction. The logical...

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The...

In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms,...

"Introduction to first-order logic", in Barwise, Jon (ed.), Handbook of Mathematical Logic, Studies in Logic and the Foundations of Mathematics, Amsterdam: North-Holland...

1967. Mathematical Logic Reprinted by Dover, 2002. ISBN 0-486-42533-9 Smullyan, Raymond M., 1961. Theory of Formal Systems: Annals of Mathematics Studies...

to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic...

timeline of mathematical logic; see also history of logic. 1847 – George Boole proposes symbolic logic in The Mathematical Analysis of Logic, defining what...

calculus Predicate (mathematical logic) Predicate logic Predicate variable Quantification Second-order predicate Sentence (mathematical logic) Universal instantiation...