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 can...

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

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

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

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

In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic...

philosophy of language, semantics, logic, and related fields. Propositions are the objects denoted by declarative sentences; for example, "The sky is blue"...

computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather...

published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally,...

In logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition...

offence Sentence (linguistics), a grammatical unit of language Sentence (mathematical logic), a formula not containing free variables Sentence (music)...

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...

false premises. Soundness has a related meaning in mathematical logic, wherein a formal system of logic is sound if and only if every well-formed formula...

the need to provide some treatment of the meaning of these sentences. The semantics of logic refers to the approaches that logicians have introduced to...

In mathematical logic, a ground term of a formal system is a term that does not contain any variables. Similarly, a ground formula is a formula that does...

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...

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

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

Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining...

In mathematical logic, a propositional variable (also called a sentence letter, sentential variable, or sentential letter) is an input variable (that can...

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

addresses the mathematical properties of formal systems of logic. However, it can also include attempts to use logic to analyze mathematical reasoning or...

foundational crisis of mathematics. The resolution of this crisis involved the rise of a new mathematical discipline called mathematical logic that includes set...

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

In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to...

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

branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. Sometimes...

In logic, especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language. In universal algebra, a signature...

fundamental theorems of mathematical logic which state inherent limitations of sufficiently powerful axiomatic systems for mathematics. The theorems were proven...

The term mathematical theory may refer to: Theory (mathematical logic), a collection of sentences in a formal language. Mathematical theory, a branch...