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

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...

In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers...

Propositional logic examines the inferential patterns of simple and compound propositions. First-order logic extends propositional logic by articulating...

and first-order logic. The sentences that are made true by a particular assignment are said to be satisfied by that assignment. In classical logic, no...

In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic in which all relation symbols[clarification...

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

classical logics such as second-order logic or infinitary logic are also studied, along with Non-classical logics such as intuitionistic logic. First-order logic...

theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts...

Extensions of First Order Logic is a book on mathematical logic. It was written by María Manzano, and published in 1996 by the Cambridge University Press...

contains logic symbols. Without proper rendering support, you may see question marks, boxes, or other symbols instead of logic symbols. In logic, a set...

In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification...

the translation of the English sentence "some men are bald" into first-order logic as ∃ x ( M ( x ) ∧ B ( x ) ) {\displaystyle \exists x(M(x)\land B(x))}...

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 understood...

commonly used system is classical logic. It consists of propositional logic and first-order logic. Propositional logic only considers logical relations...

self-reference", as in first-order logic and other logic uses, where it is contrasted with "allowing some self-reference" (higher-order logic) In detail, it may...

In first-order logic, a first-order theory is given by a set of axioms in some language. This entry lists some of the more common examples used in model...

In mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model...

formulas of propositional logic. The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, borrowing from...

answer. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. Logical systems are decidable if membership...

formal system (e.g., classical or intuitionistic propositional or first-order logics) every inconsistent theory is trivial.: 7  Consistency of a theory...

In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of...

Logic programming is a programming, database and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical...

logic, extended logics, and deviant logics. This classification is based on the idea that classical logic, i.e. propositional logic and first-order logic...

In logic, a predicate is a symbol that represents a property or a relation. For instance, in the first-order formula P ( a ) {\displaystyle P(a)} , the...

translation for propositional logic, and the Gödel–Gentzen translation and Kuroda's translation for first-order logic. The easiest double-negation translation...

second-order logic or higher-order logics. Quantifiers have been generalized beginning with the work of Andrzej Mostowski and Per Lindström. In a first-order...

of logics in contrast to one universally true logic. These logics can be divided into classical logic, usually identified with first-order logic, extended...

In mathematical logic and philosophy, Skolem's paradox is the apparent contradiction that a countable model of first-order set theory could contain an...

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