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...

zeroth-order logic. Sometimes, it is called first-order propositional logic to contrast it with System F, but it should not be confused with first-order logic...

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...

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...

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...

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

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...

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, 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...

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

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...

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

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...

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...

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

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

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

more expressive than propositional logic but less expressive than first-order logic. In contrast to the latter, the core reasoning problems for DLs are...

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

anticipations of temporal logic, and may imply an early, partially developed form of first-order temporal modal bivalent logic. Aristotle was particularly...

with first-order logic, e.g., with either Markov Logic Networks or Probabilistic Soft Logic. Other, non-probabilistic extensions to first-order logic to...

languages expressible by sentences of existential second-order logic; that is, second-order logic excluding universal quantification over relations, functions...

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))}...

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

three main directions: a graphical interface for first-order logic, a diagrammatic calculus of logics, and a graph-based knowledge representation and reasoning...

Linear logic is a substructural logic proposed by French logician Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the...