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

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...

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...

logic. It is also called (first-order) propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic....

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

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...

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...

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...

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

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 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...

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...

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...

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

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

specifically propositional and first-order logic, as opposed to the other forms of classical logic. Most semantics of classical logic are bivalent, meaning all...

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

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

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

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

Look up Appendix:Glossary of logic in Wiktionary, the free dictionary. This is a glossary of logic. Logic is the study of the principles of valid reasoning...

soundness of the deduction rule described in the previous section. In first-order logic, a substitution is a total mapping σ: V → T from variables to terms;...

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

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

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

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...

view, structures are the objects used to define the semantics of first-order logic, cf. also Tarski's theory of truth or Tarskian semantics. For a given...

theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. The completeness theorem...