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...

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

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

A second-order propositional logic is a propositional logic extended with quantification over propositions. A special case are the logics that allow second-order...

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

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...

derivative is the second Second-order logic, an extension of predicate logic Second-order perturbation, in perturbation theory Second-order cybernetics, the...

Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical...

(1924), von Neumann (1927) and Herbrand (1931). Stronger logics, such as second-order logic, are not complete. A consistency proof is a mathematical proof...

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

{\displaystyle P} . Other quantifiers are only definable within second-order logic or higher-order logics. Quantifiers have been generalized beginning with the...

In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Zeroth-order logic (propositional...

languages are precisely the ones definable in a particular monadic second-order logic called S1S. Wolfgang Thomas, "Automata on infinite objects." In Jan...

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...

extensions into a specific form of logic, many-sorted logic. Beyond many-sorted logic, its topics include second-order logic (including its incompleteness...

(graph theory) In logic, model theory and type theory: Zeroth-order logic First-order logic Second-order logic Higher-order logic Order (journal), an academic...

Independence-friendly logic (IF logic; proposed by Jaakko Hintikka and Gabriel Sandu [fr] in 1989) is an extension of classical first-order logic (FOL) by means...

first-order logic, the most important case, it follows from the completeness theorem that the two meanings coincide. In other logics, such as second-order logic...

in first-order logic. But they can be expressed in second-order logic with only a few axioms. But despite this advantage, first-order logic is still much...

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

Dependence logic is a logical formalism, created by Jouko Väänänen, which adds dependence atoms to the language of first-order logic. A dependence atom...

is the set of languages expressible in existential second-order logic—that is, second-order logic restricted to exclude universal quantification over...

Zorn's lemma.) In second-order logic, however, the well-ordering theorem is strictly stronger than the axiom of choice: from the well-ordering theorem one may...

In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative...

mathematics, logicism is a programme comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some...

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

characterize first-order logic. In general, the Löwenheim–Skolem theorem does not hold in stronger logics such as second-order logic. In its general form...

explicitly included in first-order theories when equality is treated this way. This second approach is sometimes called first order logic with equality, but many...