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

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...

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

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

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

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...

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

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

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

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

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

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...

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...

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

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...

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...

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

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

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

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...

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...

(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...

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

work on natural deduction, and included applications for modal and second-order logic. In natural deduction, a proposition is deduced from a collection...

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

respect to a fixed logic defining the syntax of allowed symbols, such as first-order logic, second-order logic or propositional logic. Rather than being...

first-order logic of graphs concerns sentences in which the variables and predicates concern individual vertices and edges of a graph, while monadic second-order...