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. Second-order logic is in turn extended by higher-order logic and type theory. First-order logic quantifies only variables that range...

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

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 is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-order...

Higher order grammar (HOG) is a grammar theory based on higher-order logic. It can be viewed simultaneously as generative-enumerative (like categorial...

that someone has these kinds of mental states. Higher-order logics do not directly apply classical logic to certain new sub-fields within philosophy but...

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

higher-order logics over polymorphic and dependent types was developed largely after this book was published. Jacobs, Bart (1999). Categorical Logic and...

case with the schemata of Induction and Replacement mentioned above. Higher-order logic allows quantified variables to range over all possible properties...

logic programming and programming language type system implementation, especially in Hindley–Milner based type inference algorithms. In higher-order unification...

character of logic. On this view, first-order logic constitutes a logical system. But this would also mean that higher-order "logics" are not logics strictly...

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...

semantics is an important topic in higher order logic. The interpretations of propositional logic and predicate logic described above are not the only possible...

The logics studied before the development of first-order logic, for example Frege's logic, had similar set-theoretic aspects. Although higher-order logics...

HOL (Higher Order Logic) denotes a family of interactive theorem proving systems using similar (higher-order) logics and implementation strategies. Systems...

Isabelle automated theorem prover is a higher-order logic (HOL) theorem prover, written in Standard ML and Scala. As a Logic for Computable Functions (LCF) style...

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))}...

elimination forms for higher-order logic is beyond the scope of this article. It is possible to be in-between first-order and higher-order logics. For example...

recognized by formulas of higher-order logic. Higher-order logic is an extension of first-order logic and second-order logic with higher-order quantifiers. There...

higher-order logics are logics in the strict sense. When understood in a wide sense, logic encompasses both formal and informal logic. Informal logic...

mathematics comparable to first-order logic plus set theory. It is a form of higher-order logic and closely related to the logics of the HOL theorem prover...

Erlang. Prolog#Higher-order programming Higher-order logic programming Reynolds, John C. (1972). "Definitional Interpreters for Higher-Order Programming...

building-blocks of propositional formulas, used in propositional logic and higher-order logics. Formulas in logic are typically built up recursively from some propositional...

(higher-order logic) didn't meet the requirements to be a logic, saying that it was "set theory in disguise". Classical logic is the standard logic of...

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...

{\displaystyle x} . In first-order logic, they can be more properly called metalinguistic variables. In higher-order logic, predicate variables correspond...

set theory. This database starts with higher-order logic and derives equivalents to axioms of first-order logic and of ZFC set theory. The Metamath website...

More expressive logics, such as higher-order logics, allow the convenient expression of a wider range of problems than first-order logic, but theorem proving...

In mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following: takes one or more functions as...