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 and, sometimes, stronger semantics.
Higher-order logic
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In mathematics and logic, a higher-order logic is a form of logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Wikipedia
Aug 1, 2019 · Variables are assigned types, just as in second-order logic we have variables for individual type, relation type and function type. In a higher ...
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Jan 25, 2019 · Higher-order logic, or simple type theory as it is often called, is then obtained from turning the above into an inductive definition allowing ...
The semantics of formulas of higher order logic is defined formally like for second order logic, except that an assignment over a structure with universe M maps ...
May 31, 2019 · Gödel's speed up theorems seem to say that higher order logics offer shorter shortest proofs of various propositions in number theory.
Aug 20, 2024 · A higher-order logic is any logic which features higher-order predicates, which are predicates of predicates or of operations. If we think of a ...
Jul 14, 2023 · A logic which doesn't just quantify over individuals (like Classical FOL does), but also over eg properties.
High-order logic refers to a variant of set theory that can be expressed in first-order logic. It allows for the representation of complex logical ...
Dec 4, 2014 · In the context of higher-order arithmetic, there are many natural third-order statements. In arithmetic, quantifiers over natural numbers are ...