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Kripke semantics for higher-order type theory applied to constraint logic programming languages

Theoretical Computer Science, 2018
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James Lipton, Susana Nieva
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Higher-Order Logic and Type Theory

2022
This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type.
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Automated theorem proving for dependent typed theories via a translation to higher-order logic

2023
Higher-order logic (HOL) offers a simple syntax and semantics for representing and reasoning about typed mathematical concepts. There are many state-of-the-art automated theorem provers for HOL. But the type system of HOL lacks advanced features where types may depend on terms. This is useful as many mathematical notions are inherently dependent typed.
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