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Automated theorem proving for dependent typed theories via a translation to higher-order logic
2023Higher-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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Higher-Order Logic and Type Theory
2022This 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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Combining Higher-Order Logic with Set Theory Formalizations
Journal of Automated Reasoning, 2023Cezary Kaliszyk +2 more
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Boolean algebras with a category theory in a weak second order logic
Algebra and Logic, 1971E A Palyutin, Palyutin E A
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The Ackermann approach for modal logic, correspondence theory and second-order reduction
Journal of Applied Logic, 2012Renate A Schmidt
exaly
A semantic study of the first-order predicate logic with uncertainty involved
Fuzzy Optimization and Decision Making, 2014Xingfang Zhang
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An algorithm for computing theory prime implicates in first order logic
International Journal of Information and Communication Technology, 2007Arindama Singh
exaly