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The Laws of Natural Deduction in Inference by DNA Computer [PDF]
The Scientific World Journal, 2014 We present a DNA-based implementation of reaction system with molecules encoding elements of the propositional logic, that is, propositions and formulas.
Łukasz Rogowski, Petr Sosík
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Natural Deduction and the Isabelle Proof Assistant [PDF]
Electronic Proceedings in Theoretical Computer Science, 2018 We describe our Natural Deduction Assistant (NaDeA) and the interfaces between the Isabelle proof assistant and NaDeA. In particular, we explain how NaDeA, using a generated prover that has been verified in Isabelle, provides feedback to the student, and
Jørgen Villadsen +2 more
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2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science, 2015 We introduce a Hyper Natural Deduction system as an extension of Gentzen's Natural Deduction system. A Hyper Natural Deduction consists of a finite set of derivations which may use, beside typical Natural Deduction rules, additional rules providing means for communication between derivations. We show that our Hyper Natural Deduction system is sound and
Arnold Beckmann, Norbert Preining
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Improving legibility of natural deduction proofs is not trivial [PDF]
Logical Methods in Computer Science, 2014 In formal proof checking environments such as Mizar it is not merely the validity of mathematical formulas that is evaluated in the process of adoption to the body of accepted formalizations, but also the readability of the proofs that witness validity ...
Karol Pąk
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Uniform Proofs of Normalisation and Approximation for Intersection Types [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 We present intersection type systems in the style of sequent calculus, modifying the systems that Valentini introduced to prove normalisation properties without using the reducibility method.
Kentaro Kikuchi
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Classical Proofs as Parallel Programs [PDF]
Electronic Proceedings in Theoretical Computer Science, 2018 We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded middle law. The
Federico Aschieri +2 more
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Application of natural deduction in Renaissance geometry [PDF]
Argument, 2014 My goal here is to provide a detailed analysis of the methods of inference that are employed in De prospectiva pingendi. For this purpose, a method of natural deduction is proposed.
Ryszadr Mirek
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Structural Rules in Natural Deduction with Alternatives
Bulletin of the Section of Logic, 2023 Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives.
Greg Restall
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Natural Deduction Assistant (NaDeA) [PDF]
Electronic Proceedings in Theoretical Computer Science, 2019 We present the Natural Deduction Assistant (NaDeA) and discuss its advantages and disadvantages as a tool for teaching logic. NaDeA is available online and is based on a formalization of natural deduction in the Isabelle proof assistant. We first provide
Jørgen Villadsen +2 more
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Gödel’s Natural Deduction [PDF]
Studia Logica, 2017 22 ...
Kosta Došen, Miloš Adžić
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