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On formal specification of a proof tool
1991Tools and methods for the specification and design of computer systems are increasing in sophistication. Much current research and development is attempting to exploit this sophistication to improve the effectiveness of systems development practices.
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A formal proof of Gödel's theorem
Journal of Symbolic Logic, 1939I. The present paper contains a formal proof of the following theorem of the elementary system ⊨ [ 1 0 ] c:This theorem means that if there were a theorem of ⊢0 ( 3 2 ) 0 stating that there is no contradiction in ⊢2 ( 5 4 ) 2, we would have a contradiction in ⊢2 ( 5 4 ) 2.
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Formalizing the Proof of the Kepler Conjecture
2004The Kepler Conjecture states that the densest packing of spheres in three dimensions is the familiar cannonball arrangement. Although this statement has been regarded as obvious by chemists, a rigorous mathematical proof of this fact was not obtained until 1998.
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The translation of formal proofs into English
Artificial Intelligence, 1976Abstract The argument of a logical proof written up in English can be represented by a formal proof in symbolic logic; this formal proof can also be taken to represent the deep structure of the written proof. This paper describes a program which generates a written proof from such a representation.
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2014
Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive ...
Nederpelt, R., Geuvers, H.
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Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive ...
Nederpelt, R., Geuvers, H.
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Annotations in formal specifications and proofs
Formal Methods in System Design, 1994In order to exploit the connection between the formal and the informal aspects of modeling, the author proposes a system of annotations that can be used to incorporate semantic information concerning the domain being reasoned about into a formal proof environment. Annotations will serve as comments, labels, or proof directives. An implementation in the
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FORMAL PROOFS OF FUNCTIONAL BSP PROGRAMS
Parallel Processing Letters, 2003The Bulk Synchronous Parallel ML (BSML) is a functional language for BSP programming, a model of computing which allows parallel programs to be ported to a wide range of architectures. It is based on an extension of the ML language by parallel operations on a parallel data structure called parallel vector, which is given by intention. We present a new
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Formal Ontology to the Proof of Facts
2019After the work of Nicola Guarino, formal ontology is available today as a powerful conceptual tool for information systems modelling. In particular, for shared conceptual models, the ontological characterization of predicative symbols may help clarifying their intended semantics.
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Formal Verification of TLS 1.2 by Automatically Generating Proof Scores
Computers and Security, 2022Duong Dinh Tran, Kazuhiro Ogata
exaly