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Sequent Calculus, Derivability, Provability. Gödel's Completeness Theorem

Marco Caminati (2011)

Formalized Mathematics

Fifth of a series of articles laying down the bases for classical first order model theory. This paper presents multiple themes: first it introduces sequents, rules and sets of rules for a first order language L as L-dependent types. Then defines derivability and provability according to a set of rules, and gives several technical lemmas binding all those concepts. Following that, it introduces a fixed set D of derivation rules, and proceeds to convert them to Mizar functorial cluster registrations...

Set arithmetic and the enclosing problem in dynamics

Marian Mrozek, Piotr Zgliczyński (2000)

Annales Polonici Mathematici

We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.

Some key research problems in automated theorem proving for hardware and software verification.

Matt Kaufmann, J. Strother Moore (2004)

RACSAM

This paper sketches the state of the art in the application of mechanical theorem provers to the verification of commercial computer hardware and software. While the paper focuses on the theorem proving system ACL2, developed by the two authors, it references much related work in formal methods. The paper is intended to satisfy the curiosity of readers interested in logic and artificial intelligence as to the role of mechanized theorem proving in hardware and software design today. In addition,...

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