Review of 'Proofs and Refutations'

Proofs and refutations: Imre Lakatos, Ed

Proofs and refutations: Imre Lakatos, Edited by John Worral and Elie Zahar. Cambridge University Press, 1976, 174 pp.

✍ Reuben Hersh 📂 Article 📅 1978 🏛 Elsevier Science 🌐 English ⚖ 179 KB

Aristotle and a refutation of naturalism

✍ Eugene E. Ryan 📂 Article 📅 1972 🏛 Springer 🌐 English ⚖ 268 KB

Inheritance of proofs

✍ Hofmann, Martin; Naraschewski, Wolfgang; Steffen, Martin; Stroup, Terry 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 176 KB

The Curry-Howard isomorphism, a fundamental property shared by many type theories, establishes a direct correspondence between programs and proofs. This suggests that the same structuring principles that ease programming should be useful for proving as well. To exploit object-oriented structuring m

Logic of proofs and provability

✍ Tatiana Yavorskaya (Sidon) 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 216 KB

In the paper the joint Logic of Proofs and Provability LPP is presented that incorporates both the modality for provability (Israel J. Math. 25 (1976) 287-304) and the proof operator <t=F representing the proof predicate "t is a proof of F " (Technical Report No. CFIS 95-29, Cornell University, 1995

Refutation of a theorem of Diliberto and

Refutation of a theorem of Diliberto and Straus

✍ V. A. Medvedev 📂 Article 📅 1992 🏛 SP MAIK Nauka/Interperiodica 🌐 English ⚖ 157 KB

Complexity of Null- and Positivstellensa

Complexity of Null- and Positivstellensatz proofs

✍ Dima Grigoriev; Nicolai Vorobjov 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 91 KB

We introduce two versions of proof systems dealing with systems of inequalities: Positivstellensatz refutations and Positivstellensatz calculus. For both systems we prove the lower bounds on degrees and lengths of derivations for the example due to Lazard, Mora and Philippon. These bounds are sharp,