The Notion of Refutation in Contemporary Logic (in Polish)

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Karolina Rożko

Abstract

The main aim of this article is to show how the notion of refutation has been changing in logic for the last few years. The idea of refutation was known to Aristotle, but the formal concept was introduced by Jan Łukasiewicz. Afterwards this notion was investigated by the Polish group of logicians headed by Jerzy Słupecki. Several interesting articles about refutation have appeared in the last years. In this article, I present in outline the history of the notion of refutation and I discuss  recent applications of refutation systems both in the theoretical and practical approach.

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“The Notion of Refutation in Contemporary Logic (in Polish)”. 2014. Diametros, no. 41 (September): 115-26. https://doi.org/10.13153/diam.41.2014.653.
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Author Biography

Karolina Rożko, University of Zielona Góra

Karolina Rożko, MA
University of Zielona Góra
Institut of Philosophy
al. Wojska Polskiego 71A,
65-762 Zielona Góra
e-mail: krozko@gmail.com

How to Cite

“The Notion of Refutation in Contemporary Logic (in Polish)”. 2014. Diametros, no. 41 (September): 115-26. https://doi.org/10.13153/diam.41.2014.653.
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References

Bryll [1996] – G. Bryll, Metody odrzucania wyrażeń, Akademicka Oficyna Wydawnicza PLJ, Warszawa 1996.

Craig [1957] – W. Craig, Three uses of the Herbrand-Gentzen Theorem in Relating Model Theory and Proof Theory, „Journal of Symbolic Logic” (3) 1957, s. 269-285.

Dutkiewicz [1988] – R. Dutkiewicz, Z badań nad metodą tablic semantycznych, Wyd. KUL, Lublin 1988.

Fiorentini [2012] – C. Fiorentini, Terminating sequent calculi for proving and refuting formulas in S4, „Journal of Logic and Computation”, 2012, doi: 10.1093/logcom/exs053.

Goranko [1994] – V. Goranko, Refutation Systems in Modal Logic, „Studia Logica” (53) 1994, s. 299-324.

Goré i Postniece [2008] – R. Goré i L. Postniece, Combining Derivations and Refutations for Cut-free Completeness in Bi-intuitionistic Logic, „Journal of Logic and Computation” (20) 2010, s. 233-260.

Kovács i Voronkov [2009] – L. Kovács i Voronkov, Interpolation and symbol elimination, [w:] Proceedings of Conference on Automated Deduction (CADE), Springer, 2009, s. 199-213.

Łukasiewicz [1988] – J. Łukasiewicz, Sylogistyka Arystotelesa z punktu widzenia współczesnej logiki formalnej, tłum. A. Chmielewski, Wyd. PWN, Warszawa 1988 r.

Mints [1988] – Mints G., Gentzen-type systems and resolution rules. Part I. Propositional logic, „Lecture Notes in Computer Science” (417) 1988, s. 198-231.

Pinto i Dyckhoff [1995] – L. Pinto i R. Dyckhoff, Loop-free construction of counter models for intuitionistic propositional logic, „Symposia Gaussiana” 1995, s. 225-232.

Scott [1960] – D. Scott, Completeness Proofs for the Intuitionistic Sentential Calculus, [w:] Summaries of talks presented at the Summer Institute for Symbolic Logic: Cornell University 1957 2nd edition, Communications Research Division, Institute for Defense Analyses, Princeton NJ 1960, s. 231-241.

Skura [1999] – T. Skura, Aspects of Refutation Procedures in the Intuitionistic Logic and Related Modal Systems, Wyd. Uniwersytetu Wrocławskiego, Wrocław 1999.

Skura [2002] – T. Skura, Refutations, Proofs, and Models in the Modal Logic K4, „Studia Logica” (70) 2002, s. 193-204.

Skura [2011] – T. Skura, Refutation Systems in Propositional Logic, [w:] Handbook of Philosophical Logic (16), red. D.M. Gabbay and F. Guenthner, Springer, Heidelberg/Dordrecht/New York/London 2011, s. 115-157.

Skura [2013] – T. Skura, What is a refutation system?, [w:] Let's Be Logical, red. Moktefi, A., Moretti, A., Schang F., College Publications, w druku.

Słupecki, Bryll, Wybraniec-Skardowska [1972] – J. Słupecki, G. Bryll, U. Wybraniec-Skardowska, Theory of rejected propositions. Part II, „Studia Logica” (30) 1971, s. 97-115.

Weissenbacher [2010] – G. Weissenbacher, Program Analysis with Interpolants, PhdThesis in Magdalen College, Trinity Term, 2010.