Welcome to our site devoted to the notion of refutation (rejection) in logic. This is a project of the researchers from the University of Zielona Góra, Poland.

**Refutation in logic has many aspects. This site aims to describe the multifaceted nature of refutation research (and as such is a work in progress). The Resources tab contains (successively extended) list of articles, expository papers, online pointers, computer code etc. Click on The People tab for a list of researchers past and present dealing with various aspects of refutation. This section also contains those directly involved in the creation of this site. The Events tab lists relevant conferences, workshops, etc, including The Goranko Challenge.**

**Comments? Suggestions? Click on the About tab to let us know!**

**NEWS:**

Valentin Goranko and Tomasz Skura, *Refutation systems in the finite* (Preprint) [pdf]

Valentin Goranko, Gabriele Pulcini and Tomasz Skura *Refutation Systems: An Overview and Some Applications to Philosophical Logics*, Knowledge, Proofs and Dynamics: The 4th Asian Workshop on Philosophical Logic,Fenrong Liu, Hiroakira Ono, Junhua Yu (editors). (Preprint) [pdf]

Tomasz Skura, *Implicational Logic, Relevance and Refutability*, Logic and Logical Philosophy [pdf]

This section contains references to some of the works dealing with various aspects of refutation. A summary and a list of keywords were added, whenever possible. Contact us if you feel that there are publications that we have not included and which should make it to one of the lists below.

Classics contains classical papers in the area.

Expository papers is the place to start for those new to the topic of refutation.

Links offers a selection of links to the websites of researchers and refutation-related events, resources etc.

This list contains research papers on refutation published in or after 2001.

- R. Caferra and N. Peltier, Accepting/Rejecting Propositions From Accepted/Rejected Propositions: A Unifying Overview,
*International Journal of Intelligent Systems*, 23:999–1020, 2008. [pdf] - R. Gore and L. Postniece, Combining Derivations and Refutations for Cut-free Completeness in Bi-intuitionistic Logic,
*Journal of Logic and Computation*, 20(1):233–260, 2010. [pdf] - J. P. Goudsmit, Admissibility and Refutation. Some Characterisations of Intermediate Logics,
*Archive for Mathematical Logic*, 53(7–8):779–808, 2014. [pdf] - T. Skura, Refutations, Proofs, and Models in the Modal Logic K4,
*Studia Logica*70:193–204, 2002. - T. Skura, Rules and Refutation Rules for the Logic of Finite n-ary Trees,
*Journal of Logic and Computation*14:429–435, 2004. - T. Skura, Refutation Systems in Propositional Logic, [in:] D. Gabbay and F. Guenthner (ed.),
*Handbook of Philosophical Logic*, Volume 16, Springer 2011, 115–157. - T. Skura,
*Refutation Methods in Modal Propositional Logic*, Wydawnictwo Naukowe Semper, Warszawa, 2013. - T. Skura, What is a refutation system? [in:] A. Moktefi, A. Moretti, F. Schang (ed.),
*Let's Be Logical*, London, College Publications, 2016. - R. Sochacki, Rejected Axioms for the Nonsense Logic and the k-valued Logic of Sobociński,
*Logic and Logical Philosophy*, 17:321–327, 2008. [pdf] - R. Sochacki, Refutation System for a System of Nonsense Logic,
*Logic and Logical Philosophy*, 20:233–239, 2011. [pdf] - J. Oetsch and H. Tompits, Gentzen-Type Refutation Systems for Three-Valued Logics with an Application to Disproving Strong Equivalence, [in:] J. P. Delgrande and W. Faber (eds),
*Logic Programming and Nonmonotonic Reasoning. LPNMR 2011. Lecture Notes in Computer Science*, vol 6645. Springer, Berlin, Heidelberg, 2011. [pdf]

This list contains research papers on refutation published before 2001.

- X. Caicedo, A Formal System for the Non-Theorems of the Propositional Calculus,
*Notre Dame Journal of Formal Logic*, 19, 1978. [pdf] - R. Dutkiewicz, The Method of Axiomatic Rejection for the Intuitionistic Propositional Logic,
*Studia Logica*, 48(4):449–459, 1989. [pdf] - V. Goranko, Proving Unprovability in some Normal Modal Logics.
*Bulletin of the Section of Logic*, 20(1), 1991. [pdf] - V. Goranko, Refutation Systems in Modal Logics.
*Studia Logica*, 53, 1994. [pdf] - T. Hailperin, A Complete Set of Axioms for Logical Formulas Invalid in Some Finite Domains,
*Zeitschrift für Mathematische Logik und Grundlagen der Mathematik*, 7:84–96. [pdf] - E. G. K. Lopez-Escobar, Refutability and Elementary Number Theory,
*Indigationes Mathematicae*, 75(4):362–374, 1972. [pdf] - G. Mints, Gentzen-type Systems and Resolution Rules,
*Lecture Notes in Computer Science*, 417:198–231, 1990. [djvu] - S. G. Morgan, Sentential Calculus for Logical Falsehoods,
*Notre Dame Journal of Formal Logic*, 14(3):347–353, 1973. [pdf] - W. Schönfeld, Proof Search for Unprovable Formulas, [in:] B. Neumann (ed)
*GWAI-83. Informatik-Fachberichte*, vol 76. Springer, Berlin, Heidelberg, 1983. [pdf] - D. Scott, Completeness Proofs for the Intuitionistic Sentential Calculus, [in:]
*Summaries of Talks Presented at the Summer Institute of Symbolic Logic*, Cornell University 1957, second edition Princeton, 1960, 231–241. - T. Skura, A Complete Syntactical Characterization of the Intuitionistic Logic,
*Reports on Mathematical Logic*, 23:75–80, 1989. - T. Skura, A New Criterion of Decidability for Intermediate Logics,
*Bulletin of the Section of Logic*, 19:10–14, 1990. - T. Skura, On Pure Refutation Formulations of Sentential Logics,
*Bulletin of the Section of Logic*, 19:102–107, 1990. - T. Skura, On Decision Procedures for Sentential Logics,
*Studia Logica*, 50:173–179, 1991. - T. Skura, Refutation Calculi for Certain Intermediate Propositional Logics,
*Notre Dame Journal of Formal Logic*, 33:552–560, 1992. - T. Skura, Refutation Rules for Three Modal Logics,
*Bulletin of the Section of Logic*, 21:31–32, 1992. - T. Skura, Some Results Concerning Refutation Procedures,
*Acta Universitatis Wratislaviensis. Logika*, 15:83–95, 1993. - T. Skura, Characterizing Propositional Logics by Formulas, [in:] J. Woleński (ed.),
*Philosophical Logic in Poland*, Kluwer, 239–245, 1994. - T. Skura, Syntactic Refutations Against Finite Models in Modal Logic,
*Notre Dame Journal of Formal Logic*, 35:595–605, 1994. - T. Skura, A Łukasiewicz-style Refutation System for the Modal Logic S4,
*Journal of Philosophical Logic*, 24:573–582, 1995. - T. Skura, Some Aspects of Refutation Rules,
*Reports on Mathematical Logic*, 29:109–116, 1995. - T. Skura, Refutations and proofs in S4, [in:] H. Wansing (ed.),
*Proof Theory of Modal Logic*, Kluwer, 1996, 45–51. - T. Skura, A Pure Refutation Calculus for the Intuitionistic Propositional Logic,
*Acta Universitatis Wratislaviensis. Logika*, 18:123–127, 1998. - T. Skura, Aspects of Refutation Procedures in the Intuitionistic Logic and Related Modal Systems, Wydawnictwo Uniwersytetu Wrocławskiego, Wrocław, 1999.
- J. Słupecki, On Aristotelian Syllogistic,
*Journal of Symbolic Logic*, 17(3): 210–211, 1952. [pdf] - J. Słupecki and G. Bryll, Proof of Ł-decidability of Lewis System S5,
*Studia Logica*, 32:99–105, 1973. [pdf] - W. Staszek, On Proofs of Rejection,
*Studia Logica*, 29(1):17–23, 1971. [pdf] - A. M. Tamminga, Logics of Rejection: Two Systems of Natural Deduction,
*Logique et Analyse*, 146:169–208, 1994. [pdf] - M. Tiomkin, Proving unprovability,
*Proceedings of the Third Annual Symposium on Logic in Computer Science*, 22–26, 1988. [pdf]

This list contains papers providing an overview of some aspect of refutation.

- G. Pulcini, Some Philosophical Aspects of Refutation. [pdf]
- T. Skura, Formal Refutation Systems. [pdf]
- U. Wybraniec-Skardowska, Rejection in Łukasiewicz's and Słupecki's Sense, [in:] A. Garido, U. Wybraniec-Skardowska (eds.),
*The Lvov-Warsaw School, Past and Present*, Springer-Birkhäuser Cham, Switzerland, 575–597. [pdf]

During the Refutation Symposium held in Poznań in 2018, Valentin Goranko (www) issued a challenge to the refutation community offering a tanglible prize for the winner. For details see: **The Goranko Challenge**. Entries and inquiries can be send at the e-mail address provided in the About section.

Organised as part of Poznań Reasoning Week, the Symposium brought together researchers from various subfields of logic. The Symposium was a joint effort of The Institute of Philosophy in Zielona Góra and The Institute of Psychology in Poznań. The book of abstracts is available here.

Chair of Logic and Methodology of Science,

Institute of Philosophy,

University of Zielona Góra

71a Wojska Polskiego

Zielona Góra 65-762

Poland

e-mail inquiries: adam DOT trybus AT gmail DOT com (Adam Trybus)

Admin: adam DOT trybus AT gmail DOT com (also for general inquiries)