100 Years of Refutation in Logic
Schedule: 08 April 2022
Schedule: 08 April 2022
9:30 -9:45 Introduction
9:45 - 10:30 Keynote talk Valentin Goranko. Hybrid Deduction–Refutation Systems: Proofs and Refutations Getting Married.
10:30 -11:00 Paola Cattabriga. Refutability as Recursive as Provability.
11:000 - 11:30 Coffee brake
11:30 - 12:15 Keynote Talk Urszula Wybraniec-Skardowska. Refutation (Rejection) in Traditional and Modal Logics.
12:15 - 12:45 Jana Chadt and Hans Tompits. Sequent-Type Rejection Systems for Different Nonsense Logics.
13:00 -14:00 Lunch
14:00 -14:30 Alexei Muravitsky. A note on Consequence and Rejection.
14:30-15:00 Alex Citkin. On Unified Logic
15:00 - 15:30 Round table discussion
ORGANIZERS
ORGANIZERS
Alex Citkin, Metropolitan Telecom munications, USA
Alex Citkin, Metropolitan Telecom munications, USA
Email: acitkin@gmail.com
Email: acitkin@gmail.com
Alexei Muravitsky, Louisiana Scholars’ College, Northwestern State University, USA
Alexei Muravitsky, Louisiana Scholars’ College, Northwestern State University, USA
Email: alexeim@nsula.edu
Email: alexeim@nsula.edu
This Workshop is dedicated to the 100th anniversary of the publication of the article “Two-Valued Logic” (1921) by Jan Lukasiewicz, where or the first time in the history of modern formal logic the falsehood of an assertion was related not to a particular circumstance (“state of affair”) but to the act of rejection. Namely he wrote: “The words “I assert” are denoted by U, and the words “I reject” by N. I consider the sentences: 𝑈 : 1, 𝑁 : 0, which are read: “I assert truth” and “I reject falsehood”, respectively, to be the fundamental principles of two-valued logic [. . . ]”
This Workshop is dedicated to the 100th anniversary of the publication of the article “Two-Valued Logic” (1921) by Jan Lukasiewicz, where or the first time in the history of modern formal logic the falsehood of an assertion was related not to a particular circumstance (“state of affair”) but to the act of rejection. Namely he wrote: “The words “I assert” are denoted by U, and the words “I reject” by N. I consider the sentences: 𝑈 : 1, 𝑁 : 0, which are read: “I assert truth” and “I reject falsehood”, respectively, to be the fundamental principles of two-valued logic [. . . ]”
Later on elsewhere, Lukasiewicz wrote that “of two intellectual acts, to assert a proposition and to reject it, only the first has been taken into account in modern formal logic [. . . ]” while “the idea of rejection [. . . ] has been neglected [. . . ]”. However, even in the traditional treatment of classical logic, a reference to refutation appears, albeit implicitly, when the assertion ‘𝐵 implies 𝐴’, where 𝐴 is an axiom, is accepted as true. This is not because the assertion 𝐵 is stronger than the assertion 𝐴, but rather because the refutation of this implication is impossible.
Later on elsewhere, Lukasiewicz wrote that “of two intellectual acts, to assert a proposition and to reject it, only the first has been taken into account in modern formal logic [. . . ]” while “the idea of rejection [. . . ] has been neglected [. . . ]”. However, even in the traditional treatment of classical logic, a reference to refutation appears, albeit implicitly, when the assertion ‘𝐵 implies 𝐴’, where 𝐴 is an axiom, is accepted as true. This is not because the assertion 𝐵 is stronger than the assertion 𝐴, but rather because the refutation of this implication is impossible.
KEYNOTE SPEAKER
KEYNOTE SPEAKER
Stockolm University, Sweden
Stockolm University, Sweden
"Hybrid Deduction–Refutation Systems: Proofs and Refutations Getting Married"
"Hybrid Deduction–Refutation Systems: Proofs and Refutations Getting Married"
Logical refutation systems are systems of formal derivations intended to derive the non-valid, i.e. semantically refutable, formulae of a given logical system. Even though the idea of formally deriving non-valid syllogisms goes back to Aristotle, it received almost no attention until the early-mid 20th century, when Jan Lukasiewicz started promoting it actively and with some of his students developed complete refutation systems for Aristotle’s syllogistic, classical and intuitionistic logics. Since then, the topic of refutation systems has been revisited and briefly entertained by several logicians, but pursued more systematically by just a few.
Logical refutation systems are systems of formal derivations intended to derive the non-valid, i.e. semantically refutable, formulae of a given logical system. Even though the idea of formally deriving non-valid syllogisms goes back to Aristotle, it received almost no attention until the early-mid 20th century, when Jan Lukasiewicz started promoting it actively and with some of his students developed complete refutation systems for Aristotle’s syllogistic, classical and intuitionistic logics. Since then, the topic of refutation systems has been revisited and briefly entertained by several logicians, but pursued more systematically by just a few.
The talk will be based mainly on the recent work [1], introducing systems of deduction that combine standard deductive systems for deriving logical validities with refutations systems deriving non-validities of a given logical system. Such combined (`hybrid’) systems of deduction employ inference rules involving both provable and refutable premises and conclusions. Simple natural examples of such rules are Modus Tollens (if A -> B is a theorem (hence, valid) and B is refuted, then A is refuted) and the Disjunction property (e.g. in Intuitionistic logic) stated as an inference rule: if A v B is a theorem and A is refuted then B is a theorem.
The talk will be based mainly on the recent work [1], introducing systems of deduction that combine standard deductive systems for deriving logical validities with refutations systems deriving non-validities of a given logical system. Such combined (`hybrid’) systems of deduction employ inference rules involving both provable and refutable premises and conclusions. Simple natural examples of such rules are Modus Tollens (if A -> B is a theorem (hence, valid) and B is refuted, then A is refuted) and the Disjunction property (e.g. in Intuitionistic logic) stated as an inference rule: if A v B is a theorem and A is refuted then B is a theorem.
After a brief historical overview and background on refutation systems (cf. [2]) in this talk I will present the basics of hybrid deduction–refutation systems, including the concept of generic hybrid rules and hybrid deduction–refutation derivations. Then, as an illustrating example, I will present such a system in Natural Deduction style for the classical propositional logic, which is sound and complete both for deductions and for refutations. I will then mention some extensions of hybrid deduction–refutation systems to modal and intuitionistic logics. Finally, I will discuss briefly an emerging hierarchy of higher-order hybrid rules and systems and will conclude with some open problems and potential applications.
After a brief historical overview and background on refutation systems (cf. [2]) in this talk I will present the basics of hybrid deduction–refutation systems, including the concept of generic hybrid rules and hybrid deduction–refutation derivations. Then, as an illustrating example, I will present such a system in Natural Deduction style for the classical propositional logic, which is sound and complete both for deductions and for refutations. I will then mention some extensions of hybrid deduction–refutation systems to modal and intuitionistic logics. Finally, I will discuss briefly an emerging hierarchy of higher-order hybrid rules and systems and will conclude with some open problems and potential applications.
References:
References:
[1] Goranko, V: "Hybrid Deduction–Refutation Systems". Axioms, Special issue on Deductive systems, 8(4), p.118-136 (2019)
[1] Goranko, V: "Hybrid Deduction–Refutation Systems". Axioms, Special issue on Deductive systems, 8(4), p.118-136 (2019)
[2] Goranko, V., Pulcini, G., Skura, T.: "Refutation systems: an overview and some applications to philosophical logics". In: Liu, F., Ono, H., Yu, J. (Eds.) Knowledge, Proof and Dynamics, Post-proceedings volume with selected papers from the Fourth Asian Workshop on Philosophical Logic, Springer, Logic in Asia: Studia Logica Library, pp. 173-197 (2020)
[2] Goranko, V., Pulcini, G., Skura, T.: "Refutation systems: an overview and some applications to philosophical logics". In: Liu, F., Ono, H., Yu, J. (Eds.) Knowledge, Proof and Dynamics, Post-proceedings volume with selected papers from the Fourth Asian Workshop on Philosophical Logic, Springer, Logic in Asia: Studia Logica Library, pp. 173-197 (2020)
CALL FOR PAPERS
CALL FOR PAPERS
Those interested in Refutation in Logic are invited to submit their proposals on any aspect related to this subject. Topics may include, but are not restricted to:
Those interested in Refutation in Logic are invited to submit their proposals on any aspect related to this subject. Topics may include, but are not restricted to:
- Logical systems including refutation
- Refutation and admissible rules
- Refutation and proof
- Refutation and paraconsistency
- Refutation and negation
- Refutation and non-Fregean logics
- Refutation as operator
- Refutation and semantics (matrix, inferentialist, etc.)
- Refutation and abductive reasoning
- Refutation and the philosophy of language
- Refutation and meaning theory
To submit a contribution, please send a one-page abstract by the deadline to the organizers of the workshop.
To submit a contribution, please send a one-page abstract by the deadline to the organizers of the workshop.
Accepted submissions will be invited to submit a paper to a book or a special issue that will be edited by the organizers after the workshop.
Accepted submissions will be invited to submit a paper to a book or a special issue that will be edited by the organizers after the workshop.
For any query, please contact the organizers of the workshop.
For any query, please contact the organizers of the workshop.
IMPORTANT DATES
IMPORTANT DATES
Submission: October 31st, 2021
Submission: October 31st, 2021
Notification: November 7, 2021
Notification: November 7, 2021
Worskhop: 6-11 April , 2022 (the workshop will take place at some point during the UNILOG congress).
Worskhop: 6-11 April , 2022 (the workshop will take place at some point during the UNILOG congress).
