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Logica Universalis - Logica Universalis Webinar 2021

The Logica Universalis Webinar is a World Seminar Series connected to the journal Logica Universalis (this opens in a new tab), the book series Studies in Universal Logic (this opens in a new tab) and the Universal Logic Project (this opens in a new tab). It is an open platform for all scholars interested in the many aspects of logic.

The LUW series started with two "extraordinary" sessions:

Video recordings of the seminars are uploaded on the YouTube channel Universal Logic Project (this opens in a new tab).

Each session of the webinar is chaired by a member of the editorial board of the journal Logica Universalis (LU), the book series Studies in Universal Logic (SUL) or an organizer of an event of the Universal Logic Project (ULP). Sessions will start with a short presentation of a logical organization related to the region of the speaker or the topic of the talk. The talk (30 min) will focus on a recently published paper in LU, on a book in SUL, on an event or on the ULP. Talks are followed by a discussion (15 min).

Webinar Schedule

Date

Speaker

Title

Organization

Chair

March 24                           

Tore Fjetland Øgaard (this opens in a new tab)
(University of Bergen, Norway)

Farewell to Suppression-Freedom (this opens in a new tab)

Watch the recording here (this opens in a new tab).

Scandinavian Logic Society (this opens in a new tab)
Valentin Goranko (this opens in a new tab), President

Jean-Yves Beziau (this opens in a new tab)
Editor-in-Chief LU        

April 14

Jean-Yves Beziau (this opens in a new tab)
(University of Brazil, Rio de Janeiro)

UNILOG’2022: 7th World Congress and School on Universal Logic April 1-11, 2022
Related LU papers: Universal Logic: Evolution of a Project (this opens in a new tab) and
Special Issue: 1st Logic Prizes Contest, vol-12, 2018 (this opens in a new tab)

Watch the recording here (this opens in a new tab).

Orthodox Academy of Crete (this opens in a new tab)
Ioannis Vandoulakis (this opens in a new tab)
Organizer UNILOG’2022 (this opens in a new tab)

Katarzyna Gan-Krzywoszyńska                                                                                   

April 21

Stephen Read (this opens in a new tab)
(University of St Andrews, UK)

Swyneshed, Aristotle and the Rule of Contradictory Pairs (this opens in a new tab)

Watch the recording here (this opens in a new tab).

Square of Opposition Project (this opens in a new tab)

Jens Lemanski (this opens in a new tab)
Editor of the LU special issue:
The Cretan Square (this opens in a new tab)

May 12

Petra Murinová (this opens in a new tab)
(University of Ostrava, Czech Republic)

Graded Structures of Opposition in Fuzzy Natural Logic (this opens in a new tab)
 
Access the presentation here (this opens in a new tab).

Watch the recording here (this opens in a new tab).

Working Group on Mathematical Fuzzy Logic (this opens in a new tab)
Tommaso Flaminio (this opens in a new tab), President

Access the presentation here (this opens in a new tab).

Sergei Odintsov (this opens in a new tab)
Editorial Board LU

May 19

Frank Sautter (this opens in a new tab)
(Federal University of Santa Maria, Brazil)

A Bunch of Diagrammatic Methods for Syllogistic (this opens in a new tab)

Watch the recording here (this opens in a new tab).

Brazilian Logic Society (this opens in a new tab)
Cezar Mortari (this opens in a new tab), President

Itala D’Ottaviano (this opens in a new tab)
Editorial Board LU                                                            

June 16

Andrzej Indrzejczak (this opens in a new tab)
(University of Łódź, Poland)

Sequents and Trees (this opens in a new tab)

Watch the recording here (this opens in a new tab).

Polish Association for Logic and Philosophy of Science (this opens in a new tab)
Marcin Miłkowski (this opens in a new tab)

Peter Schroeder-Heister (this opens in a new tab)
Editorial Board SUL

June 23

Dov Gabbay (this opens in a new tab)
(University of Luxembourg
Bar-Ilan University, Israel
King’s College London, UK)
Timotheus Kampik (this opens in a new tab)
(Umea University, Sweden)

The Talmudic Logic Project (this opens in a new tab)

Logic and Religion Association (this opens in a new tab)
Ricardo Silvestre (this opens in a new tab), President

Stanisław Krajewski (this opens in a new tab)
And Marcin Trepczyński (this opens in a new tab)
Editors of the LU special issue:
Theological Discourse and Logic (this opens in a new tab)

July 14

Laura Follesa (this opens in a new tab)
(University of Barcelona, Spain)

From Necessary Truths to Feelings: The Foundations of Mathematics in Leibniz and Schopenhauer (Chapter of Language, Logic, and Mathematics in Schopenhauer (this opens in a new tab)) Schopenhauer Society (this opens in a new tab) 
Matthias Kossler (this opens in a new tab), President
Jens Lemanski (this opens in a new tab),
Editor of Language, Logic, and Mathematics in Schopenhauer  (this opens in a new tab)                                                                                   
                                                                                                                                                      
Francesco Paoli (this opens in a new tab)
Editorial Board SUL
and
Dana Knowles (this opens in a new tab)
Publishing Editor SUL, Springer Nature

July 21

Reetu Bhattacharjee (this opens in a new tab)
(Jadavpur University, Kolkata, West Bengal, India)

A Venn Diagram System for Universe Without Boundary (this opens in a new tab)

Calcutta Logic Circle (this opens in a new tab)
Mihir Chakraborty (this opens in a new tab), President

Raja Natarajan (this opens in a new tab)
Editorial Board LU

August 11

Yale Weiss (this opens in a new tab)
(City University of New York, USA)

A Reinterpretation of the Semilattice Semantics with Applications (this opens in a new tab)

Saul Kripke Center (this opens in a new tab)
Romina Padro (this opens in a new tab), Director
Melvin Fitting (this opens in a new tab)
Editorial Board LU

August 18

Tin Perkov (this opens in a new tab)
(University of Zagreb, Croatia)

Logical constants in abstract frameworks (this opens in a new tab)
and
A Note on Logicality of Generalized Quantifiers (this opens in a new tab)

Croatian Logic Association (this opens in a new tab)
Srećko Kovač (this opens in a new tab), President

Srećko Kovač (this opens in a new tab)
Editorial Board LU

September 8

João Rasga (this opens in a new tab) and Cristina Sernadas (this opens in a new tab) (Instituto Superior Técnico, Lisbon, Portugal) Decidability of Logical Theories and Their Combination (this opens in a new tab) Security and Quantum Information Group (this opens in a new tab)
Paulo Mateus (this opens in a new tab), Founder and Coordinator
Razvan Diaconescu (this opens in a new tab)
Editorial Board SUL

September 15                      

Josué Antonio Nescolarde Selva (this opens in a new tab)
(University of Alicante, Spain)

Mathematical Perspectives on Liar Paradoxes (this opens in a new tab)

Spanish Society of Logic and Methodology and Philosophy of Science (this opens in a new tab)
Cristina Corredor (this opens in a new tab), President

Maria Manzano (this opens in a new tab)
Editorial Board LU

October 6

Paulo Guilherme Santos (this opens in a new tab) (New University of Lisbon, Portugal) and Reinhard Kahle (this opens in a new tab) (University of Tübingen, Germany) k-Provability in PA (this opens in a new tab)

Logic in Portugal - Amilcar Sernadas Logic Prize (this opens in a new tab)
Francisco Dionisio (this opens in a new tab)

Carlos Caleiro (this opens in a new tab) Board of LU

October 13

Amirouche Moktefi (this opens in a new tab)
(Ragnar Nurkse
Tallinn University of Technology, Estonia)

Why Make Things Simple When You Can Make Them Complicated? An Appreciation of Lewis Carroll’s Symbolic Logic (this opens in a new tab)

Lewis Carroll Society (this opens in a new tab)
Stephen Folan, Chairman

Read a review here (this opens in a new tab).

Leo Corry (this opens in a new tab)
Editorial Board LU

November 10

Michael Kaminski (this opens in a new tab) and Nissim Francez (this opens in a new tab) (Technion, Israel)

Calculi for Many-Valued Logics (this opens in a new tab)

Logic in Israel
Liron Cohen (this opens in a new tab)

Anna Zamansky (this opens in a new tab)
Editorial Board of SUL

November 17

Yaroslav Petrukhin (this opens in a new tab)
(University of Łódź, Poland)
Vasilyi Shangin (this opens in a new tab)
(Lomonosov Moscow State University, Russia)

Correspondence Analysis for Some Fragments of Classical Propositional Logic (this opens in a new tab)

Moscow Logic Group
Vladimir Vasyukov (this opens in a new tab)
Chairman

Andrei Rodin (this opens in a new tab)
Editorial Board LU

December 8

John Grant (this opens in a new tab)
(University of Mariland, USA)

Measuring Inconsistency in Generalized Propositional Logic (this opens in a new tab)

World Association of Paraconsistency (this opens in a new tab)
Maria Martinez-Ordaz (this opens in a new tab)

Jean-Yves Beziau (this opens in a new tab)
Editor-in-Chief LU  

December 15                                                                                                                                                          

Scott Pratt (this opens in a new tab)
(University of Oregon, USA)                                             

Decolonizing “Natural Logic” (Chapter of Logical Skills (this opens in a new tab))

Julie Brumberg-Chaumont (this opens in a new tab)
and Claude Rosental (this opens in a new tab)
Editors of the book Logical Skills (this opens in a new tab)

Raffaela Giovagnoli (this opens in a new tab)
Editorial Board of SUL

Speakers and Abstracts

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March 24, 2021 – Tore Fjetland Øgaard (this opens in a new tab)
Farewell to Suppression-Freedom (this opens in a new tab)          

Chair: Jean-Yves Beziau (this opens in a new tab)
Editor-in-Chief of Logica Universalis

Associate Organization: Scandinavian Logic Society (this opens in a new tab)
presented by its president, Valentin Goranko (this opens in a new tab)

Val Plumwood and Richard Sylvan argued from their joint paper The Semantics of First Degree Entailment (Routley and Routley in Noûs 6(4):335–359, 1972) and onward that the variable sharing property is but a mere consequence of a good entailment relation, indeed they viewed it as a mere negative test of adequacy of such a relation, the property itself being a rather philosophically barren concept. Such a relation is rather to be analyzed as a sufficiency relation free of any form of premise suppression. Suppression of premises, therefore, gained center stage. Despite this, however, no serious attempt was ever made at analyzing the concept. This paper shows that their suggestions for how to understand it, either as the Anti-Suppression Principle or as the Joint Force Principle, turn out to yield properties strictly weaker than that of variable sharing. A suggestion for how to understand some of their use of the notion of suppression which clearly is not in line with these two mentioned principles is given, and their arguments to the effect that the Anderson and Belnap logics T, E and R are suppressive are shown to be both technically and philosophically wanting. Suppression-freedom, it is argued, cannot do the job Plumwood and Sylvan intended it to do.

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April 14, 2021 – Jean-Yves Beziau (this opens in a new tab) – UNILOG’2022: 7th World Congress and School on Universal Logic – April 1-11, 2022 (this opens in a new tab)

Related LU papers:
Universal Logic: Evolution of a Project (this opens in a new tab)
Special Issue: 1st Logic Prizes Contest, vol-12, 2018 (this opens in a new tab)

Chair: Katarzyna Gan-Krzywoszyńska

Associate Organization: Orthodox Academy of Crete (this opens in a new tab)
presented by Ioannis Vandoulakis (this opens in a new tab), organizer of UNILOG’2022 (this opens in a new tab)

We describe the structure of UNILOG (World Congress and School on Universal Logic), a series of events created for promoting the universal logic project, with a school, a congress, a secret speaker and a contest. After a brief survey of   past editions in Montreux, Xi’an, Lisbon, Rio de Janeiro, Istanbul and Vichy, we present the next edition of UNILOG that will take place in Crete in 2022, in particular with the 2nd edition of the World Logic Prizes Contest with winners of logic prizes from many countries around the world competing.

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April 21, 2021 – Stephen Read (this opens in a new tab) – Swyneshed, Aristotle and the Rule of Contradictory Pairs (this opens in a new tab)

Chair: Jens Lemanski (this opens in a new tab)
Editor of the LU special issue The Cretan Square (this opens in a new tab)

Associate Organization: Square of Opposition Project (this opens in a new tab)
presented by Jean-Yves Beziau (this opens in a new tab) 

Roger Swyneshed, in his treatise on insolubles (logical paradoxes), dating from the early 1330s, drew three notorious corollaries from his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict what Whitaker, in his iconoclastic reading of Aristotle’s De Interpretatione, dubbed “The Rule of Contradictory Pairs” (RCP), which requires that in every such pair, one must be true and the other false. Whitaker argued that, immediately after defining the notion of a contradictory pair, in which one statement affirms what the other denies of the same thing, Aristotle himself gave counterexamples to the rule. This gives some credence to Swyneshed’s claim that his solution to the logical paradoxes is not contrary to Aristotle’s teaching, as many of Swyneshed’s contemporaries claimed. Insolubles are false, he said, because they falsify themselves; and their contradictories are false because they falsely deny that the insoluble itself is false. Swyneshed’s solution depends crucially on the revision he makes to the acount of truth and falsehood, brought out in his first thesis: that a false proposition can signify as it is, or as Paul of Venice, who took up and developed Swyneshed’s solution some sixty years later, puts it, a false proposition can have a true significate. Swyneshed gave a further counterexample to (RCP) when he claimed that some insolubles, like future contingents, are neither true nor false. Dialetheism, the contemporary claim that some propositions are both true and false, is wedded to the Rule, and in consequence divorces denial from the assertion of the contradictory negation. Consequently, Swyneshed’s logical heresy is very different from that found in dialetheism.

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May 12, 2021 – Petra Murinová (this opens in a new tab) – Graded Structures of Opposition in Fuzzy Natural Logic (this opens in a new tab)

Chair: Sergei Odintsov (this opens in a new tab)
Member of the Editorial Board of LU

Associate Organization: Working Group on Mathematical Fuzzy Logic (this opens in a new tab)
presented by its president, Tommaso Flaminio (this opens in a new tab)

The main objective of this paper is devoted to two main parts. First, the paper introduces logical interpretations of classical structures of opposition that are constructed as extensions of the square of opposition. Blanché’s hexagon as well as two cubes of opposition proposed by Morreti and pairs Keynes–Johnson will be introduced. The second part of this paper is dedicated to a graded extension of the Aristotle’s square and Peterson’s square of opposition with intermediate quantifiers. These quantifiers are linguistic expressions such as “most”, “many”, “a few”, and “almost all”, and they correspond to what are often called “fuzzy quantifiers” in the literature. The graded Peterson’s cube of opposition, which describes properties between two graded squares, will be discussed at the end of this paper.

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May 19, 2021 – Frank Sautter (this opens in a new tab)  – A Bunch of Diagrammatic Methods for Syllogistic (this opens in a new tab)

Chair: Itala D’Ottaviano (this opens in a new tab)
Member of the Editorial Board of LU

Associate Organization: Brazilian Logic Society (this opens in a new tab)
presented by its president, Cezar Mortari (this opens in a new tab)  

This paper presents, assesses, and compares six diagrammatic methods for Categorical Syllogistic. Venn’s Method is widely used in logic textbooks; Carroll’s Method is a topologically indistinguishable version of Venn’s Method; and the four remaining methods are my own: the Dual of Carroll’s Method, Gardner’s Method, Gardner–Peirce’s Method, and Ladd’s Method. These methods are divided into two groups of three and the reasons for switching from a method to another within each group are discussed. Finally, a comparison between the Dual of Carroll’s Method and Ladd’s Method supports the main result of the paper, which is an approximation of the two groups of methods.

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June 16, 2021 –  Andrzej Indrzejczak (this opens in a new tab) – Sequents and Trees (this opens in a new tab)

Chair: Peter Schroeder-Heister (this opens in a new tab)
Member of the Editorial Board of SUL

Associate Organization: Polish Association for Logic and Philosophy of Science (this opens in a new tab)
presented by Marcin Miłkowski (this opens in a new tab)

This textbook offers a detailed introduction to the methodology and applications of sequent calculi in propositional logic. Unlike other texts concerned with proof theory, emphasis is placed on illustrating how to use sequent calculi to prove a wide range of metatheoretical results.  The presentation is elementary and self-contained, with all technical details both formally stated and also informally explained.  Numerous proofs are worked through to demonstrate methods of proving important results, such as the cut-elimination theorem, completeness, decidability, and interpolation.  Other proofs are presented with portions left as exercises for readers, allowing them to practice techniques of sequent calculus.
After a brief introduction to classical propositional logic, the text explores three variants of sequent calculus and their features and applications.  The remaining chapters then show how sequent calculi can be extended, modified, and applied to non-classical logics, including modal, intuitionistic, substructural, and many-valued logics.

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June 23, 2021 – Dov Gabbay (this opens in a new tab) and Timotheus Kampik (this opens in a new tab) – The Talmudic Logic Project (this opens in a new tab) 

Chair: Stanisław Krajewski (this opens in a new tab) and Marcin Trepczyński (this opens in a new tab)
Editors of the LU special issue Theological Discourse and Logic (this opens in a new tab)

Associate Organization: Logic and Religion Association - LARA (this opens in a new tab)
presented by its president, Ricardo Silvestre (this opens in a new tab)

We describe the state of the Talmudic Logic project as of end of 2020. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components centuries ahead of their time. In many cases the basic principles are not explicitly formulated, which makes it difficult to formalize and make available to the modern student of Logic. This project on Talmudic Logic, aims to present logical analysis of Talmudic reasoning using modern logical tools.
The aims of the project are two fold:
(1) To import into the Talmudic study modern logical methods with a view to help understand complicated Talmudic passages, which otherwise cannot be addressed.
(2) To export from the Talmud new logical principles which are innovative and useful to modern contemporary logic.

Addition to abstract: As an example we present late-breaking results, in particular an argumentation approach for the treatment of doubt in Talmudic Logic, for which we can prove the satisfaction of a principle that comes from microeconomic theory, and which can be applied to other domains such as business decision automation and legal reasoning.

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July  14, 2021 – Laura Follesa (this opens in a new tab)  – From Necessary Truths to Feelings: The Foundations of Mathematics in Leibniz and Schopenhauer (Chapter of Language, Logic, and Mathematics in Schopenhauer (this opens in a new tab)

Chair: Francesco Paoli (this opens in a new tab)
Member of the Editorial Board of SUL

and Dana Knowles (this opens in a new tab)
Publishing Editor SUL, Springer Nature

Associate Organization: Schopenhauer Society (this opens in a new tab)
presented by its president Matthias Kossler (this opens in a new tab) and Jens Lemanski (this opens in a new tab), editor of Language, Logic, and Mathematics in Schopenhauer (this opens in a new tab)

I take into account Schopenhauer’s study of Leibniz’s work, as it emerges not only from his explicit critique in his dissertation On the Fourfold Root of the Principle of Sufficient Reason (1813) and in The World as Will and Idea (3rd edition 1859), but also from his annotations of Leibniz’s writings.
Schopenhauer owned many books of Leibniz in his private library and they are full of intriguing annotations. Many of these annotations concern the discussion on logic and mathematical truths and so they are particularly relevant for the study of Schopenhauer’s philosophy of mathematics. After a comparison between Leibniz and Schopenhauer’s definition of necessary and innate truths, I put alongside what the two authors stated about system and fundamental axioms. Two questions arise from Leibniz’s interpretation of Euclid’s axioms: the role of ‘images’ in knowledge and the notion of ‘confused’ knowledge. These two questions are worth of attention, as they allow to focus on Schopenhauer’s theory of ‘feeling’ mathematical knowledge, as I show in the last section of this paper. To Schopenhauer, knowledge works with intuitive representations, intuition, perception, and, for this reason, feeling is the basis of all conceptions. Schopenhauer’s provided a new point of view regarding feeling and intuitive knowledge that involves a special meaning for his philosophy of mathematics.

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July 21, 2021 – Reetu Bhattacharjee – A Venn Diagram System for Universe Without Boundary (this opens in a new tab)

Chair: Raja Natarajan (this opens in a new tab)
Member of the Editorial Board of LU

Associate Organization: Calcutta Logic Circle (this opens in a new tab)
presented by its president,  Mihir Chakraborty (this opens in a new tab)

A new Venn  diagram system where properties are fundamental and an object exists only w.r.t a property is presented. This work modifies both in syntax and semantics the Venn system proposed by Choudhury and Chakraborty to picturise and address issues connected with open universe. Semantics for the current system is given. Soundness and completeness w.r.t the semantics are established.

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August 11, 2021 – Yale Weiss (this opens in a new tab)  – A Reinterpretation of the Semilattice Semantics with Applications (this opens in a new tab)

Chair: Melvin Fitting (this opens in a new tab)
Member of the Editorial Board of LU

Associate Organization: Saul Kripke Center (this opens in a new tab)
presented by its director Romina Padro (this opens in a new tab)

In the early 1970s, Alasdair Urquhart proposed a semilattice semantics for relevance logic which he provided with an influential informational interpretation. In this article, I propose a BHK-inspired reinterpretation of the semantics which is related to Kit Fine's truth-maker semantics. I discuss and compare Urquhart's and Fine's semantics and show how simple modifications of Urquhart's semantics can be used to characterize both full propositional intuitionistic logic and Jankov's logic. I then present (quasi-)relevant companions for both of these systems. Finally, I provide sound and complete labelled sequent calculi for all of the systems discussed.

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August 18, 2021 – Tin Perkov (this opens in a new tab)Logical constants in abstract frameworks (this opens in a new tab)A Note on Logicality of Generalized Quantifiers (this opens in a new tab)

Chair: Srećko Kovač (this opens in a new tab)
Member of the Editorial Board of LU

Associate Organization: Croatian Logic Association (this opens in a new tab)
presented by its president Srećko Kovač (this opens in a new tab)

A possibility of defining logical constants within abstract logical frameworks is discussed, in relation to abstract definitions of logical consequence. We propose using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality. The implications of this approach to the question of logicality of generalized quantifiers will also be discussed.

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September 8 – João Rasga (this opens in a new tab) and Cristina Sernadas (this opens in a new tab) – Decidability of Logical Theories and Their Combination (this opens in a new tab)

Chair: Razvan Diaconescu (this opens in a new tab)
Member of the Editorial Board of SUL

Associate Organization: Security and Quantum Information Group (this opens in a new tab)
presented by its founder and coordinator Paulo Mateus (this opens in a new tab)

This textbook provides a self-contained introduction to decidability of first-order theories and their combination. The technical material is presented in a systematic and universal way and illustrated with plenty of examples and a range of proposed exercises.
After an overview of basic first-order logic concepts, the authors discuss some model-theoretic notions like embeddings, diagrams, and elementary substructures. The text then goes on to explore an applicable way to deduce logical consequences from a given theory and presents sufficient conditions for a theory to be decidable. The chapters that follow focus on quantifier elimination, decidability of the combination of first-order theories and the basics of computability theory. 
The inclusion of a chapter on Gentzen calculus, cut elimination, and Craig interpolation, as well as a chapter on combination of theories and preservation of decidability, help to set this volume apart from similar books in the field.
Decidability of Logical Theories and their Combination is ideal for graduate students of Mathematics and is equally suitable for Computer Science, Philosophy and Physics students who are interested in gaining a deeper understanding of the subject. The book is also directed to researchers that intend to get acquainted with first-order theories and their combination.

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September 15, 2021 – Josué-Antonio Nescolarde-Selva (this opens in a new tab) – Mathematical Perspectives on Liar Paradoxes (this opens in a new tab)

Chair: Maria Manzano (this opens in a new tab)
Member of the Editorial Board of LU

Associate Organization: Spanish Society of Logic and Methodology and Philosophy of Science (this opens in a new tab)
presented by its president Cristina Corredor (this opens in a new tab)

The liar paradox is a famous and ancient paradox related to logic and philosophy. It shows it is perfectly possible to construct sen-tences that are correct grammatically and semantically but they cannot have a truth value in the traditional sense. In this paper the authors show four approaches to interpreting paradoxes that illustrate the influence of: a) the levels of language, b) their belonging to indeterminate compatible propositions (ICP) or indeterminate propositions (IP), c) being based on universal antinomy and d) the theory of dialetheism.

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October 6 – Paulo Guilherme Santos (this opens in a new tab) and Reinhard Kahle (this opens in a new tab) – k-provability in PA (this opens in a new tab)

Chair:  Carlos Caleiro (this opens in a new tab)
Member of the Editorial Board of LU

Associate Organization: Logic in Portugal / Amilcar Sernadas Logic Prize (this opens in a new tab)
presented by Francisco Dionisio (this opens in a new tab)

We study the decidability of k-provability in PA |the relation 'being provable in PA with at most k steps'| and the decidability of the proof-skeleton problem |the problem of deciding if a given formula has a proof that has a given skeleton (the list of axioms and rules that were used)|. The decidability of k-provability for the usual Hilbertstyle formalisation of PA is still an open problem, but it is known that the proof-skeleton problem is undecidable for that theory. Using new methods, we present a characterisation of some numbers k for which k-provability is decidable, and we present a characterisation of some proof-skeletons for which one can decide whether a formula has a proof whose skeleton is the considered one. These characterisations are natural and parameterised by unification algorithms.

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October 13, 2021 – Amirouche Moktefi (this opens in a new tab)  – Why Make Things Simple When You Can Make Them Complicated? An Appreciation of Lewis Carroll’s Symbolic Logic (this opens in a new tab)

Chair: Leo Corry (this opens in a new tab)
Member of the Editorial Board of LU

Associate Organization: Lewis Carroll Society (this opens in a new tab) 
presented by its chairman Stephen Folan

It is known that Lewis Carroll developed a system of logic within the tradition of mathematical logic that was promoted by his predecessors and contemporaries Boole, Jevons, Venn, MacColl, Peirce, Schröder and others. His contributions include mature logic diagrams, a subscript notation, a system of logic trees, a large set of logic problems and two remarkable paradoxes. However, unlike his colleagues, Carroll kept in his logic several features that were characteristic of the older logic. In particular, he refused to drop the existential import of universal affirmative propositions. This ‘conservatism’ made his system much more complicated than those of his rivals. In this talk, we offer an appreciation of Carroll’s logic and his struggle to design a system that would be both easy and useful. We discuss his motivations, the difficulties he faced and the benefits he gained.  We argue that Carroll’s choices reflected his belief in the social utility of logic and allowed him to tackle more efficiently some issues that resisted to early symbolic logicians, notably the problem of the utility of mathematical logic itself.

Read a review here (this opens in a new tab).

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November 10 – Calculi for Many-Valued Logics (this opens in a new tab) – Michael Kaminski (this opens in a new tab) and Nissim Francez (this opens in a new tab)

Chair: Anna Zamansky (this opens in a new tab)
Editorial Board of SUL

Associate Organization: Logic in Israel
presented by Liron Cohen (this opens in a new tab)

We present a number of equivalent calculi for many-valued logics and prove soundness and strong completeness theorems. The calculi are obtained from the truth tables of the logic under consideration in a straightforward manner and there is a natural duality among these calculi. We also prove the cut elimination theorems for the sequent-like systems.
 

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November 17, 2021 –  Yaroslav Petrukhin (this opens in a new tab) & Vasilyi Shangin (this opens in a new tab)  – Correspondence Analysis for Some Fragments of Classical Propositional Logic (this opens in a new tab)

Chair: Andrei Rodin (this opens in a new tab)
Member of the Editorial Board of LU

Associate Organization: Moscow Logic Goup
presented by its chairman Vladimir Vasyukov (this opens in a new tab)

In the paper, we apply Kooi and Tamminga’s correspondence analysis (that has been previously applied to some notable three- and four-valued logics) to some conventional and functionally incomplete fragments of classical propositional logic. In particular, the paper deals with the implication, disjunction, and negation fragments. Additionally, we consider an application of correspondence analysis to some connectiveless fragment with certain basic properties of the logical consequence relation only. As a result of the application, one obtains a sound and complete natural deduction system for any binary extension of each fragment in question. With the focus on exclusive disjunction we comparatively study the proposed systems. Finally, we discuss Segerberg’s systems for connectiveless and negation fragments and compare them with our systems.

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December 8, 2021 – John Grant (this opens in a new tab) – Measuring Inconsistency in Generalized Propositional Logic (this opens in a new tab)

Chair:  Jean-Yves Beziau (this opens in a new tab)
Editor-in-Chief of LU

Associate Organization: World Association of Paraconsistency (this opens in a new tab)
presented by Maria Martinez-Ordaz (this opens in a new tab)

Consistency is one of the key concepts of logic; logicians have put a great deal of effort into proving the consistency of many logics. Understanding what causes inconsistency is also important; some logicians have developed paraconsistent logics that, unlike classical logics, allow some contradictions without making all formulas provable. Another direction of research studies inconsistency by measuring the amount of inconsistency of sets of formulas. While the initial attempt in 1978 was too ambitious in trying to do this for first-order logic, this research got a substantial boost when an inconsistency measure was proposed for propositional logic in 2002. Since then, researchers in logic and artificial intelligence (AI systems need the capability to deal with inconsistency) have made many interesting proposals and found related issues. Almost all of this work has been done for propositional logic. The purpose of this paper is to extend inconsistency measures to logics that also contain operators, such as modal operators. We use the terminology “generalized propositional logic” for such logics. We show how to extend propositional inconsistency measures to sets of formulas in any such generalized propositional logic. Examples are used to illustrate how various modal operators, including spatial and tense operators, fit into this framework. We also show that the addition of operators leads to a weak type of inconsistency. In all cases, the calculations for several inconsistency measures are given.

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December 15, 2021 – Scott L.Pratt (this opens in a new tab)  – Decolonizing “Natural Logic”, Chapter of Logical Skills (this opens in a new tab)

Chair:  Raffaela Giovagnoli (this opens in a new tab)
Member of the Editorial Board of SUL

Organizers: Julie Brumberg-Chaumont (this opens in a new tab) and Claude Rosental (this opens in a new tab)
Editors of Logical Skills (this opens in a new tab)

“Natural logic” was proposed by Lewis Henry Morgan (1818–1881) as
the engine of cultural evolution, concluding that the “course and manner” of cultural development “was predetermined, as well as restricted within narrow limits of divergence, by the natural logic of the human mind.” This essay argues that Morgan’s conception of natural logic aids the project of settler colonialism. Rather than being a false account of human agency, however, it is a conception of natural logic that is produced through the systematic narrowing of possibilities for agency, human, and otherwise. This narrowed logic is thus only a part of a differently conceived logic of agency that is also general (and so serves as the framework for all action) and normative (albeit with a set of norms different from those identified by Morgan). The discussion proceeds in four sections: first, a presentation of Morgan’s conception of natural logic and its origins; second, an analysis of four colonizing implications of Morgan’s view; third, examples of further developments of natural logic in the twentieth and twenty-first centuries in the work structuralist and post-structuralist theorists; and, last, a brief introduction of a decolonial logic that provides a broader alternative conception of the structure of agency, human, and otherwise, and that avoids the oppressive effects of the reductionism of the natural logic received from Morgan and his successors.

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