Join the Logica Universalis Webinar!
The Logica Universalis Webinar is a World Seminar Series connected to the journal Logica Universalis, the book series Studies in Universal Logic and the Universal Logic Project. It is an open platform for all scholars interested in the many aspects of logic.
The LUW series started with two "extraordinary" sessions:
- Introduction to the Universal Logic Project, Dec 16, 2020
- Welcome Celebration for the World Logic Day, Jan 14, 2021
The sessions take place on Wednesdays at 4pm CEST (click here to convert to your timezone). They are held via Zoom and are free to attend. Please register in advance.
Registration is now open!
Video recordings of the seminars are uploaded on the YouTube channel Universal Logic Project.
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 | Farewell to Suppression-Freedom Watch the recording here. | Scandinavian Logic Society | Jean-Yves Beziau |
April 14 | Jean-Yves Beziau | UNILOG’2022: 7th World Congress and School on Universal Logic April 1-11, 2022 | Orthodox Academy of Crete | Katarzyna Gan-Krzywoszyńska |
April 21 | Stephen Read | Jens Lemanski | ||
May 12 | Petra Murinová | Graded Structures of Opposition in Fuzzy Natural Logic | TBA | TBA |
May 19 | Frank Sautter | Brazilian Logic Society | Itala D’Ottaviano | |
June 16 | Andrzej Indrzejczak | Peter Schroeder-Heister | ||
June 23 | Dov Gabbay | Stanisław Krajewski | ||
July 14 | Laura Follesa | From Necessary Truths to Feelings: The Foundations of Mathematics in Leibniz and Schopenhauer (Chapter of Language, Logic, and Mathematics in Schopenhauer) | Schopenhauer Society | Francesco Paoli Editorial Board SUL and Jens Lemanski Editor of Language, Logic, and Mathematics in Schopenhauer |
July 21 | Reetu Bhattacharjee | Calcutta Logic Circle | Raja Natarajan | |
August 11 | Yale Weiss | A Reinterpretation of the Semilattice Semantics with Applications (to appear soon in LU) | Saul Kripke Center | Melvin Fitting Editorial Board LU |
August 18 | Tin Perkov | Croatian Logic Association | Srećko Kovač | |
September 8 | João Rasga and Cristina Sernadas (Instituto Superior Técnico, Lisbon, Portugal) | Decidability of Logical Theories and Their Combination | International Federation for Computational Logic - IFCOLOG Leon van der Torre | Razvan Diaconescu Editorial Board SUL |
September 15 | Josué Antonio Nescolarde Selva | Four Interpretations of the Liar Paradox (to appear soon in LU) | Spanish Society of Logic and Methodology and Philosophy of Science | Maria Manzano |
October 6 | Paulo Guilherme Santos (University of Lisbon, Portugal) and Reinhard Kahle (University of Tübingen, Germany) | k-provability in PA | Logic in Portugal - Amilcar Sernadas Logic Pizre | Carlos Caleiro Board of LU |
October 13 | Amirouche Moktefi | Why make things simple when you can make them complicated? An appreciation of Lewis Carroll’s symbolic logic | Lewis Carroll Society | Leo Corry |
November 10 | Michael Kaminski and Nissim Francez (Technion, Israel) | Proof-theoretical frameworks for many-valued logics | Logic in Israel | Arnon Avron |
November 17 | Yaroslav Petrukhin | Correspondence Analysis for Some Fragments of Classical Propositional Logic | Moscow Logic Group | Andrei Rodin |
December 8 | John Grant | TBA | TBA | |
December 15 | Scott Pratt | Decolonizing “Natural Logic” (Chapter of Logical Skills) | Julie Brumberg-Chaumont | TBA |
Speakers and Abstracts
March 24, 2021 – Tore Fjetland Øgaard –
Farewell to Suppression-Freedom
Chair: Jean-Yves Beziau
Editor-in-Chief of Logica Universalis
Associate Organization: Scandinavian Logic Society
presented by its president, Valentin Goranko
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.
-----
April 14, 2021 – Jean-Yves Beziau – UNILOG’2022: 7th World Congress and School on Universal Logic – April 1-11, 2022
Related LU papers:
Universal Logic: Evolution of a Project
Special Issue: 1st Logic Prizes Contest, vol-12, 2018
Chair: Katarzyna Gan-Krzywoszyńska
Associate Organization: Orthodox Academy of Crete
presented by Ioannis Vandoulakis, organizer of UNILOG’2022
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 2^{nd} edition of the World Logic Prizes Contest with winners of logic prizes from many countries around the world competing.
-----
April 21, 2021 – Stephen Read – Swyneshed, Aristotle and the Rule of Contradictory Pairs
Chair: Jens Lemanski
Editor of the LU special issue The Cretan Square
Associate Organization: Square of Opposition Project
presented by Jean-Yves Beziau
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.
-----
May 12, 2021 – Petra Murinová – Graded Structures of Opposition in Fuzzy Natural Logic
Chair: Sergei Odintsov
Member of the Editorial Board of LU
Associate Organization: TBA
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.
-----
May 19, 2021 – Frank Sautter – A Bunch of Diagrammatic Methods for Syllogistic
Chair: Itala D’Ottaviano
Member of the Editorial Board of LU
Associate Organization: Brazilian Logic Society
presented by its president, Cezar Mortari
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.
-----
June 16, 2021 – Andrzej Indrzejczak – Sequents and Trees
Chair: Peter Schroeder-Heister
Member of the Editorial Board of SUL
Associate Organization: Polish Association for Logic and Philosophy of Science
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.
-----
June 23, 2021 – Dov Gabbay – The Talmudic Logic Project
Chair: Stanisław Krajewski and Marcin Trepczyński
Editors of the LU special issue Theological Discourse and Logic
Associate Organization: Logic and Religion Association - LoRA
presented by its president, Ricardo Silvestre
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.
-----
July 14, 2021 – Laura Follesa – From Necessary Truths to Feelings: The Foundations of Mathematics in Leibniz and Schopenhauer (Chapter of Language, Logic, and Mathematics in Schopenhauer)
Chair: Francesco Paoli
Member of the Editorial Board of SUL
Associate Organization: Schopenhauer Society
presented by its president Matthias Kossler and Jens Lemanski, editor of Language, Logic, and Mathematics in Schopenhauer
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.
-----
July 21, 2021 – Reetu Bhattacharjee – A Venn Diagram System for Universe Without Boundary
Chair: Raja Natarajan
Member of the Editorial Board of LU
Associate Organization: Calcutta Logic Circle
presented by its president, Mihir Chakraborty
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.
-----
August 11, 2021 – Yale Weiss – A Reinterpretation of the Semilattice Semantics with Applications
Chair: Melvin Fitting
Member of the Editorial Board of LU
Associate Organization: Saul Kripke Center
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.
-----
August 18, 2021 – Tin Perkov – Logical constants in abstract frameworks
Chair: Srećko Kovač
Member of the Editorial Board of LU
Associate Organization: Croatian Logic Association
presented by its president Srećko Kovač
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.
-----
September 8 – João Rasga and Cristina Sernadas – Decidability of Logical Theories and Their Combination
Chair: Razvan Diaconescu
Member of the Editorial Board of SUL
Associate Organization: International Federation for Computational Logic - IFCOLOG
presented by Leon van der Torre
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.
-----
September 15, 2021 – Josué-Antonio Nescolarde-Selva – Four Interpretations of the Liar Paradox
Chair: Maria Manzano
Member of the Editorial Board of LU
Associate Organization: Spanish Society of Logic and Methodology and Philosophy of Science
presented by its president Cristina Corredor
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.
-----
October 6 – k-provability in PA – Paulo Guilherme Santos and Reinhard Kahle
Chair: Carlos Caleiro
Member of the Editorial Board of LU
Associate Organization: Logic in Portugal / Amilcar Sernadas Logic Pizre
presented by Francisco Dionisio
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.
-----
October 13, 2021 – Amirouche Moktefi – Why make things simple when you can make them complicated? An appreciation of Lewis Carroll’s symbolic logic
Chair: Leo Corry
Member of the Editorial Board of LU
Associate Organization: Lewis Carroll Society
presented by its chairman Steve 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.
-----
November 10 – Proof-theoretical frameworks for many-valued logics – Michael Kaminski and Nissim Francez
Chair: Arnon Avron
Editorial Board of LU
Associate Organization: Logic in Israel
presented by Liron Cohen
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.
-----
November 17, 2021 – Yaroslav Petrukhin & Vasilyi Shangin – Correspondence Analysis for Some Fragments of Classical Propositional Logic
Chair: Andrei Rodin
Member of the Editorial Board of LU
Associate Organization: Moscow Logic Goup
presented by its chairman Vladimir Vasyukov
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.
-----
December 8, 2021 – John Grant – Measuring Inconsistency in Generalized Propositional Logic
Chair: TBA
Associate Organization: TBA
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.
-----
December 15, 2021 – Scott L.Pratt – Decolonizing “Natural Logic”, Chapter of Logical Skills
Chair: Francesco Paoli
Member of the Editorial Board of SUL
Organizers: Julie Brumberg-Chaumont and Claude Rosenthal
Editors of Logical Skills
“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.
-----