Logica Universalis - Logica Universalis Webinar 2022
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 project started in 2021. Click here to access last year's webinar website.
The LUW 2022 series started with an "extraordinary" session:
LUA celebration of the fourth World Logic Day: Roundtable on "The Exceptionality of Logic", Jan 14, 2022. See here fore more information.
Video recordings of the seminars are uploaded on the YouTube channel Universal Logic Project until the end of this year 2022 and on the Cassyni platform, which will continue also in the future.
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
Speakers and Abstracts
February 9, 2022 – Antonino Drago –
An Intuitionist Reasoning Upon Formal Intuitionist Logic: Logical Analysis of Kolmogorov’s 1932 Paper
Chair: Francesco Paoli
Editorial Board SUL
Associate Organization: Italian Society of Logic and Philosophy of Science (SILFS),
presented by its president Vincenzo Fano
Two dichotomies are considered as the foundations of a scientific theory: the kind of infinity—either potential or actual-, and the kind of organization of the theory—axiomatic or problem-based. The original intuitionist program relied on the choices of potential infinity and the problem-based organization. I show that the logical theory of Kolmogorov’s 1932 paper relied on the same choices. A comparison of all other theories sharing the same foundational choices allows us to characterize their common theoretical development through a few logical steps. The theory illustrated by Kolmogorov’s paper is then rationally re-constructed according to the steps of this kind of development. One obtains a new foundation of intuitionist logic, which is of a structural kind since it is based on and developed according to the structure of the above mentioned two fundamental choices. In addition, Kolmogorov’s illustration of his theory of intuitionist logic is an instance of rigorous reasoning of the intuitionist kind.
-----
February 16, 2022 – Alexandre Costa-Leite, Edelcio G. de Souza and Diogo H. B. Dias – Paraconsistent Orbits of Logics
Chair: Itala D'Ottaviano
Editorial Board LU
Associate Organization: Logic in the Plane (Lógica no Avião),
presented by its president Rodrigo Freire
Some strategies to turn any logic into a paraconsistent system are examined. In the environment of universal logic, we show how to paraconsistentize logics at the abstract level using a transformation in the class of all abstract logics called paraconsistentization by consistent sets . Moreover, by means of the notions of paradeduction and paraconsequence we go on applying the process of changing a logic converting it into a paraconsistent system. We also examine how this transformation can be performed using multideductive abstract logics. To conclude, the conceptual notion paraconsistent orbit of a logic is proposed.
-----
March 9, 2022 – Jean-Yves Beziau –
The 2nd World Logic Prizes Contest
Chair: Göran Sundholm,
President of the Jury of the 1st World Logic Prizes Contest
Associate Organization: Logica Universalis Association,
presented by its secretary Katarzyna Gan-Krzywoszyńska
We discuss the development of the logic prizes and we present the 2nd World Logic Prizes Contest, that will take place in Crete in April 2022 during the 7th UNILOG (World Congress and School on Universal Logic)
-----
March 16, 2022 – Eunsuk Yang – Implicational Tonoid Logics and Implicational Partial Galois Logics
Chair: Jui-Lin Lee
Editorial Board SUL
Associate Organization: Korean Association of Logic,
presented by its Secretary Ilho Park
This paper combines two classes of generalized logics, one of which is the class of weakly implicative logics introduced by Cintula and the other of which is the class of gaggle logics introduced by Dunn. For this purpose we introduce implicational tonoid logics. More precisely, we first define implicational tonoid logics in general and examine their relation to weakly implicative logics. We then provide algebraic semantics for implicational tonoid logics. Finally, we consider relational semantics, called Routley–Meyer–style semantics, for finitary those logics.
Implicational tonoid logics and their relational semantics have been introduced by Yang and Dunn. This paper extends this investigation to implicational partial Galois logics. For this, we first define some implicational partial gaggle logics as special kinds of implicational tonoid logics called “implicational partial Galois logics.” Next, we provide Routley–Meyer-style relational semantics for finitary those logics.
-----
April 13, 2022 – Andrew Schumann (Head of the Department of Cognitive Science and Mathematical Modeling, University of Information Technology and Management in Rzeszow, Poland) – On the Origin of Logical Determinism in Babylonia
Chair: Jean-Yves Beziau,
Editor-in-Chief Logica Universalis
Associate Organization: Warsaw Scientific Society,
presented by Jan Woleński
In this paper, I show that the idea of logical determinism can be traced back from the Old Babylonian period at least. According to this idea, there are some signs (omens) which can explain the appearance of all events. These omens demonstrate the will of gods and their power realized through natural forces. As a result, each event either necessarily appears or necessarily disappears. This idea can be examined as the first version of eternalism – the philosophical belief that each temporal event (including past and future events) is actual. In divination lists in Akkadian presented as codes we can reconstruct Boolean matrices showing that the Babylonians used some logical-algebraic structures in their reasoning. The idea of logical contingency was introduced within a new mood of thinking presented by the Greek prose – historical as well as philosophical narrations. In the Jewish genre ’aggādōt, the logical determinism is supposed to be in opposition to the Greek prose.
-----
April 20, 2022 – Nate Ackermann (Harvard University, USA) – Encoding Complete Metric Structures by Classical Structures
Chair: Andrei Rodin,
Editorial Board LU
Associate Organization: Cambridge/Boston Logic Group,
presented by Rehana Patel
We show how to encode, by classical structures, both the objects and the morphisms of the category of complete metric spaces and uniformly continuous maps. The result is a category of, what we call, cognate metric spaces and cognate maps. We show this category relativizes to all models of set theory (unlike the category of complete metric spaces and uniformly continuous maps). We extend this encoding to an encoding of complete metric structures by classical structures. This provide us with a general technique for translating results about infinitary logic on classical structures to the setting of infinitary continuous logic on continuous structures. Our encoding will also allow us to talk about not only the relations between complete metric structures, but also the potential relations between complete metric structures, i.e. those which are satisfied in some larger model of set theory. For example we will show that given any two complete metric structures we can determine if they are potentially isomorphic by looking at any admissible set which contains them both.
-----
May 11, 2022 – Alexei Muravitsky (Louisiana Scholars’ College, Northwestern State University, USA) – On Nonmonotonic Consequence Relations
Chair: Melvin Fitting,
Editorial Board LU
Associate Organization: Moscow Logic School,
presented by Alex Citkin
We discuss nonmonotonic reasoning in terms of consequence relations and corresponding operators. Based on the matrix consequence that gives the monotonic case, we define a restricted matrix consequence that illustrates the nonmonotonic case. The latter is a generalization of the relation of logical friendliness introduced by D. Makinson. We prove that any restricted single matrix consequence, although it may be nonmonotonic, is always weakly monotonic and, in the case of a finite matrix, the restricted matrix consequence is very strongly finitary. Further, by modifying the definition of logical friendliness relation formulated specifically in a proof-theoretic manner, we show a possibility of obtaining other reflexive nonmonotonic consequence relations, for which a limited result towards finitariness is proved. This leads to numerous questions about nonmonotonic consequence relations in the segment between the monotonic consequence relation based on intuitionistic propositional logic and logical friendliness.
-----
May 18, 2022 – Roland Bolz (Humboldt University, Berlin, Germany) – Visualization Criteria and Boolean Algebras (Chapter of the book The Exoteric Square of Opposition)
Chair: Ioannis Vandoulakis,
Vice-President of LUA (Logica Universalis Asssociaton) and co-editor of the book The Exoteric Square of Opposition
Associate Organization: Organizers of the 7th SQUARE,
Hans Smessaert, Dany Jaspers and Lorenz Demey
This paper presents logical diagrams as attempts to visualize facts about logical/linguistic/conceptual systems. It introduces four criteria for assessing visualization: 1) completeness, 2) correctness, 3) lack of distortion, and 4) legibility. It then studies presents well-known families of diagrams, based on the geometrical figures of a) the hexagon, and b) the tetrakis hexahedron. These are usually presented as exemplary diagrams. To understand better why they succeed so well at visualizing logical information, they are presented as visualizations of complete (finite) Boolean algebras. This also establishes the connection between the combinatorial concept of partition and the logical concept of opposition (i.e. contradiction, contrariness, and subcontrariness). Finally, the paper suggests that the two geometrical figures in question are part of a larger family of polytopes with deep connections to Boolean algebras.
-----
June 8, 2022 – Ciro Russo (Federal University of Bahia, Salvador, Brazil) – Coproduct and Amalgamation of Deductive Systems by Means of Ordered Algebras
Chair: Ivan Varzinczak,
Editorial Board LU and President of the 2nd Word Logic Prizes Contest
Associate Organization: Logica Universalis Organization,
presented by its President Jean-Yves Beziau, Founder and Organizer of the World Logic Prizes Contest
We propose various methods for combining or amalgamating propositional languages and deductive systems. We make heavy use of quantales and quantale modules in the wake of previous works by the present and other authors. We also describe quite extensively the relationships among the algebraic and order-theoretic constructions and the corresponding ones based on a purely logical approach.
-----
June 15, 2022 – Anne-Françoise Schmid (Ecole des Mines, Paris, France) – The Place and Value of Logic in Louis Couturat’s Philosophical Thinking (Collected in the book Logic in Question - Talks from the Annual Sorbonne Logic Workshop (2011- 2019))
Chair: Razvan Diaconescu,
Editorial Board SUL
Associate Organization: Organizers of the workshop Logic in Question and editors of the book Logic in Question - Talks from the Annual Sorbonne Logic Workshop (2011- 2019),
Jean-Yves Beziau, Jean-Pierre Desclés, Amirouche Moktefi, Anca Christine Pascu
Louis Couturat is known for affirming and defending the works of logic available during his lifetime, especially those of Russell and the Italian school. His work of conceptual analysis is exceptional and unique in its ability to put in relation the mathematicians of his time, for which his reputation is well deserved. Taking a closer look at his work at large, the place and value of logic are not simple problems for Couturat. On one hand, the new logic differs from the Greek methods of Aristotelian logic, and yet it has no place in mathematics unlike the algebraic school Couturat frequently addresses. On the other hand, he discovers the logic of Russell as a novelty and invention, to which he gives, in agreement with Lalande and Itelson, the old name of Logistics. He complicates things further in his unpublished Manuel de Logistique (written in 1905), where he presents it as an ancient science to which symbols have been added (however, we know he does not like the use of symbols as Peano instituted). Couturat is therefore in a complex relationship with the logic of his time. The following is an attempt to unfold the consequences. Our main source for this lecture on Louis Couturat will be the correspondences with Bertrand Russell between 1897 and 1913, edited and annotated by us. It is all the more valuable because we have letters from both contributors and it is the most important scientific correspondence of Russell.
-----
July 6, 2022 – Stepan I. Bashmakov (Siberian Federal University, Krasnoyarsk, Russia) – Unification in Pretabular Extensions of S4
Chair: Vladimir Vasyukov,
Editorial Board SUL
Associate Organization: Siberian Logic Group,
presented by Nikolay Bazhenov
L.L. Maksimova and L. Esakia, V. Meskhi showed that the modal logic S4 has exactly 5 pretabular extensions PM1–PM5. In this paper, we study the problem of unification for all given logics. We showed that PM2 and PM3 have finitary, and PM1, PM4, PM5 have unitary types of unification. Complete sets of unifiers in logics are described.
-----
July 14, 2022 – Mateusz Klonowski (Nicolaus Copernicus University in Toruń, Poland) – Axiomatization of Some Basic and Modal Boolean Connexive Logics
Chair: Raja Natarajan,
Editorial Board LU
Associate Organization: Toruń Logic Group,
presented by Jacek Malinowski
Boolean connexive logic is an extension of Boolean logic that is closed under Modus Ponens and contains Aristotle’s and Boethius’ theses. According to these theses (i) a sentence cannot imply its negation and the negation of a sentence cannot imply the sentence; and (ii) if the antecedent implies the consequent, then the antecedent cannot imply the negation of the consequent and if the antecedent implies the negation of the consequent, then the antecedent cannot imply the consequent. Such a logic was first introduced by Jarmużek and Malinowski, by means of so-called relating semantics and tableau systems. Subsequently its modal extension was determined by means of the combination of possible-worlds semantics and relating semantics. In the following article we present axiomatic systems of some basic and modal Boolean connexive logics. Proofs of completeness will be carried out using canonical models defined with respect to maximal consistent sets.
-----
August 3, 2022 – Norihiro Kamide (Teikyo University, Japan) – An Extended Paradefinite Logic Combining Conflation, Paraconsistent Negation, Classical Negation, and Classical Implication: How to Construct Nice Gentzen-type Sequent Calculi
Chair: Arnon Avron,
Editorial Board LU
Associate Organization: TBA,
presented by
In this study, an extended paradefinite logic with classical negation (EPLC), which has the connectives of conflation, paraconsistent negation, classical negation, and classical implication, is introduced as a Gentzen-type sequent calculus. The logic EPLC is regarded as a modification of Arieli, Avron, and Zamansky’s ideal four-valued paradefinite logic (4CC) and as an extension of De and Omori’s extended Belnap–Dunn logic with classical negation (BD+) and Avron’s self-extensional four-valued paradefinite logic (SE4). The completeness, cut-elimination, and decidability theorems for EPLC are proved and EPLC is shown to be embeddable into classical logic. The strong equivalence substitution property and the admissibilities of the rules of negative symmetry, contraposition, and involution are shown for EPLC. Some alternative simple Gentzen-type sequent calculi, which are theorem-equivalent to EPLC, are obtained via these characteristic properties.
-----
August 10, 2022 – Kenji Tokuo (National Institute of Technology, Japan) – Natural Deduction for Quantum Logic
Chair: Francesco Paoli,
Editorial Board SUL
Associate Organization: International Quantum Structures Association - IQSA,
presented by Christian de Ronde
This paper presents a natural deduction system for orthomodular quantum logic. The system is shown to be provably equivalent to Nishimura’s quantum sequent calculus. Through the Curry-Howard isomorphism, quantum l-calculus is also introduced for which strong normalization property is established.
-----
September 7, 2022 – David Makinson – Frege’s Ontological Diagram Completed
Chair: Valentin Goranko,
Editorial Board LU
Associate Organization: Australasian Association of Logic,
presented by its president Guillermo Badia
In a letter of 1891, Frege drew a diagram to illustrate his logical ontology. We observe that it omits features that play an important role in his thought on the matter, propose an extension of the diagram to include them, and compare with a diagram of the ontology of current first-order logic.
-----
September 28, 2022 – Tin Adlešic – A Modern Rigorous Approach to Stratification in NF/NFU
Chair: Srecko Kovac,
Editorial Board LU
Associate Organization: European Set Theory Society,
presented by its president Philip Welch
The main feature of NF/NFU is the notion of stratification, which sets it apart from other set theories. We define stratification and prove constructively that every stratified formula has the (unique) least assignment of types. The basic notion of stratification is concerned only with variables, but we extend it to abstraction terms in order to simplify further development. We reflect on nested abstraction terms, proving that they get the expected types. These extensions enable us to check whether some complex formula is stratified without rewriting it in the basic language. We also introduce natural numbers and a variant of the axiom of infinity, in order to precisely introduce type level ordered pairs, which are crucial in simplifying the definitions in the last part of the article. Using these notions we can easily define the sets of ordinal and cardinal numbers, which we show at the end of the article. The same approach can be readily applied to NF.
-----
October 19, 2022 – Lorenz Demey – Leonardi.DB: A Database of Aristotelian Diagrams
Chair: Sergei Odintsov,
Editorial Board LU
Associate Organization: Belgian National Centre for Research in Logic,
presented by Jan Heylen
Aristotelian diagrams, such as the square of opposition, are among the oldest and most well-known types of logical diagrams. Within the burgeoning research program of logical geometry, we have been developing a comprehensive database of Aristotelian diagrams that occur in the extant literature: Leonardi.DB (the Leuven Ontology for Aristotelian Diagrams, and its corresponding Database). In this talk, which is based on joint work with Hans Smessaert, I will present Leonardi.DB to the universal logic research community. We describe the philosophical background and main motivations for Leonardi.DB, focusing on how the database provides a solid empirical foundation for theoretical research within logical geometry. We also discuss some of the main methodological and technical aspects of the database development. As a proof-of-concept, we provide some examples of the new kinds of research that will be facilitated by Leonardi.DB, e.g., regarding broad trends in the usage and visual properties of Aristotelian diagrams.
-----
October 26, 2022 – Cheng Liao – Games and Lindström Theorems
Chair: Janusz Czelakowski,
Editorial Board LU
Associate Organization: Institute for Logic, Language and Computation, Amsterdam,
presented by TBA
The Ehrenfeucht–Fraïsse game for a logic usually provides an intuitive characterization of its expressive power while in abstract model theory, logics are compared by their expressive powers. In this paper, I explore this connection in details by proving a general Lindström theorem for logics which have certain types of Ehrenfeucht–Fraïsse games. The results generalize and uniform some known results and may be applied to get new Lindström theorems for logics.
-----
November 16, 2022 – María del Rosario Martínez-Ordaz – A Methodological Shift in Favor of (Some) Paraconsistency in the Sciences
Chair: Peter Verdée,
Editorial Board LU
Associate Organization: Mexican Academy of Logic,
presented by its president Abel Rubén Hernández Ulloa
Many have contended that non-classical logicians have failed at providing evidence of paraconsistent logics being applicable in cases of inconsistency toleration in the sciences. With this in mind, my main concern here is methodological. I aim at addressing the question of how should we study and explain cases of inconsistent science, using paraconsistent tools, without ruining into the most common methodological mistakes. My response is divided into two main parts: first, I provide some methodological guidance on how to approach cases of inconsistent science; and second, I focus on a peculiar type of formal methodologies for the scrutiny of inconsistent reasoning, the Paraconsistent Alternative Approach (henceforth, PAA) and argue that PAA can enhance a more accurate understanding of sensible reasoning in inconsistent contexts.
-----
Cancelled and postponed to a date to be determined.
Andrew Schumann and Jens Lemanski present the special issue Logic, Spatial Algorithms and Visual Reasoning.
November 30, 2022 – Andrew Adamatzky – Logics in Fungal Mycelium Networks
Chair: Jean-Yves Beziau,
Editor-in-Chief LU
Presentation of the special issue of LU (Logic, Spatial Algorithms and Visual Reasoning),
edited by Andrew Schumann and Jens Lemanski
The living mycelium networks are capable of efficient sensorial fusion over very large areas and distributed decision making. The information processing in the mycelium networks is implemented via propagation of electrical and chemical signals en pair with morphological changes in the mycelium structure. These information processing mechanisms are manifested in experimental laboratory findings that show that the mycelium networks exhibit rich dynamics of neuron-like spiking behaviour and a wide range of non-linear electrical properties. On an example of a single real colony of Aspergillus niger, we demonstrate that the non-linear transformation of electrical signals and trains of extracellular voltage spikes can be used to implement logical gates and circuits. The approaches adopted include numerical modelling of excitation propagation on the mycelium network, representation of the mycelium network as a resistive and capacitive network and an experimental laboratory study on mining logical circuits in mycelium bound composites.
-----
December 14, 2022 – Šejla Dautović – A Probabilistic Logic Between LPP1 and LPP2
Chair: Raja Natarajan
Editorial Board LU
Associate Organization: Seminar for Mathematical Logic,
presented by its chairman Predrag Tanović
An extension of the propositional probability logic LPP2 given in Ognjanović et al. (Probability Logics. Probability-Based Formalization of Uncertain Reasoning, Theoretical Springer, Cham, Switzerland, 2016) that allows mixing of propositional formulas and probabilistic formulas is introduced. We describe the corresponding class of models, and we show that the problem of deciding satisfiability is in NP. We provide infinitary axiomatization for the logic and we prove that the axiomatization is sound and strongly complete.