Logica Universalis - Logica Universalis Webinar 2023
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 project started in 2021. Click here (this opens in a new tab) to access the webinar series of past editions.
The LUW 2023 series started with an "extraordinary" session:
LUA celebration of the fifth World Logic Day: Roundtable on "The Importance of Logic For Humanity (this opens in a new tab)", Jan 14, 2023. See here (this opens in a new tab)fore more information.
Video recordings of the seminars are uploaded on the Cassyni platform (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
Speakers and Abstracts
January 25, 2023 – Zalán Gyenis (this opens in a new tab) –
Universal Algebraic Logic - Dedicated to the Unity of Science (this opens in a new tab)
Chair: Razvan Diaconescu (this opens in a new tab)
Editorial Board SUL
Associate Organization: Italian Society of Studies in Universal Logic, Birkhäuser / Springer-Nature (this opens in a new tab), presented by its publishing editor Frida Trotter
This is the presentation of a book that gives a comprehensive introduction to Universal Algebraic Logic. The three main themes are (i) universal logic and the question of what logic is, (ii) duality theories between the world of logics and the world of algebra, and (iii) Tarskian algebraic logic proper including algebras of relations of various ranks, cylindric algebras, relation algebras, polyadic algebras and other kinds of algebras of logic. One of the strengths of our approach is that it is directly applicable to a wide range of logics including not only propositional logics but also e.g. classical first order logic and other quantifier logics. Following the Tarskian tradition, besides the connections between logic and algebra, related logical connections with geometry and eventually spacetime geometry leading up to relativity are also part of the perspective of the book. Besides Tarskian algebraizations of logics, category theoretical perspectives are also touched upon.
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February 15, 2023 – Sayantan Roy (this opens in a new tab) –
Lindenbaum-type Logical Structures (this opens in a new tab)
Chair: Raja Natarajan (this opens in a new tab)
Editorial Board LU
Associate Organization: Indraprastha Institute of Information Technology, presented by Sankha S. Basu (this opens in a new tab) and São Paulo School of Advanced Science on Contemporary Logic, Rationality, and Information (this opens in a new tab), presented by its organizers Itala D’Ottaviano (this opens in a new tab) and Walter Carnielli (this opens in a new tab)
In this talk, we present some classes of logical structures from the universal logic standpoint, viz., those of the Tarski- and the Lindenbaum-types. The characterization theorems for the Tarski- and two of the four different Lindenbaum-type logical structures will be mentioned as well. The separations between the five classes of logical structures, viz., the four Lindenbaum-types and the Tarski-type have been established via examples. Finally, we study the logical structures that are of both Tarski- and a Lindenbaum-type, show their separations, and end with characterization, adequacy, minimality, and representation theorems for one of the Tarski-Lindenbaum-type logical structures.
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February 22, 2023 – Isabelle Bloch (this opens in a new tab) –
Abstract Categorical Logic (this opens in a new tab)
Chair: Andrei Rodin (this opens in a new tab)
Editorial Board LU
Associate Organization: GDR IA, CNRS (this opens in a new tab), presented by Meghyn Bienvenu (this opens in a new tab)
We present in this talk an abstract categorical logic based on an abstraction of quantifier. More precisely, the proposed logic is abstract because no structural constraints are imposed on models (semantics free). By contrast, formulas are inductively defined from an abstraction both of atomic formulas and of quantifiers. In this sense, the proposed approach differs from other works interested in formalizing the notion of abstract logic and of which the closest to our approach are the institutions, which in addition to be semantics free do not also impose any syntactic contingencies on the structure of formulas. To define the semantical framework in which formulas will be interpreted, we propose to follow the idea from categorical logic which defines the semantical interpretation of formulas from context and as subobjects of an object of a given category. In the spirit of Lawvere’s hyperdoctrines, we use a more abstract notion which generalizes the notion of subobject, standard in category theory: Pitt’s prop-categories. Always in the spirit of categorical logic, we propose a sequent calculus of which we show correctness and completeness for all semantical frameworks defined over any prop-categories. We then study some conditions which allow us to get this completeness result for particular classes of prop-categories.
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March 22, 2023 – Nirmal Selvamony (this opens in a new tab) –
Chapter of the book Logic in tolkāppiyam (this opens in a new tab)
Chair: Raja Natarajan (this opens in a new tab)
Editorial Board LU
Presentation of the book Handbook of Logical Thought in India (this opens in a new tab) by Sundar Sarukkai (this opens in a new tab)
Tolkāppiyam shows us that logic had an important place in the primal society (known as tiṇai). Such primal cultural practices as “tarukkam,” “vākai,” analogical reasoning, the use of the criteria of knowledge (“aḷavai”) in premarital life situations and in oral texts (such as mutumoḻi and kāṇṭikai), and also the primal social institution, namely, the assembly (avai) where public debates were held, were all part of the philosophical tradition of this society. Such philosophy embraced logic, which had rhetorical as well as epistemic functions. If rhetorical logic was persuasive (as in tarukkam) and contestatory (as in vākai in combat and in the assembly), epistemic logic (aḷavai) was validative. In fact, early Tamil logic was a complex discipline not easily distinguishable from philosophy (especially, epistemology and ethics) and rhetoric.
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March 29, 2023 – Urszula Wybraniec-Skardowska (this opens in a new tab) –
The book Logic - Language - Ontology (this opens in a new tab)
Chair: Janusz Czelakowski
Editorial Board LU
Associate Organization: Polish Association of Logic and Philosophy of Science (this opens in a new tab), presented by its vice-president Dorota Leszczyńska-Jasion
How should we think about the meaning of the words that make up our language? How does reference of these terms work, and what is their referent when these are connected to abstract objects rather than to concrete ones? Can logic help to address these questions? This collection of papers aims to unify the questions of syntax and semantics of language, which span across the fields of logic, philosophy and ontology of language. The leading motif of the presented selection is the differentiation between linguistic tokens (material, concrete objects) on the one hand and linguistic types (ideal, abstract objects) on the other. Through a promenade among articles that span over all of the Author’s career, this book addresses the complex philosophical question of the ontology of language by following the crystalline conceptual tools offered by logic. At the core of Wybraniec-Skardowska’s scholarship is the idea that language is an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. The application throughout the book of tools of classical logic and set theory results fosters the emergence of a general formal logical theory of syntax, semantics and of the pragmatics of language, which takes into account the duality token-type in the understanding of linguistic expressions. Via a functional approach to language itself, logic appears as ontologically neutral with respect to existential assumptions relating to the nature of linguistic expressions and their extra-linguistic counterparts.
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April 19, 2023 – Hugolin Bergier (this opens in a new tab) –
An Intensional Formalization of Generic Statements (this opens in a new tab)
Chair: Srecko Kovac (this opens in a new tab),
Editorial Board LU
Associate Organization: InterPARES (this opens in a new tab), presented by one of its collaborators, Kenneth Thibodeau (this opens in a new tab)
A statement is generic if it expresses a generalization about the members of a kind, as in, ’Pear trees blossom in May,’ or, ’Birds lay egg’. In classical logic, generic statements are formalized as universally quantified conditionals: ’For all x, if ..., then ....’ We want to argue that such a logical interpretation fails to capture the intensional character of generic statements because it cannot express the generic statement as a simple proposition in Aristotle’s sense, i.e., a proposition containing only one single predicate. On the contrary, we’ll show that lambda abstraction and combinatory logic can help us transform the classical, non-simple and extensional expression of generic statements into a new, simple and intensional formalization, through the introduction of an operator that we will call ALL*. We will show that this new operator allows for the possibility of a single predication, e.g. fly(), because it builds, out of a concept like ’bird’, a concrete universal, e.g. ’birds’, upon which the single predicate can be applied to authentically formalize a generic statement, e.g. ’birds fly’.
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April 26, 2023 – Angelina Ilic Stepic (this opens in a new tab) – Probability Logics for Reasoning About Quantum Observations (this opens in a new tab)
From the Logic in Question 10 (this opens in a new tab) (Sorbonne, Paris) with also the launch of the book Logic in Question (this opens in a new tab) - Talks from the Annual Sorbonne Logic Workshop (2011- 2019)
Chair: Andrei Rodin (this opens in a new tab),
Editorial Board LU
Associate Organization: Logica Universalis Association (this opens in a new tab), presented by its president Jean-Yves Beziau (this opens in a new tab)
In this paper we present two families of probability logics (denoted QLP and QLPORT ) suitable for reasoning about quantum observations. Assume that a means “O = a”. The notion of measuring of an observable O can be expressed using formulas of the form ??a which intuitively means “if we measure O we obtain a”. In that way, instead of non-distributive structures (i.e., non-distributive lattices), it is possible to relay on classical logic extended with the corresponding modal laws for the modal logic B. We consider probability formulas of the form CSz1,?1;...;zm,?m??a related to an observable O and a possible world (vector) w: if a is an eigenvalue of O, w1, . . . , wm form a base of a closed subspace of the considered Hilbert space which corresponds to eigenvalue a, and if w is a linear combination of the basis vectors such that w = c1·w1+. . .+cm·wm for some ci ? C, then ?c1 - z1? = ?1, . . . , ?cm - zm? = ?m, and the probability of obtaining a while measuring O in the state w is equal to Sm i=1?ci?2. Formulas are interpreted in reflexive and symmetric Kripke models equipped with probability distributions over families of subsets of possible worlds that are orthocomplemented lattices, while for QLPORT also satisfy ortomodularity. We give infinitary axiomatizations, prove the corresponding soundness and strong completeness theorems, and also decidability for QLP-logics.
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May 10, 2023 – Ekaterina Kubyshkina (this opens in a new tab) and Mattia Petrolo (this opens in a new tab) – Revising the Elenchus via Belief Revision
Chair: Ioannis Vandoulakis,
Vice-President of the Logica Universalis Association (this opens in a new tab)
Associate Organization: LUCI (this opens in a new tab) (Logic, Uncertainty, Computation and Information Group) presented by Giuseppe Primiero (this opens in a new tab)
Vlastos’ famous characterization of the Socratic elenchus focuses on two main aspects of this method: its epistemic roots and its dialogical nature. Our aim is to lay the groundwork to formally capture this characterization. To do so, first, we outline an epistemic framework in which the elenchus can be inscribed. More precisely, we focus our analysis on the passage from unconscious ignorance to conscious (or Socratic) ignorance and provide new insights about the epistemic outcome of an elenctic argument. Secondly, from a logical perspective, we consider the elenchus as a dynamic exchange allowing Socrates’ respondents to revise their beliefs, on pain of inconsistency. By stressing this point, we represent this method as a process of belief revision in dynamic epistemic logic and provide a new logical solution to what Vlastos called the problem of the elenchus.
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May 17, 2023 – Olivia Caramello (this opens in a new tab) – The Unification of Mathematics via Topos Theory (this opens in a new tab)
Chair: Francesco Paoli (this opens in a new tab),
Editorial Board SUL
Associate Organization: Grothendieck Institute (this opens in a new tab), presented by Laurent Lafforgue (this opens in a new tab)
We present a set of principles and methodologies which may serve as foundations of a unifying theory of Mathematics. These principles are based on a new view of Grothendieck toposes as unifying spaces being able to act as “bridges” for transferring information, ideas, and results between distinct mathematical theories.
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June 14, 2023 – Nathan Salmon (this opens in a new tab) – The Decision Problem for Effective Procedures (this opens in a new tab)
Chair: Melvin Fitting (this opens in a new tab),
Editorial Board LU
Associate Organization: Celebration of the 120th birthday of Alonzo Church (this opens in a new tab), presented by his last PhD student Gary R.Mar (this opens in a new tab)
The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined even if it is not sufficiently formal and precise to belong to mathematics proper (in a narrow sense)—and even if (as many have asserted) for that reason the Church–Turing thesis is unprovable. It is proved logically that the class of effective procedures is not decidable, i.e., that there is no effective procedure for ascertaining whether a given procedure is effective. This result is proved directly from the notion itself of an effective procedure, without reliance on any (partly) mathematical lemma, conjecture, or thesis invoking recursiveness or Turing-computability. In fact, there is no reliance on anything very mathematical. The proof does not even appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of an effective procedure. Though the result that effectiveness is undecidable is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure invariably terminates with the correct verdict.
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June 28, 2023 – Krzysztof A. Krawczyk (this opens in a new tab) – Ultravaluations and their Applications in Classical Propositional Logic (this opens in a new tab)
Chair: Eunsuk Yang (this opens in a new tab),
Editorial Board LU
Associate Organization: Kraków Logic Group (this opens in a new tab) and CLoCk (this opens in a new tab) presented by Tomasz Kowalski (this opens in a new tab)
This paper introduces the construct of an ultravaluation inspired by the well-known ultraproduct. Basic properties and exemplary applications of this notion are shown: for compactness and definability theorems. We also use ultravaluations to check failure of compactness and undefinability.
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July 12, 2023 – Hamzeh Mohammad (this opens in a new tab) – Rooted Hypersequent Calculus for Modal Logic S5 (this opens in a new tab)
Chair: Musa Akrami,
Editorial Board LU
Associate Organization: Iranian Association for Logic presented by its president Hamed Bastin (this opens in a new tab)
We present a rooted hypersequent calculus for modal propositional logic S5. We show that all rules of this calculus are invertible and that the rules of weakening, contraction, and cut are admissible. Soundness and completeness are established as well.
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July 19, 2023 – Gennady Shtakser (this opens in a new tab) – Epistemic Logics with Quantification Over Epistemic Operators: Decidability and Expressiveness (this opens in a new tab)
Chair: Carlos Caleiro (this opens in a new tab),
Editorial Board LU
Associate Organization: Ukrainian Logic Society presented by its president Mykola Nikitchenko (this opens in a new tab)
The optimal balance between decidability and expressiveness is a big problem of logical systems, in particular, of quantified epistemic logics (QELs). On the one hand, decidability is a very significant characteristic of logics that allows us to use such logics in the framework of artificial intelligence. On the other hand, QELs have important expressive capabilities that should not be lost when we construct decidable fragments of these logics. QELs are known to be much more expressive than first-order logics. One important example of their extra expressive power is that they allow us to distinguish between de dicto and de re readings of epistemic sentences. It is clear that such capabilities should be preserved as much as possible in decidable fragments. In this paper, we consider extensions of QELs that include quantification over modalities. Denote this extensions by Q□Ls. Q□Ls allows us to make more subtle distinctions between de dicto and de re readings of epistemic sentences, and we also should keep these new features as much as possible in decidable fragments. It is known that there are not much interesting decidable QELs. The situation with Q□Ls is the same. But in recent years (after 2018), we have obtained a variety of decidable Q□Ls constructed in different ways. We distinguish between (1) the approach in which for every undecidable Q□L and for every variant of its decidable fragment, a specific proof is constructed, and (2) the approach in which a class of decidable Q□Ls is obtained using general tools and a uniform method for all Q□Ls of this class. In this paper, we compare the results of these approaches.
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August 23, 2023 – Chai Wah Wu (this opens in a new tab) – On rearrangement inequalities for triangular norms and co-norms in multi-valued logic (this opens in a new tab)
Chair: Sayantan Roy,
Assistant Editor Logica Universalis
Associate Organization: Mathematics of AI group of IBM Watson Research Center (this opens in a new tab) presented by Kenneth L. Clarkson (this opens in a new tab)
The rearrangement inequality states that the sum of products of permutations of 2 sequences of real numbers are maximized when the terms are similarly ordered and minimized when the terms are ordered in opposite order. We show that similar inequalities exist in algebras of multi-valued logic when the multiplication and addition operations are replaced with various T-norms and T-conorms respectively. For instance, we show that the rearrangement inequality holds when the T-norms and T-conorms are derived from Archimedean copulas.
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August 30, 2023 – Edward Swiderski (this opens in a new tab) – Józef Maria Bocheński: biography, philosophical views, his contributions to logic
Chair: Sayantan Roy,
Assistant Editor Logica Universalis
Presentation of the book "The Lvov-Warsaw School. Past and Present" (this opens in a new tab), by Jan Woleński (this opens in a new tab)
Celebration of the 121th anniversary of Józef Maria Bocheński (this opens in a new tab) born August 30, 1902.
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September 20, 2023 – Alexei Muravitsky (this opens in a new tab) – On Consequence and Rejection as Operators (this opens in a new tab)
Chair: Ioannis Vandoulakis,
Vice-President of the Logica Universalis Association (this opens in a new tab)
Presentation of the special issue or Logica Universalis on Rejection by Alexei Muravitsky
Workshop at the 7th World Congress and School on Universal Logic 100 Years of Refutation in Logic (this opens in a new tab)
This paper is devoted to the concepts of consequence and rejection, formulated as operators on a nonempty set of sentences, which may initially be unstructured. One of the issues that we pay attention to is the “cyclicity” of these concepts when they are defined one through the other. In addition, we explore this cyclicity, when the set of all sentences acquires some structure, or we can assume some structure of sentences in the sense that the operation of substitution can be applied to them.
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October 4, 2023 – Gabriele Pulcini (this opens in a new tab) – Complementary Proof Nets for Classical Logic (this opens in a new tab)
Chair: Ioannis Vandoulakis,
Vice-President of the Logica Universalis Association (this opens in a new tab)
Presentation of the special issue or Logica Universalis on Rejection by Alex Citkin
Workshop at the 7th World Congress and School on Universal Logic 100 Years of Refutation in Logic (this opens in a new tab)
A complementary system for a given logic is a proof system whose theorems are exactly the formulas that are not valid according to the logic in question. This article is a contribution to the complementary proof theory of classical propositional logic. In particular, we present a complementary proof-net system, CPN, that is sound and complete with respect to the set of all classically invalid (one-side) sequents. We also show that cut elimination in CPN enjoys strong normalization along with strong confluence (and, hence, uniqueness of normal forms).
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October 18, 2023 – Maristela Rocha (this opens in a new tab) – A Study of the Metatheory of Assertoric Syllogistic (this opens in a new tab)
Chair: Jean-Yves Beziau,
Editor-in-Chief LU
Associate Organization: Salzburg Logic Group presented by Paul Weingartner
We show how a semantics based on Aristotle’s texts and ecthetic proofs can be reconstructed. All truth conditions are given by means of set inclusion. Perfect syllogisms reveal to be valid arguments that deserve a validity proof. It turns out of these proofs that transitivity of set inclusion is the necessary and sufficient condition for the validity and perfection of a syllogism. The proofs of validity for imperfect syllogisms are direct proofs without conversion in a calculus of natural deduction. Transitivity of set inclusion turns out to be a necessary condition for the validity of imperfect syllogisms. As a consequence, it can be established what the main metalogical difference between a perfect and an imperfect syllogism is. The validity of the laws of conversion is also obtained by direct proofs. Finally, it is shown that and explained why some imperfect syllogisms satisfy the definition of a perfect syllogism.
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November 15, 2023 – Alexander De Klerck (this opens in a new tab) – Morphisms between Aristotelian Diagrams
Chair: Srecko Kovac,
Editorial board LU
Associate Organization: STARTDIALOG (this opens in a new tab) (ERC project) - Towards a Systematic Theory of Aristotelian Diagrams in Logical Geometry presented by its director Lorenz Demey (this opens in a new tab)
In logical geometry, Aristotelian diagrams are studied in a precise and systematic way. Although there has recently been a good amount of progress in logical geometry, it is still unknown which underlying mathematical framework is best suited for formalizing the study of these diagrams. Hence, in this paper, the main aim is to formulate such a framework, using the powerful language of category theory. We build multiple categories, which all have Aristotelian diagrams as their objects, while having different kinds of morphisms between these diagrams. The categories developed here are assessed according to their ability to generalize previous work from logical geometry as well as their interesting category-theoretical properties. According to these evaluations, the most promising category has as its morphisms those functions on fragments that increase in informativity on both the opposition and implication relations. Focusing on this category can significantly increase the effectiveness of further research in logical geometry.
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November 29, 2023 – William Troiani (this opens in a new tab) – The internal logic and finite colimits (this opens in a new tab)
Chair: Roberto Giuntini (this opens in a new tab),
Editorial Board LU
Associate Organization: LoVe: Logic and Verification (this opens in a new tab) presented by Morgan Rogers
We describe how finite colimits can be described using the internal language, also known as the Mitchell-Benabou language, of a topos, provided the topos admits countably in finite colimits. This description is based on the set theoretic definitions of colimits and coequalizers, however the translation is not direct due to the di erences between set theory and the internal language, these differences are described as internal versus external. Solutions to the hurdles which thus arise are given.
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December 13, 2023 – Julio Michael Stern (this opens in a new tab) – Dynamic Oppositional Symmetries for Color, Jungian and Kantian Categories
Chair: Ioannis Vandoulakis (this opens in a new tab),
Vice-President LUA
Associate Organization: World Logic Day - 6th Edition (this opens in a new tab) presented by Jean-Yves Beziau
This paper investigates some classical oppositional categories, like synthetic vs. analytic, posterior vs. prior, imagination vs. grammar, metaphor vs. hermeneutic, metaphysics vs. observation, innovation vs. routine, and image vs. sound, and the role they play in epistemology and philosophy of science. The epistemological framework of objective cognitive constructivism is of special interest in these investigations. Oppositional relations are formally represented using algebraic lattice structures like the cube and the hexagon of opposition, with applications in the contexts of modern color theory, Kantian philosophy, Jungian psychology, and linguistics.
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