Toruń Logic Group: Logica Copernicana Seminar

13.06.2024

Visual Perception, Affordences, and Concepts

Ivo Duntsch

Brock University
Canada

Abtsract. Over a period of fifty years, the psychologist J.J. Gibson developed an “Ecological Approach to Visual Perception” that was radically different from the prevailing views of the time – and, to some extent, from those of today. The term ecological in the sense used by Gibson pertains to the natural environment, to the “everyday things” of the acting individual – no molecules, no galaxies, no nanoseconds, no eons. Gibson claims that the observer and the observed are an inseparable pair, related by affordances: ‘‘The affordances of the environment are what it offers the animal, what it provides or furnishes, either for good or ill... I mean by it something that refers to both the environment and the animal in a way that no existing term does. It implies the complementarity of the animal and the environment.”

Though controversial, Gibson’s concept of direct perception and affordances was applied in many areas, for example, to theories of design and to robot control architecture that enables a robot to perceive more interaction possibilities than a traditional architecture that relies on appearance–based object recognition alone. In the presentation I shall outline Gibson’s theory and the concept of affordances, and I will sketch a connection to a theory of concepts.



15.04. and 16.04.2024

Paradoxes and Truth in a Logic of Sentential Operators

Michal Walicki

Department of Informatics
University of Bergen
Norway

Abstract. We show how to extend any classical (first or higher order) language with the sentential quantifiers and operators. Graph-based semantics coincides with the classical one for the classical sublanguage. The self-referential capabilities allow to express paradoxes, which arise due to unfortunate definitions of operators. They do not entail explosion, differing thus from the contradictions. For such an extension of FOL, a complete reasoning system is obtained by adding to Gentzen's LK two rules for the sentential quantifiers.

For any given structure, an operator defining the semantics can be introduced, allowing to define a nontrivial truth operator. This extension entails unrestricted Convention T and compositionality axioms. It is also semantically conservative, so -- unlike in the standard setting with the arithmetized syntax and truth predicate - every consistent theory can be augmented with the truth operator without introducing any inconsistency. A general form of such an extension (not relative to any structure) is under investigation, and the second part of the presentation will address some open issues.



12.03.2024

Quantifiers in Connexive Logic

Heinrich Wansing

Ruhr-Universitat Bochum
Germany



11.03.2024

Logical Bilateralism and Non-Trivial Negation Inconsistency

Heinrich Wansing

Ruhr-Universitat Bochum
Germany



04.03.2024

On Two Seminal Approaches to Paraconsistency: da Costa and Jaśkowski

Abilio Rodrigues Filho

Federal University of Minas Gerais
and University of Campinas
Brazil

Abstract. The aim of this paper is to analyze and compare two seminal approaches to paraconsistency, proposed by Jaśkowski (1948) and da Costa (1963). This talk corresponds to the first part of the paper and is devoted to technical, conceptual, and historical aspects of the work of da Costa's and his collaborators on paraconsistent logics. (Joint work with Marek Nasieniewski.)



17.10.2023

Inconsistency-Tolerant Nonmonotonic Logics: In Search of New Approaches to Inconsistency-Adaptive Logics

Sanderson Molick

Federal Institute of Para
Brazil

Abstract. In this talk, I will introduce a new family of first-order nonmonotonic paraconsistent logics (dubbed inconsistency-tolerant nonmonotonic logics). Based on a novel approach to inconsistency-adaptive logics, I will show that inconsistency-tolerant nonmonotonic logics are capable of overcoming various shortcomings discovered in first-order extensions of nonmonotonic paraconsistent logics introduced by authors such as Graham Priest and Diderik Batens. The talk is based on joint work with Christian StraSer (Ruhr-University Bochum).



17.10.2023

What do 'Evidence' and 'Truth' Mean in the Logics of Evidence and Truth

Abilio Rodrigues Filho

Federal University of Minas Gerais
and University of Campinas
Brazil

Abstract. Logics of evidence and truth (LETs) are paraconsistent and paracomplete logics that extend the logic of first degree entailment, also known as Belnap-Dunn 4-valued logic, with a classicality operator that recovers classical logic for sentences in its scope.

The aim of this talk is twofold. First, I present and discuss some recent developments in the logics of evidence and truth, namely, finitely-valued propositional versions and first-order versions with Kripke-style semantics.

Second, in order to answer some criticisms raised against LETs, I explain the notions of evidence and information underlying the intuitive interpretation of LETs, and also clarify in which sense the deductive behavior of conclusive evidence is expressed in terms of preservation of truth.



23.05.2023

Models of Set Theory and the Torunian Plan

Santiago Jockwich

University of Oslo
Norway

Abstract. In this presentation, I will introduce my MSCA project entitled "Unifying Classicality and Non-classicality", which will be carried out at the University of Oslo from 2023 to 2025. The primary objective of this project is to merge the realms of classicality and non-classicality within the domains of mathematical logic and the philosophy of logic. This project consists of two distinct parts. Firstly, our aim is to unify the classical and non-classical foundations of mathematics using a set-theoretic framework. What sets our approach apart from previous attempts is our belief that only an algebraic methodology possesses the necessary generality to accomplish such a task. Secondly, we intend to extend our reconciliation of classicality and non-classicality into the realm of philosophy of logic and philosophy of set theory. Specifically, we plan to unify the study of set-theoretic and logical pluralism. This integration holds potential for generating fresh insights in both fields of study. Lastly, I would like to highlight the potential for future research by establishing connections between the first part of the project and the field of relating semantics. By exploring these connections, we anticipate uncovering valuable avenues for further research.

05.05.2023

Expressive AI for Rational Arguments, Ethical Decision-Making, and Cognitive Modeling

Andrea Vestrucci

University of California
Berkeley, USA

Abstract. Recent implementations of highly expressive logical embeddings are pushing boundaries of automated reasoning systems. This prompts applications of sophisticated rule-based AI for intelligent automated agency. My talk focuses on three applications. First, the research in computational philosophy: the implementation of non-classical logics in automated proof assistants allows to mechanize complex reasonings involving e.g. metaphysical concepts and ethical theories; this fosters concrete and effective multidisciplinary dialogues. Second, I present how normative and legal theories can be effectively implemented in interactive reasoning environments: this is the condition for building automated ethical governors for decision-making processes coming from other AI systems. Third, the application to cognitive models: in collaboration with neuroscience-informed cognitive research on belief, I outline expressive modeling for believing processes, with emphasis on consistency maintenance and decision-makings in agents and communities.



16.12.2022

On a Logico-Algebraic Approach to AGM Belief Revision Theory

Davide Fazio

Universita degli Studi di Teramo
Italy

Abtsract. In this talk we investigate an algebraic approach to AGM (Alchourrón, Gardenfors, Makinson) logic of theory change by using the tools of abstract algebraic logic. Specifically, we generalize the notions involved in the definition of epistemic operators, in particular contraction, to arbitrary finitary propositional logics, and we show how to switch from a syntactic-based approach to a semantic one. This allows to build a solid bridge between the validity of AGM postulates in a propositional logic and specific algebraic properties of its intended algebraic counterpart. Such a connection deserves particular attention when we deal with maxichoice contractions. We close the talk by discussing open problems and further developments of the above framework.



21.11.2022

Czy koncepcja falsyfikacjonizmu Poppera stosuje się do testowania hipotez w psychologii?
(Does Popper's concept of falsificationism apply to hypothesis testing in psychology?)

Tytus Sosnowski

Nicolaus Copernicus University in Toruń
Poland

04.10.2022

On the Proof Theory and Correspondence Theory of Atomic and Molecular Logics

Guillaume Aucher

University of Rennes
France



19.09.2022

Generalised Explosion and Stratified Paraconsistency

Sankha Basu

Indraprastha Institute of Information Technology-Delhi
India

Abtsract. Paraconsistency is commonly defined and/or characterized as the failure of a principle of explosion. The various standard forms of explosion involve one or more logical operators, among which negation is the most frequent. In this talk, I will explore the possibility of describing notions of paraconsistency via the failure of principles of explosion that do not involve a negation operator. The questions thus raised are the following. Is the negation operator essential for defining paraconsistency? More broadly, is it possible to describe a notion of paraconsistency that is independent of connectives? I will present two such notions of negation-free paraconsistency, one that is entirely independent of connectives and another that uses a conjunction-like binary connective that we call 'fusion'. Next, I will discuss a 'quasi-negation' that can be derived from one of these notions of negation-free paraconsistency. Finally, I will end with a relativized/stratified notion of paraconsistency.

10.09.2022

A Polynomial Calculus Representing Plain Fibring of Matrices

Juliana Bueno-Soler

Centre for Logic, Epistemology and the History of Science - CLE
and School of Technology
University of Campinas-Unicamp
Brazil

Abtsract. Our aim is to propose a method which produces an algebraic polynomial representation for a fibred product of logics L1 + L2, starting from the algebraic representation of the components L1 and L2. As there are different methods to combine logics, we expect that to each one there will be a corresponding method to combine polynomial ring calculi, introduced by W. Carnielli. In this talk we restrict our analysis to the method of plain fibring,,mproposing a method for combining polynomial calculi called P F-Polynomial Calculus that preserves the product obtained by plain fibring.

10.09.2022

Credal Calculi via Paraconsistent Possibilistic Logics

Walter Carnielli

Centre for Logic, Epistemology and the History of Science - CLE
University of Campinas-Unicamp
Brazil

Abtsract. This paper defends the use of possibility and necessity models based on the Logics of Formal Inconsistency, taking profit of their expressivity in terms of the notions of consistency (◦) and inconsistency (•). It is shown, by revisiting a paradigmatic example, how paraconsistent possibility and necessity reasoning in general can attain realistic models for artificial judgement, which we call credal calculi, with appealing consequences.

09.09.2022

Enlarging Popper’s Conditional Probability as a Primitive Notion: Towards General Non-Standard Theories of Probability

Juliana Bueno-Soler

Centre for Logic, Epistemology and the History of Science - CLE
and School of Technology
University of Campinas-Unicamp
Brazil

Abtsract. There is a continuing discussion in the literature around the concept of conditional probability because concepts such as dependence and independence between events, which can be derived from the definition of conditional probability are sometimes paradoxical. I discuss the proposal for an extension of Popper’s axiomatization of conditional probability by employing the language of paraconsistent logic, even if Popper’s account is autonomous. The results of this move will, at the same time, tighten the connections between paraconsistency and the Popperian philosophy, and offer an alternative account of paraconsistent probability.

09.09.2022

The Brazilian Paraconsistency Program: A Survey

Walter Carnielli

Centre for Logic, Epistemology and the History of Science - CLE
University of Campinas-Unicamp
Brazil

Abtsract. In this talk I summarize the main research trends of the last decade of the Group of Theoretical and Applied Logic Group of the Centre for Logic, Epistemology and the History of Science at the University of Campinas.

09.09.2022

The Principle of Ariadne and the Axiom of Choice

Walter Carnielli

Centre for Logic, Epistemology and the History of Science - CLE
University of Campinas-Unicamp
Brazil

Abtsract. This talk surveys some results on combinatorial aspects of infinite Ramsey-type problems inspired by finite properties, and intends to explain the relevance of an alternative set-theoretical principle, the so-called Principle of Ariadne. This principle is a rival of the Axiom of Choice, can be consistently added to the usual axiom stock of ZF set theory under certain conditions. Such a new axiom, which preserves all the finite contents of mathematics but deviates from the standard in the infinite contents, may help us to understand the finite-infinite divide in mathematics, making clear that there is more than one way to generalize from finite principles of order (or choice) to the infinite. In other words, several infinite principles are possible starting from the same finitary content.