Bochum Nonclassical Logic Workshop IV

Date & Venue

• Date: January 30, 2025.

• Venue: Ruhr University Bochum, Building GD, Room 2/148.  

Speakers:

• Jitka Kadlečíková (Rensselaer Polytechnic Institut)

• Thomas Macaulay Ferguson (Rensselaer Polytechnic Institut)

• Antonio Piccolomini d'Aragona (University of Tübingen)

• Satoru Niki (Ruhr University Bochum)

• Andrew Tedder (Ruhr University Bochum)

Program 

10:00 to 11:00: Thomas Macaulay Ferguson, "Topological Models for Topic-Transformative Operators"

11:15 to 12:15: Andrew Tedder, "Topically Constrained Implications and the Logic of Fiction"

12:15 to 14:00: Lunch 

14:00 to 15:00: Antonio Piccolomini d'Aragona, "From normalisation to proof-theoretic semantics: the semantic role of harmony, atomic bases and reductions"

15:15 to 16:15: Jitka Kadlečíková, "A Defense of Logical Externalism"

16:30 to 17:30: Satoru Niki, "Abelian logic on the Bochum Plan (and the American Plan as well)"

19:00 Workshop Dinner, (Restaurant "Levarosa", Herner Straße 36, Bochum)

Abstracts

Thomas Macaulay Ferguson, "Topological Models for Topic-Transformative Operators" 

Recent work challenging principles of topic transparency in topic-sensitive logics has relied on providing accounts of connectives that are topic-transformative, that is, which non-trivially influence the overall topic assigned to a complex. This leads naturally to the question of what operators in natural language might also act as topic-transformative functions. This talk reviews work in progress studying “qua”, “per se”, and other topic-transformative operators. After discussing ways to analyze these operators through topological methods, we will emphasize how such analyses are likely to assist in a parallel project of updating Richard Sylvan’s work on relevant containment logic. (This is joint work with Pietro Vigiani and Jitka Kadlečíková.)

Andrew Tedder, "Topically Constrained Implications and the Logic of Fiction" 

The question of what follows from sentences stated in a fiction is the domain of the logic of fiction. Recently, Proudfoot (2018) has suggested, in light of discussions surrounding inconsistent fictions and related topics, that there is no substantial positive logic of fiction. Others (Priest, Berto and Jago) have suggested the use of open worlds (i.e., worlds with no substantial closure conditions) to model stories and their consequences. In this paper, we suggest that an alternative is to treat ``follows within the fiction'' as a topically constrained implication. That is, those sentences p follow from a story S which are such that (1) S implies p (in the usual way) and (2) the topic of p is contained in that of S. That is, the story-implications are those implications which concerns topics which the story is about. Using modeling apparatus for topics introduced in Tedder (Forthcoming), this idea can be formalised in a simple and elegant way, so that the story-closure of a set of sentences in a model is the intersection of (1) the filter generated by the set and (2) the subalgebra generated thereby. This talk explores this formalisation and its consequences. (Joint work with Ed Mares.)

Antonio Piccolomini d'Aragona, "From normalisation to proof-theoretic semantics: the semantic role of harmony, atomic bases and reductions"

Going back to Prawitz's papers from the 70s, when PTS was first formulated, may be crucial for answering questions about the relation between the current, "sentential" way of developing PTS, with a primitive notion of proof-theoretic consequence, and the original version developed by Prawitz himself, where proof-theoretic consequence is instead defined in terms of existence of suitable valid arguments from given assumptions to a given conclusion. My starting claim will be that PTS is a semantic generalisation of Prawitz's normalisation theory of Gentzen's Natural Deduction. More precisely, I will maintain that PTS stems from two intertwined sources: first, a  semantic reading of Prawitz's inversion principle, which in turn interprets Gentzen's claim that introductions fix the meaning of the connectives, while eliminations are consequences of these meaning definitions; second, a Dummett-based reading of a corollary which might be implied by normalisation results, according to which every closed derivation ends by applying an introduction. This semantic generalisation underwent an intermediate stage where normalisation techniques were understood as giving rise to a general property of derivations, whose semantic flavour, however, was still mainly oriented at proving (strong) normalisation results only. Something similar happened for the other two crucial components of PTS, namely, atomic theories and reductions. As a second aim of my talk, I will focus on the semantic role of these components, by showing that the semantic understanding of them also underwent an intermediate stage between a (strong) normalisation-based reading, and the current PTS treatment.

Jitka Kadlečíková, "A Defense of Logical Externalism"

The goal of this talk is to outline a philosophical synthesis between semantic externalism (as defined by Putnam and Burge) and normative inferentialism (as defined by Sellars, Brandom, and Peregrin). I argue that both semantic externalism and normative inferentialism criticize representationism and defend the position that sees language as inherently social. I further argue that inferentialism informed by bilateralism (as found, e.g., in Rumfitt, Restall, and Ripley) and the theory of topic (as applied by Ferguson), can be interpreted as an application of externalism to logic. The resulting theory, which I call logical externalism, states that the meanings of logical expressions, as well as the consequence relation, are determined by society through a division of "reasoning labor.''

Satoru Niki, "Abelian logic on the Bochum Plan (and the American Plan as well)"

In this paper, we introduce two new semantic presentations of Abelian logic, the non-trivial negation inconsistent logic of Abelian lattice-ordered groups, which was independently developed by Ettore Casari, and by Robert Meyer and John Slaney. Abelian logic is presented through a methodology that combines elements of what is sometimes referred to as the “Bochum Plan” and the “American Plan.” While the Bochum Plan is an approach to defining contra-classical logics, the American Plan–developed by Nuel Belnap and Michael Dunn–in particular offers a conception of negation that invites an application of the Bochum Plan. The first semantics is a ternary frame Kripke semantics, and the second is based on ideas from Edwin Mares’ work. Thereby emerges a condition for the falsity of Abelian implication to be supported, which we analyse further in the separate context of the first-degree entailment logic. The perspectives are united in the end to provide a defence against the scepticism concerning the status of the Abelian negation as a negation. (Joint work with Heinrich Wansing)

Acknowledgment

The Bochum Nonclassical Logic Workshop IV is supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, grant agreement ERC-2020-ADG, 101018280, ConLog.

Bochum Nonclassical Logic Workshop III

Date & Venue

• Date: November 28-29, 2024.

• Venue: Ruhr University Bochum

    Thursday, Nov. 28: Mensa building, Conference Room no. 2, upper floor opposite the “Rote Beete” restaurant 

    Friday, Nov. 29: Building GD, Room 02/208. 

Speakers:

• Sara Ayhan (Ruhr University Bochum)

• Elena Ficara (University of Paderborn, Graduate Center, City University of New York)

• Andreas Kapsner (Ludwig-Maximilians-University of Munich)

• Edwin Mares (Te Herenga Waka — Victoria University of Wellington) 

• Hitoshi Omori, (Tohoku University, Sendai)

• Ivo Pezlar (Institute of Philosophy of the Czech Academy of Sciences)

• Graham Priest (Graduate Center, City University of New York, RUB)

• David Santamaría Legarda (Graduate Center, City University of New York)

• Heinrich Wansing (Ruhr University Bochum)

Program 

November 28

10:00 to 11:00: Edwin Mares, "Substructural Philosophy"

11:00 to 12:00: David Santamaría Legarda, "Cantor’s notion of inconsistent multiplicity"

12:15 to 13:15: Sara Ayhan, "Queer feminist logic & contradictory logics: A symbiotic relationship"

13:15 to 14:30: Lunch 

14:30 to 15:30: Ivo Pezlar, "Hyperintensions as computations"

15:30 to 16:30: Elena Ficara (via Zoom), "Antidiscrimination Logic" 

17:00 to 18:00: Graham Priest, "The Paradox at the Limit of Everything"

19:30 Workshop Dinner (Restaurant "Levarosa", Herner Straße 36, Bochum)

November 29

10:00 to 11:00: Hitoshi Omori, "Dunn is neither Belnap nor Routley"

11:15 to 12:15: Heinrich Wansing, "Theorems and Theories"

12:15: Lunch 

Abstracts

Sara Ayhan, "Queer feminist logic & contradictory logics: A symbiotic relationship"

In this talk I want to investigate possible applications of queer feminist views on (philosophy of) logic with respect to contradictory logics and especially bilateral representations of these. Thereby I want to show that, on the one hand, the formal set-up of contradictory logics makes them well-suited from the perspectives of feminist logic and, on the other hand, that queer feminist theories provide a relevant, and so far undeveloped, conceptual motivation for contradictory logics. Thus, applying contradictory logics to reasoning about queer feminist issues may prove fruitful both as a ‘real-life’ motivation for these rather marginalized logical systems and as a formal basis for a philosophical field that is still characterized by a distrust of formalism.

Elena Ficara, "Antidiscrimination Logic"

My paper revolves around the notion of discrimination and its connection to logic. I have already treated the theme in Ficara 2024, focusing on the contribution of Plumwood 1993. Now I further deepen this consideration, and have three main objectives. First, I aim to clarify the concepts of logic and discrimination at the basis of my analysis. Second, I intend to focus on the structures of thought that ground discriminatory practices. Finally, I aim to work towards a notion and practice of logic that could be profitably applied to anti-discriminatory discourses and measures.

Edwin Mares, "Substructural Philosophy"

I present an operational-relational semantics for a wide range of substructural logics and discuss a philosophical interpretation of it. I look at the sorts of conditions that are appropriate for theories of entailment and theories of contingent implication. The semantics is closely connected with algebraic semantics, and this connection suggests a treatment of the quantifiers from algebraic logic (in particular, a form of polyadic algebra).

Ivo Pezlar, "Hyperintensions as computations"

In this paper, we show that the hyperintensional typed lambda calculus (HTLC) of Fait and Primiero (Journal of Applied Logics, 8(2):469–495, 2021) inspired by transparent intensional logic is equivalent to the computational lambda calculus (CLC) of Moggi (Information and Computation, 93(1): 55–92, 1991) extended by a simple axiom. We demonstrate this by first establishing a link between HTLC and propositional lax logic (PLL) which corresponds to CLC via the Curry-Howard isomorphism. Our result puts on a solid formal ground a long-held assumption that there is a close connection between the notions of structured hyperintension and computation.

Hitoshi Omori, "Dunn is neither Belnap nor Routley"

In this talk, I wish to present two small observations related to FDE. First, it is common to group Belnap’s four-valued semantics and Dunn’s two-valued semantics together under the label of the American plan. Against this, I observe that a problem discussed by Andreas Kapsner may give us a reason to clearly separate Dunn from Belnap. Second, it is well known that the American plan and the Australian plan start to diverge upon adding certain connectives. I observe that by building on Graham Priest’s modal expansion of FDE, there are interesting differences between the two plans, and some systems can be seen as following the direction suggested by Sergei Odintsov and Heinrich Wansing. This observation will give us another reason to clearly separate Dunn from Routley.

Graham Priest, "The Paradox at the Limit of Everything"

Beyond everything is nothing(ness). But nothing appears to be a paradoxical object, both something and nothing. In this talk I will look at the paradox of nothing more closely, defining nothing in mereological terms, and proving that it is a dialetheic object. The Inclosure Scheme is a scheme into which all the standard paradoxes of self-reference fit. The paradox of nothing is not a paradox of self-reference, but I will also show that it fits the Inclosure Schema, and so has the same structure. As we will see, the paradox of nothing is a paradox at the limit of everything.

David Santamaria Legarda, "Cantor’s notion of inconsistent multiplicity" 

In this talk I will (i) discuss the distinction between consistent and inconsistent multiplicities that we find in Georg Cantor’s (1845-1918) set theory. I will then (ii) examine whether Cantor’s theory was at some point vulnerable to the paradoxes of set theory and (iii) evaluate the claim that  inconsistent multiplicities were introduced by Cantor in an ad hoc fashion to resolve these paradoxes. I will also (iv) look at the use Cantor makes of inconsistent multiplicities in his alleged proof that every set can be well-ordered and (v) draw some conclusions as to why he did not publish this proof.

Heinrich Wansing, "Theorems and Theories" 

In this talk I will discuss the notion of a theory and whether a theory should be thought of as containing the theorems of the underlying logic. I will (i) recall various notions of theories and a polemical quote from Meyer and Slaney (1989), (ii) consider a certain hyperconnexive version of David Lewis's (1968) counterpart theory, (iii) claim that Meyer and Slaney in their dismissal of a commitment to logical theorems fail to take into consideration substantial logical pluralism, (iv) claim that connexive counterpart theory is an example of an especially clear case of a theory that brings to the fore the importance of logical truths (and falsities) when it comes to theory endorsement, and (v) look at a peculiarity of Lewis's counterpart theory, namely that it is not only an axiomatic theory.

David Lewis, Counterpart Theory and Quantified Modal Logic, Journal of Philosophy 65 (1968), 113–26.
Robert K. Meyer and John Slaney, Logic from A to Z, in: G. Priest, R. Routley, and J. Norman (eds), Paraconsistent Logic: Essays on the Inconsistent, Philosophia Verlag, Munich, 1989, 245–288.

Acknowledgment

The Bochum Nonclassical Logic Workshop III is supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, grant agreement ERC-2020-ADG, 101018280, ConLog.

A Logic Day in Bochum

With the visits of Roberto Giuntini and Bernhard Weiss, we will have a special Logic Day workshop at RUB. 

Date & Venue

• Date: June 13, 2024.

• Venue: Ruhr University Bochum, Mensa building, room 01/54 "La Réunion". 

Program

10:30 to 11:30: Bernhard Weiss (University of Cape Town), "Molecularity in the Theory of Meaning and the Topic Neutrality of Logic"

11:45 to 12:45: Nils Kürbis, (Ruhr University Bochum), "Deductive Semantics" 

13:00 to 14:00: Lunch 

14:00 to 15:00: Grigory Olkhovikov (Ruhr University Bochum), "Conditionals over some constructive logics"

15:15 to 16:15: Roberto Giuntini (University of Cagliari, TU Munich), "Machine Learning meets Quantum Mechanics"

19:00 Workshop Dinner at Karawane, Große Beckstraße 27, 44787 Bochum.

Acknowledgment

The Logic Day in Bochum is supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, grant agreement ERC-2020-ADG, 101018280, ConLog.

Abstracts

Bernhard Weiss, "Molecularity in the Theory of Meaning and the Topic Neutrality of Logic"

Abstract: The aim here is to uncover requirements on a justification of logic. The paper begins by endorsing and explaining a view of molecularity in the theory of meaning, conceived in terms of the notion of conservative extension. It raises Brandom inspired concerns about Dummett’s implementation of the view as a global requirement of harmony; but also sees a tension between Brandom’s holistic inferential view of meaning and his presumption that newly introduced vocabulary can incorporate inferential proprieties which are not affected by the very meanings introduced. I find a path between Brandom and Dummett, by accepting the Dummettian constraint of global conservativeness; but move towards Brandom by arguing that this need only be a tacit presupposition of speakers, and need not be demonstrable. Using Brandom’s notion of an autonomous discursive practice, I explain a notion of topic neutrality, arguing that logical vocabulary is topic neutral in this sense. The last phase of the paper combines these two thoughts—about conservative extensions and topic neutrality—to argue that logical vocabulary needs to be conceived of as demonstrably conservative with respect to any autonomous base vocabulary, because only if this is so can it be known to be topic neutral. This, combined with the fact that an assertor commits herself to providing her grounds for assertion, delivers a conception of harmony as a general constraint on the acceptability of a putative piece of logical vocabulary.

Nils Kürbis, "Deductive Semantics" 

Abstract: According to a common view going back to Gentzen, the meanings of logical expressions can be defined by the rules of inference governing them. This often forms part of a verificationist theory of meaning, in which the meanings of sentences are determined by the grounds that justify their assertion. But it can equally form part of a pragmatist theory of meaning, where the meanings of sentences are determined by the consequences of their assertions. In fact, according to Dummett, it should not matter which theory we choose, as these two aspects of use should be in harmony. The grounds and consequences of assertions should stand in a perfect balance, and one aspect is determined by the other. Following Dummett and Prawitz there is some consensus of how to spell out harmony when it comes to the logical constants. In a system of natural deduction the introduction rules for a connective specify the canonical grounds for asserting a formula with the expression as main operator, and the elimination rules their canonical consequences. The elimination rules should not license the deduction of more consequences from a formula than are justified by the grounds for inferring it as specified by the introduction rules for its main operator; and moreover they should allow the inference of all justified consequences. There is some consensus of what this means, but it leaves much implicit. In this talk I’ll propose a list of necessary conditions that rules of inference should satisfy if they are to define the meanings of the connectives they govern completely. They are motivated in part by logical, in part by more general meaning-theoretical considerations.  

Grigory Olkhovikov , "Conditionals over some constructive logics"

Abstract: We consider the question of finding the correct basic logic of conditionals conservatively extending a given constructive propositional logic. We focus on two cases in which the extended logic is either the intuitionistic or the paraconsistent variant of Nelson's logic of strong negation (often referred to as N4 in literature), respectively. In vindicating our replies to the said question in these two cases, we rely on the set of adequacy criteria set forth by A. Simpson (in A. Simpson. The Proof Theory and Semantics of Intuitionistic modal Logic, PhD Thesis, University of Edinburgh (1994)) for the intuitionistic modal logic, adapting their formulation to the particularities of our problem.

When discussing a version of Simpson's requirements for constructive conditional logics, we place the main weight upon  the existence of an explanation of conditional semantics in terms of the first-order version of the underlying constructive logic. We interpret this requirement as demanding the faithfulness of the embedding given by the classical notion of standard translation of conditional formulas.

Roberto Giuntini, "Machine Learning meets Quantum Mechanics"

Abstract: Research in the broad area of pattern recognition, machine learning, and quantum computing has inspired new ideas about some important general problems that arise in several disciplines, including information theory (classical and quantum), logic, cognitive science and neuroscience, and philosophy.

One of the fundamental questions that these disciplines often face is the following: How are abstract concepts formed and recognized on the basis of previous (natural or artificial) experiences? This problem has been studied, with a variety of methods and tools, both in the context of human intelligence and artificial intelligence.  In this seminar, the problem will be addressed within the framework of machine learning and quantum computing

Machine learning can be defined as the art and science of making computers learn from data how to solve problems (or recognize and classify new objects) without being explicitly programmed. Quantum computing describes the processing of information usiong tools based on the laws of quantum theory. Today, we are witnessing a dramatic explosion of data, and the problem of extracting and recognizing only “useful information’’ from these data is crucial but extremely resource consuming. On the other hand, quantum computing has shown that there exist quantum algorithms that allow a formidable acceleration in solving problems that, in their current state, would require exponential times. The realization of the so-called noisy intermediate-scale quantum (NISQ) computers is now a reality. Therefore, the combination of machine learning and   quantum computing appears inevitable. This "marriage" is favored by the fact that one of the fundamental features of quantum theory is that it can deal with incomplete information in a particularly natural and efficient way, a feature that is of primary importance in machine learning.  The approach that I will present in this seminar (called Quantum-Inspired Machine Learning) consists of formally translating the process of (supervised) classification of (classical) machine learning by using the formalism  of quantum theory in such a way that the resulting classification algorithms can be implemented on non-necessarily quantum computers. In particular, I will address the problem of binary classification of classical datasets, presenting a classifier (called the Helstrom Quantum Classifier (HQC), based on the Helstrom protocol, which is used to distinguish between two quantum states (mathematically represented by density matrices). HQC acts on density matrices, which, in our model, encode the patterns of a classical dataset. Experimental benchmark results show that, in many cases, the accuracy of HQC is superior to that of many classical classifiers. Finally, we will show how the improvement in HQC performance is positively correlated with the increase in the number of "quantum copies" of each (encoded) classical pattern.

1st Workshop on Contradictory Logics 

December 6–8, 2023

Ruhr University Bochum, Germany

https://sites.google.com/view/1stworkshoponcontradictorylogi/home

Acknowledgment

The 1st Workshop on Contradictory Logics is supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, grant agreement ERC-2020-ADG, 101018280, ConLog.

Second Bochum-Łodz Workshop on Logic 

Date & Venue

• Date: November 17 and 18, 2022.

• Venue: Ruhr Universität Bochum, GABF 04/609. 

The second Bochum-Łodz Logic Workshop will be held in person in Bochum and online on the 17th and 18th of November. This time, the two ERC Advanced Grants held at the departments are the focus. The event provides an opportunity for the PIs of the grants and their collaborators and PhD students to present their work. Heinrich Wansing’s project “Contradictory Logics: ConLog: A Radical Challenge to Logical Orthodoxy” is held at the Department of Philosophy I of Ruhr Universität Bochum. Andrzej Indrzejczak’s project “ExtenDD: Coming to Terms: Proof Theory Extended to Definite Descriptions and other Terms” is held at the Department of Logic and Methodology of Science of the University of Lodz.

Program

Thursday, November 17.

14:00: Opening

14:15-14:45: Andrzej Indrzejczak "The coming to terms project: Extending proof theory by 𝜄"

14:45-15:15: Nils Kürbis "Definite descriptions via binary quantification"

15:30-16:00: Heinrich Wansing "The contradictory logics project"

16:00-16:30: Caitlin Canonica "Contradictions in the Wild; toward an experimental approach to contradictory logics"

Friday, November 18

10:00-11:00: Grigory Olkhovikov "On some first-order connexive logics"

11:15-12:15: Leonard Kupś "Methods of modelling linear time in hypersequent calculus"

12:15-12:45: Yaroslav Petrukhin "Cut-free sequent calculi for some three-valued logics obtained via correspondence analysis"

12:45-14:15: Lunch 

14:15-15:15: Satoru Niki "Provable contradictions and Kamide's negations"

15:30-16:00: Sara Ayhan "Two-sorted typed lambda-calculus for 2Int"

16:00-16:30: Michał Zawidzki "When iota meets lambda: The case of interpolation"

16:30-17:00: Przemysław Wałȩga "DatalogMTL: a logic for reasoning about temporal databases"

Acknowledgment

The second Bochum-Łodz Logic Workshop is supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, grant agreement ERC-2020-ADG, 101018280, ConLog.

Bochum Nonclassical Logic Workshop II

Aim

The aim of this workshop is to discuss and exchange new ideas and recent developments related to nonclassical logics, with an emphasis on constructive logics, relevant logics and conditional logics.

Date & Venue

• Date: April 19, 2022.

• Venue: Room Shanghai, Beckmanns Hof, Ruhr University Bochum. (Beckmanns Hof is not in this map. Here is a map.)

Speakers

• Nicholas Ferenz (The Czech Academy of Sciences)

• Satoru Niki (Ruhr University Bochum)

• Hitoshi Omori (Ruhr University Bochum)

• Andrew Tedder (Ruhr University Bochum)

• Heinrich Wansing (Ruhr University Bochum)

Program

10:15-11:15 Heinrich Wansing, "Some remarks on conditional connexive logic"

11:15-11:30 Coffee

11:30-12:30 Hitoshi Omori, "A note on Sasaki's conditional in view of Garson's question"

12:30-14:00 Lunch

14:00-15:00 Satoru Niki, "Provable contradictions in constructive logics"

15:00-15:15 Coffee

15:15-16:15 Nicholas Ferenz, "Some Results, Thoughts, and Historical Notes on Quantified (Modal) Relevant Logics"

16:15-16:30 Coffee

16:30-17:30 Andrew Tedder, "The Algebraic Structure of Mares-Goldblatt Models"

Acknowledgment

The Bochum Nonclassical Logic Workshop II is supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, grant agreement ERC-2020-ADG, 101018280, ConLog, as well as by a Sofja Kovalevskaja Award of the Alexander von Humboldt-Foundation, funded by the German Ministry for Education and Research.