Logic in Bochum 1

Logic in Bochum 1

 

Venue

RUB , June 22: 9:00 –18:00, GABF 04/358; June 23: 9:00 –14:00, GA 3/143

Programme

 

Speakers

Mathieu Beirlaen, Roberto Ciuni, Marcus Kracht, Grigory Olkhovikov, Hitohsi Omori, Graham Priest, Dunja Šešelja, Daniel Skurt, Stanislav Speranski,Christian Straßer, Heinrich Wansing

Titles & abstracts

Mathieu Beirlaen*

Inconsistency-adaptive dialogical logic, or how to dialogue in the presence of inconsistencies

Abstract: In Batens’ inconsistency-adaptive approach, all rules of classical logic are applicable to those parts of our premise set which we can safely consider untainted by inconsistency, without having to specify beforehand which parts of our premises behave consistently.

In order to bring this dynamic approach to paraconsistency closer to our actual argumentative practice, we use its machinery to extend the paraconsistent approach to dialogical logic as developed by Rahman and Carnielli. This way, we obtain a very powerful formalism for the systematic study of dialogues in which two parties exchange arguments over a central claim, in the possible presence of inconsistent information.

* Joint work with Matthieu Fontaine (UNAM, Mexico City)

 

Roberto Ciuni

From Bayesian Games to Modal Logic

 Abstract: In this paper, I try to make first steps toward a general logical setting for strategic interaction under uncertainty, that help us  reason about both the epistemic and the agentive dimension, together with their interaction. In doing this, I will hint at a mathematical setting where step-by-step elease of information to agents can help reduce uncertainty so that, in the last (possible) stage, the interaction is transformed into an interaction under complete information. This procedure will allow to generate situations that approximate more and more the ideal case where agents have complete information.

In developing the setting, I will focus on the knowledge and beliefs agents have and on the actions available to them, while leaving considerations about the agents'  preferences to some other occasion.

Also, my proposal is based on some reference structures and methodology:

I focus on those cases of uncertainty that are represented by Bayesian Games, and I capture the qualitative features of these cases of interaction under uncertainty. I leave the quantitative aspects (payoff functions and probability distributions) aside.

 

Marcus Kracht 

Using Each Other's Words

Abstract: It is a fact that the same words do not always have the same meaning for everyone. This much can even be shown to follow from the fact that languages are learned in finite time. Yet, there seems to be no tool available to represent this formally. Logic forces us to assume uniform meanings. In this talk I shall outline a logic of meaning variation. It allows not only to reflect just about any variation in meaning but also the ability of speakers to borrow each other's semantics.

Grigory Olkhovikov

Action logic and agent ontology: STIT and beyond 

Hitoshi Omori

Remarsk on many-valued approach to modality

Abstract: The most popular semantics for modality is the so-called Kripke semantics. However, there were several attempts aiming at a reasonable semantics for modality even before Kripke. Jan Lukasiewicz gave two accounts, and, in this paper, I focus on the second account which turned out to be an approach through many-valued semantics. This attempt is now evaluated as a failed project after an observation by Josep Maria Font and Petr Hajek. Recently, Jean-Yves Beziau suggested a four-valued semantics for modality. Based on these, the aim of the paper is twofold. First, I establish some technical results related to Beziau's observation. Second, I clarify what is required to motivate or reject the many-valued approach to modality, through the attempt by Beziau.


Graham Priest

What’s Special about Classical Mathematics?

Abstract: Classical mathematics is the mathematics which was developed before the end of the 19th century, and its 20th century articulations. The 20th century has taught us that there are also non-classical mathematics, such as intuitionist and paraconsistent mathematics. What is the specificity of classical mathematics? In this paper I argue that this resides in a certain conception of conditionality: essentially that the conditional is material, and that this is best seen as a mathematical
matter, not a logical one.

Dunja Šešelja

Concerning Peter Vicker's Recent Treatment of 'Paraconsistencitis'

Abstract: This talk will be based on a review article of Peter Vickers's book "Understanding Inconsistent Science", which is a joint work with Christian Straßer. In response to the application of paraconsistent logics to the explication of scientific reasoning, Vickers’s book has reopened the debate on the role of inconsistencies in scientific reasoning and on the relevance of paraconsistent logics in this context. His investigation is anchored in a thorough re-examination of classical examples of inconsistent science and in a specific methodological account which he dubs ‘theory eliminativism’.

After presenting a brief overview of Vickers’s book, I will turn to our critical commentary. We start with Vickers’s criteria for what is to count as a significant inconsistency, and proceed towards his conclusions regarding the relevance of paraconsistent logics for an explication of scientific reasoning. We show that, while Vickers raises a number of important points, his attack on the paraconsistent modelling is insufficiently elaborated and leaves some fundamental questions open. We conclude that despite our critical points, Vickers’s book is a highly valuable contribution to the literature on inconsistencies in scientific reasoning and to the philosophy of science in general.

 

Daniel Skurt

Beyond Arnold Koslow's Implication Relations

 

Stanislav Speranski

A structural perspective on probabilistic logics

 

Christian Straßer*

Dynamic Proof Theories as Structured Argumentation 

Abstract: In this talk we will relate two traditions in the formal modeling of defeasible reasoning: on the one hand the tradition in formal argumentation [1] and on the other hand the tradition of adaptive logics [2,3]. We show how adaptive logics define a class of structured argumentation frameworks. We translate adaptive logics in the standard format and several generalisations (such as lexicographic [4], colexicographic adaptive logics, etc.) into the ASPIC-framework [5] or the assumption-based argumentation framework [6]. Moreover, we show how stages of adaptive dynamic proofs can be associated with gradually growing attack diagrams. Finally, we define a new family of dynamic proofs that are highly expressive and whose retraction mechanism is based on argumentative attacks.

  1. Dung, P. M. (1995). On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence, 77, 321–358.
  2. Batens, D. (2007). A universal logic approach to adaptive logics. Logica Universalis, 1, 221–242.
  3. Straßer, Ch. (2014). Adaptive logic and defeasible reasoning. Applications in argumentation, normative reasoning and default reasoning. Springer.
  4. Van De Putte, F., Straßer, C. (2013). Three formats of prioritized adaptive logics: a comparative study. Logic Journal of the IGPL, 2(21), 127–159.
  5. Prakken, H. (2011). An abstract framework for argumentation with structured arguments. Argument & Computation, 1(2), 93–124.
  6. Dung, P., Kowalski, R., & Toni, F. (2009). Assumption-based argumentation. Argumentation in Artificial Intelligence, 199–218.

* Joint work with Jesse Heyninck  (Ruhr-Universität Bochum, Germany)


Heinrich Wansing

On symmetry between verification and falsification

Abstract: In this talk I will consider some criticism that has been put forward against strong, constructive negation in comparison to a certain example of Galois connected negations. The general background to this discussion is the informational interpretation of substructural logics, and the key issue is whether there exists an asymmetry or not between positive and negative information and between verification and falsification. I will confirm the view that a symmetrical conception is adequate for both direct and indirect variants of verification and falsification.