Gestures are usually regarded as a casual element of communication processes between logicians. By contrast, we aim to show that gestures have played a significant role in logic. We argue that the development of communication techniques and their standardization have led to the rise of formal notation systems commonly used in logic today. In order to substantiate this claim, the historical development of the use of gestures in (early) modern logic is investigated. This investigation uncovers exemplary communication and proof techniques (...) that illustrate the efficacy of gestures as representational media in formal logic. Revisiting the tradition of gestures in logic offers promising paths and insights for today’s logic as a communication practice in the digital age. (shrink)

The paper explores the potential of Byzantine diagrams in syllogistic logic. Byzantine diagrams are originated by Byzantine scholars in the early modern period to use as tools for teaching and studying Aristotelian logic. This paper presents pioneering work on employing Byzantine diagrams for checking syllogistic validity through reduction.

In this paper, we analyze and discuss Schopenhauer’s n-term diagrams for eristic dialectics from a graph-theoretical perspective. Unlike logic, eristic dialectics does not examine the validity of an isolated argument, but the progression and persuasiveness of an argument in the context of a dialogue or even controversy. To represent these dialogue situations, Schopenhauer created large maps with concepts and Euler-type diagrams, which from today’s perspective are a specific form of graphs. We first present the original method with Euler-type diagrams, then (...) give the most important graph-theoretical definitions, then discuss Schopenhauer’s diagrams graph-theoretically and finally give an example of how the graphs or diagrams can be used to analyze dialogues. (shrink)

Euler diagrams often require several figures to adequately represent propositions and syllogisms. Euler’s followers, notably Friedrich Ueberweg, endeavored to overcome this difficulty with the use of dotted lines to express uncertainty about the relation between the terms of a proposition. Subsequently, Venn regarded such attempts as ineffectual and went to construct his own celebrated scheme. In this paper, we argue that Ueberweg’s method could be expanded to meet Venn’s expectations, and hence, produce alternative Venn-like diagrams.

Venn diagram system has been extended by introducing names of individuals and their absence. Absence gives a kind of negation of singular propositions. We have offered here a non-classical interpretation of this negation. Soundness and completeness of the present diagram system have been established with respect to this interpretation.

CL diagrams – the abbreviation of Cubus Logicus – are inspired by J.C. Lange’s logic machine from 1714. In recent times, Lange’s diagrams have been used for extended syllogistics, bitstring semantics, analogical reasoning and many more. The paper presents a method for testing statistical syllogisms (also called proportional syllogisms or inductive syllogisms) by using CL diagrams.

In the rapidly evolving landscape of multimodal communication research, this paper explores the transformative role of machine learning (ML), particularly using multimodal large language models, in tracking, augmenting, annotating, and analyzing multimodal data. Building upon the foundations laid in our previous work, we explore the capabilities that have emerged over the past years. The integration of ML allows researchers to gain richer insights from multimodal data, enabling a deeper understanding of human (and non-human) communication across modalities. In particular, augmentation methods (...) have become indispensable because they facilitate the synthesis of multimodal data and further increase the diversity and richness of training datasets. In addition, ML-based tools have accelerated annotation processes, reducing human effort while improving accuracy. Continued advances in ML and the proliferation of more powerful models suggest even more sophisticated analyses of multimodal communication, e.g., through models like ChatGPT, which can now “understand” images. This makes it all the more important to assess what these models can achieve now or in the near future, and what will remain unattainable beyond that. We also acknowledge the ethical and practical challenges associated with these advancements, emphasizing the importance of responsible AI and data privacy. We must be careful to ensure that benefits are shared equitably and that technology respects individual rights. In this paper, we highlight advances in ML-based multimodal research and discuss what the near future holds. Our goal is to provide insights into this research stream for both the multimodal research community, especially in linguistics, and the broader ML community. In this way, we hope to foster collaboration in an area that is likely to shape the future of technologically mediated human communication. (shrink)

‘Byzantine logic diagrams’ have been used since at least late antiquity, and became popular in Europe in the 16th century. However, since the criticism of W. Hamilton and J. Venn in the 19th century, Byzantine diagrams have been largely dismissed as obsolete. This paper challenges this prevailing view. Initially, we provide a comprehensive overview of the current state of research pertaining to these diagrams, illustrating their applicability in analyzing assertoric syllogisms. Subsequently, we propose that the expressive capacity of these diagrams (...) extends far beyond their traditional use. In particular, we demonstrate that the expressivity of these diagrams is not limited to checking the validity of syllogisms. Rather, we show that there are various extensions of Byzantine diagrams, including opposition relations, modal logic, particular instances, n-term diagrams and logical connectives. These extensions are compositional and can therefore be combined to create very complex Byzantine diagrams that go far beyond what has been commonly believed since Hamilton and Venn. (shrink)

A new diagram system \ where properties are fundamental and an object exists only w.r.t a property is presented. This work modifies both in syntax and semantics the system \ proposed by Choudhury and Chakraborty to picturise and address issues connected with open universe. Semantics for the current system is given. Soundness and completeness w.r.t the semantics are established.

This book constitutes the refereed proceedings of the 14th International Conference on the Theory and Application of Diagrams, Diagrams 2024, held in Münster, Germany, during September 27–October 1, 2024. -/- The 17 full papers, 19 short papers and 11 papers of other types included in this book were carefully reviewed and selected from 69 submissions. They were organized in topical sections as follows: Keynote Talks; Analysis of Diagrams; Euler and Venn Diagrams; Diagrams in Logic; Diagrams and Applications; Diagram Tools; Historical (...) Aspects of Diagrams; and Posters. (shrink)