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Ebook: Combining Concepts
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What is a concept? Philosophy, cognitive science, psychology, logic, and AI have long been inquiring into this question. However, answers rarely converge.
The question of how humans represent and combine concepts has become increasingly relevant to AI. Despite advancements in Large Language Models and statistical models generally, the goal of developing formal representations of human thinking remains as crucial as ever. Cognitive models of human conceptualisation are of pivotal importance for AI and Knowledge Representation. Nevertheless, such models often lack proper formalisation, which makes it difficult to capture them precisely in computational systems. At the same time, the cognitive adequacy of computational systems is frequently overlooked in favour of better performance.
This book, Combining Concepts - Integrating Logical and Cognitive Theories of Concepts, bridges the gap between computational and cognitive models of concepts. The author explores the relationship between conceptual combination, the associated cognitive phenomena, and standard logical operators. The book introduces a representation of concepts motivated by the literature in cognitive psychology, combining ontological analysis, logical methods, and insights from statistical learning to offer a more cognitively grounded approach to modelling concepts and concept combination in Knowledge Representation and AI. It thus contributes to the development of hybrid AI modelling techniques, bridging learning and reasoning, and ensuring that they are theoretically sound, cognitively adequate, psychologically motivated, and practically applicable.
Offering a thorough exploration of concepts and concept combinations as they relate to current applications, the book will be of interest to all those working in the fields of AI and Knowledge Representation.
How do human minds represent, and then combine, concepts? And how should artificial intelligence do the same? The concept of concept has been a subject of inquiry for centuries across various disciplines, including philosophy, cognitive science, psychology, logic, and, more recently, AI.
Although the recent spotlight in AI has been on subsymbolic models, the pursuit of establishing formal representations of human thinking remains as fundamental as ever. Unlike humans, who effortlessly craft novel concepts by combining well-established ones, machines currently lack the means to achieve this robustly.
Research in experimental and cognitive psychology has extensively sought to answer the question of the nature of concepts, giving rise to complex representation models. Nevertheless, these models often lack a clear or complete formalisation, which makes it difficult to capture them precisely in computational models.
Knowledge Representation aims to represent knowledge about the world in a format suitable for re-use in computational systems, with the general goal of advancing Artificial Intelligence. Cognitive models of human conceptualisation are thus of pivotal importance for the field. However, formal work in AI and Knowledge Representation does not always consider these models and the cognitive adequacy of computational systems is frequently sacrificed in favour of better performance.
This work aims to bridge the gap between computational and cognitive models of concepts. Its primary goal is to offer a more cognitively adequate modelling of concepts and concept combination in Knowledge Representation and Artificial Intelligence. This aim is achieved by using a representation of concepts motivated by the literature in cognitive psychology, combining ontological analysis, logical methods and insights from statistical learning. This approach thus contributes to the development of hybrid AI modelling techniques, bridging learning and reasoning, ensuring that they are theoretically sound, cognitively adequate, psychologically motivated, and practically applicable.
This book is a mildly edited version of my PhD dissertation, which I concluded at the Free University of Bozen-Bolzano under the careful supervision of Professors Oliver Kutz and Daniele Porello.
Early in my PhD, I was deeply inspired by the seminal work of Professor James Hampton on the psychology of concepts and conceptual combination. This sparked my interest in exploring the relationship between conceptual combination and standard logical operators, as well as the broader cognitive phenomena associated with conceptual combination. The research presented in the following chapters is the result of countless fruitful discussions with my supervisors and numerous colleagues, whose insights greatly enriched this work.
There are many people to thank.
First and foremost my supervisors Oliver Kutz and Daniele Porello, without whom none of this would have happened.
For the extensive brainstorming, contributions, and patient assistance, in alphabetical order: Roberto Confalonieri, Pietro Galliani, Maria Hedblom, Claudio Masolo, and Nicolas Troquard.
Professor James Hampton and Professor Sebastian Rudolph for their precious evaluation, advice and encouragement.
For the helpful feedback and discussion: John Bateman, Antonella De Angeli, Fabian Neuhaus, and Mihai Pomarlan.
Finally, my family and friends, for their unwavering support.
