Related papers: Analogical proportions
It is known that recommendations of AI-based systems can be incorrect or unfair. Hence, it is often proposed that a human be the final decision-maker. Prior work has argued that explanations are an essential pathway to help human…
This paper presents a comprehensive overview on the applications of artificial intelligence (AI) in mathematical research, highlighting the transformative role AI has begun to play in this domain. Traditionally, AI advancements have heavily…
Learning physics requires understanding the applicability of fundamental principles in a variety of contexts that share deep features. One way to help students learn physics is via analogical reasoning. Students can be taught to make an…
This Article introduces the generative reasonable person, a new tool for estimating how ordinary people judge reasonableness. As claims about AI capabilities often outpace evidence, the Article proceeds empirically: adapting randomized…
This review aims to contribute to the quest for artificial general intelligence by examining neuroscience and cognitive psychology methods for potential inspiration. Despite the impressive advancements achieved by deep learning models in…
Starting from the Boolean notion of logical proportion in Piaget's sense, which turns out to be equivalent to analogical proportion, this note proposes a definition of analogical proportion between numerical values based on triangular norms…
In the statistical analysis of objects, samples and populations with quantitative variables, in many occasions we are interested in knowing the proportions that exist between the different variables from a same object; if these proportions…
People's decision-making abilities often fail to improve or may even erode when they rely on AI for decision-support, even when the AI provides informative explanations. We argue this is partly because people intuitively seek contrastive…
The exploration of geometrical patterns stimulates imagination and encourages abstract reasoning which is a distinctive feature of human intelligence. In cognitive science, Gestalt principles such as symmetry have often explained…
Analogical Reasoning problems challenge both connectionist and symbolic AI systems as these entail a combination of background knowledge, reasoning and pattern recognition. While symbolic systems ingest explicit domain knowledge and perform…
As artificial intelligence (AI) continues to advance, it demonstrates capabilities comparable to human intelligence, with significant potential to transform education and workforce development. This study evaluates OpenAI o1-preview's…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
In conceptual modeling (CM), humans apply abstraction to represent excerpts of reality for means of understanding and communication, and processing by machines. Artificial Intelligence (AI) is applied to vast amounts of data to…
Analogy-making gives rise to reasoning, abstraction, flexible categorization and counterfactual inference -- abilities lacking in even the best AI systems today. Much research has suggested that analogies are key to non-brittle systems that…
Associative memory and probabilistic modeling are two fundamental topics in artificial intelligence. The first studies recurrent neural networks designed to denoise, complete and retrieve data, whereas the second studies learning and…
Artificial intelligence (AI) is the name popularly given to a broad spectrum of computer tools designed to perform increasingly complex cognitive tasks, including many that used to solely be the province of humans. As these tools become…
Humans regularly engage in analogical thinking, relating personal experiences to current situations (X is analogous to Y because of Z). Analogical thinking allows humans to solve problems in creative ways, grasp difficult concepts, and…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…
In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…