Related papers: Proportoids
Analogical reasoning is the ability to detect parallels between two seemingly distant objects or situations, a fundamental human capacity used for example in commonsense reasoning, learning, and creativity which is believed by many…
Analogy-making is at the core of human and artificial intelligence and creativity with applications to such diverse tasks as proving mathematical theorems and building mathematical theories, common sense reasoning, learning, language…
Analogical proportions are expressions of the form ``$a$ is to $b$ what $c$ is to $d$'' at the core of analogical reasoning which itself is at the core of human and artificial intelligence. The author has recently introduced {\em from first…
Analogical proportions are statements of the form "$a$ is to $b$ as $c$ is to $d$", which expresses that the comparisons of the elements in pair $(a, b)$ and in pair $(c, d)$ yield similar results. Analogical proportions are creative in the…
Analogical proportions are statements of the form "A is to B as C is to D". They constitute an inference tool that provides a logical framework to address learning, transfer, and explainability concerns and that finds useful applications in…
Analogical proportions compare pairs of items (a, b) and (c, d) in terms of their differences and similarities. They play a key role in the formalization of analogical inference. The paper first discusses how to improve analogical inference…
Analogical proportions are statements of the form "A is to B as C is to D" that are used for several reasoning and classification tasks in artificial intelligence and natural language processing (NLP). For instance, there are analogy based…
Analogical proportions are statements expressed in the form "A is to B as C is to D" and are used for several reasoning and classification tasks in artificial intelligence and natural language processing (NLP). In this paper, we focus on…
It has been argued that analogy is the core of cognition. In AI research, algorithms for analogy are often limited by the need for hand-coded high-level representations as input. An alternative approach is to use high-level perception, in…
Building on a specific formalization of analogical relationships of the form "A relates to B as C relates to D", we establish a connection between two important subfields of artificial intelligence, namely analogical reasoning and…
The author has recently introduced abstract algebraic frameworks of analogical proportions and similarity within the general setting of universal algebra. The purpose of this paper is to build a bridge from similarity to analogical…
The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form "$P$ transforms into $Q$ as…
The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. The purpose of this paper is to lift that framework from universal algebra to the strictly more…
Analogy is core to human cognition. It allows us to solve problems based on prior experience, it governs the way we conceptualize new information, and it even influences our visual perception. The importance of analogy to humans has made it…
Object ranking or "learning to rank" is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects represented as feature vectors, the goal is to learn a ranking…
This work presents a formalization of analogy on numbers that relies on generalized means. It is motivated by recent advances in artificial intelligence and applications of machine learning, where the notion of analogy is used to infer…
Analogical reasoning is a powerful qualitative reasoning tool that enables humans to connect two situations, and to generalize their knowledge from familiar to novel situations. Cognitive Science research provides valuable insights into the…
Principles of analogical reasoning have recently been applied in the context of machine learning, for example to develop new methods for classification and preference learning. In this paper, we argue that, while analogical reasoning is…
Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects…
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…