Related papers: Analogical proportions II
Analogy is one of the core capacities of human cognition; when faced with new situations, we often transfer prior experience from other domains. Most work on computational analogy relies heavily on complex, manually crafted input. In this…
Abstraction is key to human and artificial intelligence as it allows one to see common structure in otherwise distinct objects or situations and as such it is a key element for generality in AI. Anti-unification (or generalization) is…
Neuro-symbolic and statistical relational artificial intelligence both integrate frameworks for learning with logical reasoning. This survey identifies several parallels across seven different dimensions between these two fields. These…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
In the rapidly growing literature on explanation algorithms, it often remains unclear what precisely these algorithms are for and how they should be used. In this position paper, we argue for a novel and pragmatic perspective: Explainable…
The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts…
This paper serves as a bridge between quantum computing and analogical modeling (a general theory for predicting categories of behavior in varying contexts). Since its formulation in the early 1980s, analogical modeling has been…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. This paper studies analogical proportions in the boolean domain consisting of two elements 0 and 1…
We consider a class of visual analogical reasoning problems that involve discovering the sequence of transformations by which pairs of input/output images are related, so as to analogously transform future inputs. This program synthesis…
Analogical reasoning is a core cognitive faculty essential for narrative understanding. While LLMs perform well when surface and structural cues align, they struggle in cases where an analogy is not apparent on the surface but requires…
Comparison of geometric quantities usually means obtaining generally true equalities of different algebraic expressions of a given geometric figure. Today's technical possibilities already support symbolic proofs of a conjectured theorem,…
The testimony and practice of notable mathematicians indicate that there is an important phenomenological and epistemological difference between superficial and deep analogies in mathematics. In this paper, we offer a descriptive theory of…
Four-term word analogies (A:B::C:D) are classically modeled geometrically as ''parallelograms,'' yet recent work suggests this model poorly captures how humans produce analogies, with simple local-similarity heuristics often providing a…
The aim of this paper is to show that the concept of probability is best understood by dividing this concept into two different types of probability, namely physical probability and analogical probability. Loosely speaking, a physical…
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…
There have been several efforts to extend distributional semantics beyond individual words, to measure the similarity of word pairs, phrases, and sentences (briefly, tuples; ordered sets of words, contiguous or noncontiguous). One way to…
Similarity functions measure how comparable pairs of elements are, and play a key role in a wide variety of applications, e.g., notions of Individual Fairness abiding by the seminal paradigm of Dwork et al., as well as Clustering problems.…
Biological intelligence is remarkable in its ability to produce complex behaviour in many diverse situations through data efficient, generalisable and transferable skill acquisition. It is believed that learning "good" sensory…
Human reasoning is grounded in an ability to identify highly abstract commonalities governing superficially dissimilar visual inputs. Recent efforts to develop algorithms with this capacity have largely focused on approaches that require…