Related papers: Analogical proportions II
Counterfactual reasoning is a foundational topic in both philosophical and logical studies \cite{Stalnaker1968-STAATO-5, Lewis1973-LEWC-2}. A pivotal component of counterfactual analysis is the concept of similarity between possible worlds…
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…
This paper proposes a research direction to advance AI which draws inspiration from cognitive theories of human decision making. The premise is that if we gain insights about the causes of some human capabilities that are still lacking in…
Attributes of words and relations between two words are central to numerous tasks in Artificial Intelligence such as knowledge representation, similarity measurement, and analogy detection. Often when two words share one or more attributes…
The problem of replicating the flexibility of human common-sense reasoning has captured the imagination of computer scientists since the early days of Alan Turing's foundational work on computation and the philosophy of artificial…
We present a technique for estimating the similarity between objects such as movies or foods whose proper representation depends on human perception. Our technique combines a modest number of human similarity assessments to infer a pairwise…
This article is a brief personal account of the past, present, and future of algorithmic randomness, emphasizing its role in inductive inference and artificial intelligence. It is written for a general audience interested in science and…
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…
Reasoning is a hallmark of human intelligence, enabling adaptive decision-making in complex and unfamiliar scenarios. In contrast, machine intelligence remains bound to training data, lacking the ability to dynamically refine solutions at…
Neural networks represent data as projections on trained weights in a high dimensional manifold. The trained weights act as a knowledge base consisting of causal class dependencies. Inference built on features that identify these…
Alignments, i.e., position-wise comparisons of two or more strings or ordered lists are of utmost practical importance in computational biology and a host of other fields, including historical linguistics and emerging areas of research in…
Relating formal grammars is a hard problem that balances between language equivalence (which is known to be undecidable) and grammar identity (which is trivial). In this paper, we investigate several milestones between those two extremes…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to reveal the dynamical notions inherent in logical computational systems. The fundamental notions of proposition and truth-value in standard logic…
Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…
The present work investigates whether different quantification mechanisms (set comparison, vague quantification, and proportional estimation) can be jointly learned from visual scenes by a multi-task computational model. The motivation is…
We propose an approach to analogical inference that marries the neuro-symbolic computational power of complex-sampled hyperdimensional computing (HDC) with Conceptual Spaces Theory (CST), a promising theory of semantic meaning. CST…
Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns…
The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other.…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…