Related papers: Learnability and Positive Equivalence Relations

Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…

As reinforcement learning (RL) achieves more success in solving complex tasks, more care is needed to ensure that RL research is reproducible and that algorithms herein can be compared easily and fairly with minimal bias. RL results are,…

Shapiro's notations for natural numbers, and the associated desideratum of acceptability - the property of a notation that all recursive functions are computable in it - is well-known in philosophy of computing. Computable structure theory,…

Learning performed over finite time is inherently irreversible. In Part~I of this series, we modeled learning as a transport process in the space of parameter distributions and derived the Epistemic Speed Limit (ESL), which lower-bounds…

In this paper, based on results of exact learning, test theory, and rough set theory, we study arbitrary infinite families of concepts each of which consists of an infinite set of elements and an infinite set of subsets of this set called…

Beyond binary classification, learnability can become a logically fragile notion: in EMX, even the class of all finite subsets of $[0,1]$ is learnable in some models of ZFC and not in others. We argue the paradox is operational. The…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

Reproducibility is one of the core dimensions that concur to deliver Trustworthy Artificial Intelligence. Broadly speaking, reproducibility can be defined as the possibility to reproduce the same or a similar experiment or method, thereby…

In his pioneering work in the field of Inductive Inference, Gold (1967) proved that a set containing all finite languages and at least one infinite language over the same fixed alphabet is not learnable in the exact sense. Within the same…

We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or…

In language learning in the limit, the most common type of hypothesis is to give an enumerator for a language. This so-called $W$-index allows for naming arbitrary computably enumerable languages, with the drawback that even the membership…

Why do some languages like Czech permit free word order, while others like English do not? We address this question by pretraining transformer language models on a spectrum of synthetic word-order variants of natural languages. We observe…

In the paper hereditary classes of ${\rm L}$-structures are studied with language of the form ${{\rm L} = {\rm L_{fin}} \cup {\rm L_\infty}}$, where ${{\rm L_{fin}} = \langle R_1,R_2,\ldots, R_m, = \rangle}$ and ${{\rm L_\infty} = \langle…

Humans can flexibly generalize knowledge across domains by leveraging structured relational representations. While prior research has shown how such representations support analogical reasoning, less is known about how they are recruited to…

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…

In this paper we extend the approach of M. Cavaleri to effective amenability to the class of computably enumerable groups, i.e. in particular we do not assume that groups are finitely generated. In the case of computable groups we also…

We study a new notion of reduction between structures called enumerable functors related to the recently investigated notion of computable functors. Our main result shows that enumerable functors and effective interpretability with the…

Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This…

We introduce new combinatorial quantities for concept classes, and prove lower and upper bounds for learning complexity in several models of query learning in terms of various combinatorial quantities. Our approach is flexible and powerful…

We investigate the problem of learning description logic ontologies from entailments via queries, using epistemic reasoning. We introduce a new learning model consisting of epistemic membership and example queries and show that polynomial…