Related papers: An Algebraic Approach to Learning and Grounding

We extend our formulation of Merge and Minimalism in terms of Hopf algebras to an algebraic model of a syntactic-semantic interface. We show that methods adopted in the formulation of renormalization (extraction of meaningful physical…

Models trained on semantically related datasets and tasks exhibit comparable inter-sample relations within their latent spaces. We investigate in this study the aggregation of such latent spaces to create a unified space encompassing the…

This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…

We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…

We develop basic notions and methods of algebraic geometry over the algebraic objects called hyperrings. Roughly speaking, hyperrings generalize rings in such a way that an addition is `multi-valued'. This paper largely consisits of two…

Learning Spaces are certain set systems that are applied in the mathematical modeling of education. We propose a suitable compression (without loss of information) of such set systems to facilitate their logical and statistical analysis.…

Algebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely…

The algebraic method provides useful techniques to identify models in designs and to understand aliasing of polynomial models. The present note surveys the topic of Gr\"obner bases in experimental design and then describes the notion of…

This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…

Effective human-robot interaction, such as in robot learning from human demonstration, requires the learning agent to be able to ground abstract concepts (such as those contained within instructions) in a corresponding high-dimensional…

We present a general theory and corresponding declarative model for the embodied grounding and natural language based analytical summarisation of dynamic visuo-spatial imagery. The declarative model ---ecompassing spatio-linguistic…

We present an approach for acquiring grounded representations of words from mixed-initiative, situated interactions with a human instructor. The work focuses on the acquisition of diverse types of knowledge including perceptual, semantic,…

Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…

We consider the problem of answering queries about formulas of propositional logic based on background knowledge partially represented explicitly as other formulas, and partially represented as partially obscured examples independently…

Autonomous systems require the management of several model views to assure properties such as safety and security among others. A crucial issue in autonomous systems design assurance is the notion of emergent behavior; we cannot use their…

Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…

Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…

A robot's ability to understand or ground natural language instructions is fundamentally tied to its knowledge about the surrounding world. We present an approach to grounding natural language utterances in the context of factual…

This paper studies algebras arising as algebraic semantics for logics used to model reasoning with incomplete or inconsistent information. In particular we study, in a uniform way, varieties of bilattices equipped with additional…

Sentence fusion is the task of joining related sentences into coherent text. Current training and evaluation schemes for this task are based on single reference ground-truths and do not account for valid fusion variants. We show that this…