Related papers: Algebraic anti-unification
Anti-unification (AU) is a fundamental operation for generalization computation used for inductive inference. It is the dual operation to unification, an operation at the foundation of automated theorem proving. Interest in AU from the AI…
The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static…
Anti-unification refers to the process of generalizing two (or more) goals into a single, more general, goal that captures some of the structure that is common to all initial goals. In general one is typically interested in computing what…
Conceptual abstraction and analogy-making are key abilities underlying humans' abilities to learn, reason, and robustly adapt their knowledge to new domains. Despite of a long history of research on constructing AI systems with these…
Anti-unification in logic programming refers to the process of capturing common syntactic structure among given goals, computing a single new goal that is more general called a generalization of the given goals. Finding an arbitrary common…
Recent advances in AI -- including generative approaches -- have resulted in technology that can support humans in scientific discovery and forming decisions, but may also disrupt democracies and target individuals. The responsible use of…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
There has been a gap between artificial intelligence and human intelligence. In this paper, we identify three key elements forming human intelligence, and suggest that abstraction learning combines these elements and is thus a way to bridge…
Generalization techniques have many applications, including template construction, argument generalization, and indexing. Modern interactive provers can exploit advancement in generalization methods over expressive type theories to further…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
The rapid development of artificial intelligence (AI) systems has created an urgent need for their scientific quantification. While their fluency across a variety of domains is impressive, AI systems fall short on tests requiring…
The field of artificial intelligence (AI) is devoted to the creation of artificial decision-makers that can perform (at least) on par with the human counterparts on a domain of interest. Unlike the agents in traditional AI, the agents in…
We characterise the problem of abstraction in the context of deep reinforcement learning. Various well established approaches to analogical reasoning and associative memory might be brought to bear on this issue, but they present…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Humans are capable of abstracting away irrelevant details when studying problems. This is especially noticeable for problems over grid-cells, as humans are able to disregard certain parts of the grid and focus on the key elements important…
Automatic data abstraction is an important capability for both benchmarking machine intelligence and supporting summarization applications. In the former one asks whether a machine can `understand' enough about the meaning of input data to…
We study nominal anti-unification, which is concerned with computing least general generalizations for given terms-in-context. In general, the problem does not have a least general solution, but if the set of atoms permitted in…
The field of artificial intelligence (AI) represents an enormous endeavour of humankind that is currently transforming our societies down to their very foundations. Its task, building truly intelligent systems, is underpinned by a vast…
Abstraction plays a key role in concept learning and knowledge discovery; this paper is concerned with computational abstraction. In particular, we study the nature of abstraction through a group-theoretic approach, formalizing it as…
The intention of the present study is to establish the mathematical fundamentals for automated problem solving essentially targeted for robotics by approaching the task universal algebraically introducing knowledge as realizations of…