Related papers: Algebraic anti-unification
Novel user interfaces based on artificial intelligence, such as natural-language agents, present new categories of engineering challenges. These systems need to cope with uncertainty and ambiguity, interface with machine learning…
Artificial intelligence (AI) has demonstrated impressive progress in mathematical reasoning, yet its integration into the practice of mathematical research remains limited. In this study, we investigate how the AI Mathematician (AIM) system…
We introduce the open-ended, modular, self-improving Omega AI unification architecture which is a refinement of Solomonoff's Alpha architecture, as considered from first principles. The architecture embodies several crucial principles of…
Analogical reasoning is the ability to detect parallels between two seemingly distant objects or situations, a fundamental human capacity used for example in commonsense reasoning, learning, and creativity which is believed by many…
We extend the notion of anti-unification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of E-generalization sets. We present a framework to combine Inductive Logic…
The rise of Artificial Intelligence (AI) recently empowered researchers to investigate hard mathematical problems which eluded traditional approaches for decades. Yet, the use of AI in Universal Algebra (UA) -- one of the fields laying the…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
Everyone from AI executives and researchers to doomsayers, politicians, and activists is talking about Artificial General Intelligence (AGI). Yet, they often don't seem to agree on its exact definition. One common definition of AGI is an AI…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete…
The problem of quantizing theories defined over configuration spaces described by non-commuting parameters is considered. In this paper we describe the first step in this direction, that is the definition of an integral over a general…
This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave)…
Recently machine learning using neural networks (NN) has been developed, and many new methods have been suggested. These methods are optimized for the type of input data and work very effectively, but they cannot be used with any kind of…
A foundational principle in cognitive science holds that intelligent agents do not learn by storing experiences as isolated instances, but by forming abstract schemas that capture relational structure shared across situations. Even though…
In conceptual modeling (CM), humans apply abstraction to represent excerpts of reality for means of understanding and communication, and processing by machines. Artificial Intelligence (AI) is applied to vast amounts of data to…
This paper leverages various philosophical and ontological frameworks to explore the concept of embodied artificial general intelligence (AGI), its relationship to human consciousness, and the key role of the metaverse in facilitating this…
Lists, multisets, and sets are well-known data structures whose usefulness is widely recognized in various areas of Computer Science. These data structures have been analyzed from an axiomatic point of view with a parametric approach in (*)…
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…
Is intelligence realized by connectionist or classicist? While connectionist approaches have achieved superhuman performance, there has been growing evidence that such task-specific superiority is particularly fragile in systematic…
Artificial intelligence (AI) has undergone a renaissance recently, making major progress in key domains such as vision, language, control, and decision-making. This has been due, in part, to cheap data and cheap compute resources, which…