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Prolog's very useful expressive power is not captured by traditional logic programming semantics, due mainly to the cut and goal and clause order. Several alternative semantics have been put forward, exposing operational details of the…
We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may…
A number of generalizations of stochastic and information-theoretic randomness are known in the literature. However, they are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore explainable…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
The computing continuum, a novel paradigm that extends beyond the current silos of cloud and edge computing, can enable the seamless and dynamic deployment of applications across diverse infrastructures. By utilizing the cloud-native…
This paper presents the definition and implementation of a quantum computer architecture to enable creating a new computational device - a quantum computer as an accelerator In this paper, we present explicitly the idea of a quantum…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
Large language models (LLMs) are increasingly integrated into autonomous systems, giving rise to a new class of software known as Agentware, where LLM-powered agents perform complex, open-ended tasks in domains such as software engineering,…
Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different fields, such as computer vision, natural language processing, and…
This short paper describes a simple and intuitive Prolog program, a metainterpreter, that computes the bottom up meaning of a simple positive Horn clause definition. It involves a simple transformation of the object program rules into…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
Dynamic evaluation is a paradigm in computer algebra which was introduced for computing with algebraic numbers. In linear algebra, for instance, dynamic evaluation can be used to apply programs which have been written for matrices with…
Many AI applications rely on knowledge encoded in a locigal knowledge base (KB). The most essential benefit of such logical KBs is the opportunity to perform automatic reasoning which however requires a KB to meet some minimal quality…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
Reasoning capabilities in large language models (LLMs) have substantially advanced through methods such as chain-of-thought and explicit step-by-step explanations. However, these improvements have not yet fully transitioned to multimodal…
We show how automatic tools for the verification of linear and branching time properties of procedural, multi-threaded, and functional programs as well as program synthesis can be naturally and uniformly seen as solvers of constraints in…
Cobweb, a human-like category learning system, differs from most cognitive science models in incrementally constructing hierarchically organized tree-like structures guided by the category utility measure. Prior studies have shown that…
Operationalizing definitions of fairness is difficult in practice, as multiple definitions can be incompatible while each being arguably desirable. Instead, it may be easier to directly describe algorithmic bias through ad-hoc assumptions…
While Large Language Models excel at semantic tasks, they face a critical bottleneck in financial quantitative reasoning, frequently suffering from "Arithmetic Hallucinations" and a systemic failure mode we term "Cognitive Collapse". To…
An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…