Related papers: Does resolving PvNP require a paradigm shift?
This work introduces a novel framework of uniform realizability that unifies and generalizes various realizability interpretations of logic, particularly focussing on the treatment of atomic formulas and quantifiers. Traditional…
Mechanistic interpretability aims to reverse engineer the computation performed by a neural network in terms of its internal components. Although there is a growing body of research on mechanistic interpretation of neural networks, the…
This paper presents an extension of Defeasible Deontic Logic to deal with the Pragmatic Oddity problem. The logic applies three general principles: (1) the Pragmatic Oddity problem must be solved within a general logical treatment of CTD…
Mechanistic interpretability (MI) is an emerging framework for interpreting neural networks. Given a task and model, MI aims to discover a succinct algorithmic process, an interpretation, that explains the model's decision process on that…
It is generally accepted that the incompleteness of first-order number theory (PA) is established by an application of Godel's proof. This paper shows that the arithmetization of the syntax of PA implies that the hypothesised class of PA…
The overarching theme of the following pages is that mathematical logic -- centered around the incompleteness theorems -- is first and foremost an investigation of $\textit{computation}$, not arithmetic. Guided by this intuition we will…
Central to the success of artificial neural networks is their ability to generalize. But does neural network generalization primarily rely on seeing highly similar training examples (memorization)? Or are neural networks capable of…
How to interpret a data mining model has received much attention recently, because people may distrust a black-box predictive model if they do not understand how the model works. Hence, it will be trustworthy if a model can provide…
Modal logics allow reasoning about various modes of truth: for example, what it means for something to be possibly true, or to know that something is true as opposed to merely believing it. This report describes embeddings of propositional…
Explainability algorithms aimed at interpreting decision-making AI systems usually consider balancing two critical dimensions: 1) \textit{faithfulness}, where explanations accurately reflect the model's inference process. 2)…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable…
In this article, we present a leap-forward expansion to the study of explainability in neural networks by considering explanations as answers to abstract reasoning-based questions. With $P$ as the prediction from a neural network, these…
Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
The paper contains a proof for the P != NP hypothesis with the help of the two "natural" postulates. The postulates restrict capacity of the Turing machines and state that each independent and necessary condition of the problem should be…
Explainable artificial intelligence and interpretable machine learning are research domains growing in importance. Yet, the underlying concepts remain somewhat elusive and lack generally agreed definitions. While recent inspiration from…
Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several…
Machine learning algorithms enable advanced decision making in contemporary intelligent systems. Research indicates that there is a tradeoff between their model performance and explainability. Machine learning models with higher performance…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…