Related papers: Artifical intelligence and inherent mathematical d…
The introduction of generative artificial intelligence applications to the public has led to heated discussions about its potential impacts and risks for K-12 education. One particular challenge has been to decide what students should learn…
Teaching logic effectively requires an understanding of the factors which cause logic students to struggle. Formalization exercises, which require the student to produce a formula corresponding to the natural language sentence, are a good…
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
Mechanistic interpretability is the program of explaining what AI systems are doing in terms of their internal mechanisms. I analyze some aspects of the program, along with setting out some concrete challenges and assessing progress to…
We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to…
There is a significant lack of unified approaches to building generally intelligent machines. The majority of current artificial intelligence research operates within a very narrow field of focus, frequently without considering the…
The interest in explainability in artificial intelligence (AI) is growing vastly due to the near ubiquitous state of AI in our lives and the increasing complexity of AI systems. Answer-set Programming (ASP) is used in many areas, among them…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
There are two important things in science: (A) Finding answers to given questions, and (B) Coming up with good questions. Our artificial scientists not only learn to answer given questions, but also continually invent new questions, by…
Readability assessment is the task of evaluating the reading difficulty of a given piece of text. Although research on computational approaches to readability assessment is now two decades old, there is not much work on synthesizing this…
Artificial intelligence systems are transforming scientific discovery by accelerating specific research tasks, from protein structure prediction to materials design, yet remain confined to narrow domains requiring substantial human…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…
In this paper we offer a formal definition of Artificial Intelligence and this directly gives us an algorithm for construction of this object. Really, this algorithm is useless due to the combinatory explosion. The main innovation in our…
Computational complexity has often been ignored in philosophy of mind, in philosophical artificial intelligence studies. The purpose of this paper is threefold. First and foremost, to show the importance of complexity rather than…
Abstract argumentation frameworks (AFs) provide a formal setting to analyze many forms of reasoning with conflicting information. While the expressiveness of general infinite AFs make them a tempting tool for modeling many kinds of…
We describe basic ideas underlying research to build and understand artificially intelligent systems: from symbolic approaches via statistical learning to interventional models relying on concepts of causality. Some of the hard open…
AI has become pervasive in recent years, but state-of-the-art approaches predominantly neglect the need for AI systems to be contestable. Instead, contestability is advocated by AI guidelines (e.g. by the OECD) and regulation of automated…