相关论文: The Problem Of Grue Isn't
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
A new concept, primitive chaos, was proposed, as a concept closely related to the fundamental problems of sciences themselves such as determinism, causality, free will, predictability, and time asymmetry [{\em J. Phys. Soc. Jpn.} {\bf…
Motivated by the Gilbreath conjecture, we develop the notion of the gap sequence induced by any sequence of numbers. We introduce the notion of the path and associated circuits induced by an originator and study the conjecture via the…
Understanding sources of a model's uncertainty regarding its predictions is crucial for effective human-AI collaboration. Prior work proposes using numerical uncertainty or hedges ("I'm not sure, but ..."), which do not explain uncertainty…
This article seeks to encourage a mathematical dialog regarding a possible solution to Beals Conjecture. It breaks down one of the worlds most difficult math problems into laymans terms and encourages people to question some of the most…
This paper includes notes to accompany a reading of Thue's 1914 paper "Probleme uber Veranderungen von Zeichenreihen nach gegebenen Reglen", along with a translation of that paper. Thue's 1914 paper is mainly famous for proving an early…
In his seminal paper ``Computing Machinery and Intelligence'', Alan Turing introduced the ``imitation game'' as part of exploring the concept of machine intelligence. The Turing Test has since been the subject of much analysis, debate,…
All priors are not created equal. There are right and there are wrong priors. That is the main conclusion of this contribution. I use, a cooked-up example designed to create drama, and a typical textbook example to show the pervasiveness of…
Natural languages can express some logical propositions that humans are able to understand. We illustrate this fact with a famous text that Conan Doyle attributed to Holmes: 'It is an old maxim of mine that when you have excluded the…
Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…
The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for…
High-dimensional computational challenges are frequently explained via the curse of dimensionality, i.e., increasing the number of dimensions leads to exponentially growing computational complexity. In this commentary, we argue that…
While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…
The article attempts to demonstrate the rich history of one truly remarkable problem situated at the confluence of probability theory and theory of numbers - finding the probability of co-primality of two randomly selected natural numbers.…
Riddles are concise linguistic puzzles that describe an object or idea through indirect, figurative, or playful clues. They are a longstanding form of creative expression, requiring the solver to interpret hints, recognize patterns, and…
Uncertainty may be taken to characterize inferences, their conclusions, their premises or all three. Under some treatments of uncertainty, the inferences itself is never characterized by uncertainty. We explore both the significance of…
The probabilistic rule that links the formalism of Quantum Mechanics (QM) to the real world was stated by Born in 1926. Since then, there were many attempts to derive the Born postulate as a theorem, Gleason's being the most prominent. The…
In this paper, we make a preliminary interpretation of Cook's theorem presented in [1]. This interpretation reveals cognitive biases in the proof of Cook's theorem that arise from the attempt of constructing a formula in CNF to represent a…
This is the transcript of a lecture given at UMass-Lowell in which I compare and contrast the work of Godel and of Turing and my own work on incompleteness. I also discuss randomness in physics vs randomness in pure mathematics.
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…