Related papers: Aspects of Superdeterminism Made Intuitive
An explanation for the political processes leading to the sudden collapse of empires and states would be useful for understanding both historical and contemporary political events. We seek a general description of state collapse spanning…
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…
The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that is powerful and broadly applicable. While the general form of the reinforcement learning problem enables…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
We show that, under mild assumptions, some unimaginable events - which we refer to as Black Swan events - must necessarily occur. It follows as a corollary of our theorem that any computational model of decision-making under uncertainty is…
Goedel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proofs. Our purpose is to look for a connection between these two…
We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known. The framework, in gambling terms, is that the size of a bet is proportional to the gambler's perceived…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially…
With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet,…
Recently, there has been a discussion on the origin of the quantum probability rules (Deutsch quant-ph/9906015, Polley quant-ph/9906124, Barnum et al. quant-ph/9907024, Finkelstein quant-ph/9907004). This contribution, which is a slightly…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
Coalition Logic is an important logic in logical studies of strategic reasoning, whose models are concurrent game models. In this paper, first, we systematically discuss three assumptions of concurrent game models and argue that they are…
The issue of whether we make decisions freely has vexed philosophers for millennia, Resolving this is vital for solving a diverse range of problems, from the physiology of how the brain makes decisions (and how we assign moral…
What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which…
We formalize the idea of probability distributions that lead to reliable predictions about some, but not all aspects of a domain. The resulting notion of `safety' provides a fresh perspective on foundational issues in statistics, providing…
The likelihood principle makes strong claims about the nature of statistical evidence but is controversial. Its claims are undermined by the existence of several examples that are assumed to show that it allows, with unity probability,…
Interpretability and explainability have gained more and more attention in the field of machine learning as they are crucial when it comes to high-stakes decisions and troubleshooting. Since both provide information about predictors and…