Knowledge, probability, and adversaries

Knowledge Probability and Adversaries Preliminary Report

What should it mean for an agent to know or believe an assertion is true with probability Di erent papers FH FZ HMT give di er ent answers choosing to use quite di erent probabil ity spaces when computing the probability an agent assigns to an event We show that each choice can be understood in terms of a betting game and that each choice corresponds to betting against a di erent opponent We co...

Likelihood, Probability, and Knowledge

The modal logic LL was introduced by Halpern and Rabin [HR] as a means of doing qualitative reasoning about likelihood. Here the relationship between LL and probability theory is examined. It is shown that there is a way of translating probability assertions into LL in a sound manner, so that LL in some sense can capture the probabilistic interpretation of likelihood. However, the translation i...

Knowledge-based Design and Evolutionary Design: Adversaries or Compatriots?

Conditional Belief, Knowledge and Probability

A natural way to represent beliefs and the process of updating beliefs is presented by Bayesian probability theory, where belief of an agent a in P can be interpreted as a considering that P is more probable than not P. This paper attempts to get at the core logical notion underlying this. The paper presents a sound and complete neighbourhood logic for conditional belief and knowledge, and trac...

Update, Probability, Knowledge and Belief

The paper compares two kinds of models for logics of knowledge and belief, neighbourhood models and epistemic weight models. We give sound and complete calculi for both, and we show that our calculus for neighbourhood models is sound but not complete for epistemic weight models. Epistemic weight models combine knowledge and probability by using epistemic accessibility relations and weights to d...