Results 1 
5 of
5
Questions of Reasoning Under Logical Uncertainty
"... A logically uncertain reasoner would be able to reason as if they know both a programming language and a program, without knowing what the program outputs. Most practical reasoning involves some logical uncertainty, but no satisfactory theory of reasoning under logical uncertainty yet exists. A b ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
A logically uncertain reasoner would be able to reason as if they know both a programming language and a program, without knowing what the program outputs. Most practical reasoning involves some logical uncertainty, but no satisfactory theory of reasoning under logical uncertainty yet exists. A better theory of reasoning under logical uncertainty is needed in order to develop the tools necessary to construct highly reliable artificial reasoners. This paper introduces the topic, discusses a number of historical results, and describes a number of open problems. 1
Learning Agents with Evolving Hypothesis Classes
"... Abstract. It has recently been shown that a Bayesian agent with a universal hypothesis class resolves most induction problems discussed in the philosophy of science. These ideal agents are, however, neither practical nor a good model for how real science works. We here introduce a framework for lear ..."
Abstract
 Add to MetaCart
Abstract. It has recently been shown that a Bayesian agent with a universal hypothesis class resolves most induction problems discussed in the philosophy of science. These ideal agents are, however, neither practical nor a good model for how real science works. We here introduce a framework for learning based on implicit beliefs over all possible hypotheses and limited sets of explicit theories sampled from an implicit distribution represented only by the process by which it generates new hypotheses. We address the questions of how to act based on a limited set of theories as well as what an ideal sampling process should be like. Finally, we discuss topics in philosophy of science and cognitive science from the perspective of this framework. 1
Unifying Probability and Logic for Learning
"... Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem head on. Uncertain knowledge can be modeled by using graded probabilities rather tha ..."
Abstract
 Add to MetaCart
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem head on. Uncertain knowledge can be modeled by using graded probabilities rather than binary truthvalues, but so far a completely satisfactory integration of logic and probability has been lacking. In particular the inability of confirming universal hypotheses has plagued most if not all systems so far. We address this problem head on. The main technical problem to be discussed is the following: Given a set of sentences, each having some probability of being true, what probability should be ascribed to other (query) sentences? A natural wishlist, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii)