Real-world applications of automated theorem proving require modern software environments that enable modularisation, networked inter-operability, robustness, and scalability. These requirements are met by the Agent-Oriented Programming paradigm of Distributed Artificial Intelligence. We argue that a reasonable framework for automated theorem proving in the large regards typical mathematical services as autonomous agents that provide internal functionality to the outside and that, in turn, are able to access a variety of existing external services. This article describes...

Controlling a robot involves making decisions that modify its behavior. Making good decisions may require time-consuming computation. Changes in the environment over time affect when this computation can be done (e.g., after obtaining the necessary information) , and when a result is useful (e.g., before some event occurs). This sensitivity to when computation is performed and when decisions are made is what makes these problems "time-dependent." A controller with more than one decision to make must trade off computation time, based on the expected effect on the system's behavior. We call the resulting meta-level scheduling problem a "deliberation-scheduling" problem. We have

Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and long-standing problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test’s (pre-data) error probabilities are to be used for (post-data) inductive inference as opposed to inductive behavior. We argue that the relevance of error probabilities is to ensure that only statistical hypotheses that have passed severe or probative tests are inferred from the data. The severity criterion supplies a meta-statistical principle for evaluating proposed statistical inferences, avoiding classic fallacies from tests that are overly sensitive, as well as those not sensitive enough to particular errors and discrepancies.

as a testbed for designing intelligent agents. The system consists of an overall agent architecture and five components within the architecture. The five components are: 1. Goal-Directed Learning (GDL), a decision-theoretic method for selecting learning goals. 2. Probabilistic Bias Evaluation (PBE), a technique for using probabilistic background knowledge to select learning biases for the learning goals. 3. Uniquely Predictive Theories (UPTs) and Probability Computation using Independence (PCI), a probabilistic representation and Bayesian inference method for the agent's theories. 4. A probabilistic learning component, consisting of a heuristic search algorithm and a Bayesian method for evaluating proposed theories. 5. A decision-theoretic probabilistic planner, which searches through the probability space defined by the agent's current theory to select the best action. PAGODA is given as input an initial planning goal (its ove

We review the definition of the Full Bayesian Significance Test (FBST), and summarize its main statistical and epistemological characteristics.

Abstract: In this paper epistemological, ontological and sociological questions concerning the statistical significance of sharp hypotheses in scientific research are investigated within the framework provided by the Cognitive Constructivism and the FBST-Full Bayesian Significance Test. The constructivist framework is contrasted with Decision Theory and Falsificationism, the traditional epistemological settings for orthodox Bayesian and frequentist statistics.

In probability theory, the random variables Y1,...,YN are said to be exchangeable (or permutable or symmetric) if their joint distribution F(y1,...,yN) is symmetric; that is, if F is invariant under permutation of its arguments, so that F(z1,...,zN) = F(y1,...,yN) whenever z1,...,zN is a permutation of y1,...,yN. There is a related epidemiologic usage which is described in the article on confounding. In many ways, sequences of exchangeable random variables play a role in subjective Bayesian theory analogous to that played by independent identically distributed (iid) sequences in classical frequentist theory. In particular, the assumption that a sequence of random variables is exchangeable allows the development of inductive statistical procedures for inference from observed to unobserved members of the sequence [1–3, 5, 6, 9]. Exchangeable random variables are identically distributed, and iid variables are exchangeable. Now suppose that Y1,...,YN are iid given an unknown parameter θ that indexes their joint distribution (see Identifiability). Such variables will not be unconditionally independent when θ is a random variable, but will be exchangeable. Consider, for example, the case in which Y1,...,YN have a joint density. The unconditional density of Y1,...,YN will be f(y1,...,yN) = f(y1,...,yN|θ) dF(θ)

equency of that colour. There are imprecise probability models for the learning process which have these properties, which treat all colours symmetrically, and which are coherent. Imprecise probability models are needed in many applications of probabilistic and statistical reasoning. They have been used in the following kinds of problems: when there is little information on which to evaluate a probability, as in Walley [35, 37, 38] to model nonspecic information, e.g., knowing the proportions of black, white and coloured balls in an urn gives only upper and lower bounds for the chance of drawing a red ball (see Dempster [6], Klir and Folger [23] and Shafer [30]) to model the uncertainty produced by vague statements such as \it will probably rain" or \there is a good chance that it will be mainly ne" (Walley [36], Zadeh [46]) in robust Bayesian inference, to model uncertainty about a prior distribution (see Ber

Whatever the interpretation, dealing with probability (uncertainty) is a key reasoning ability. PHL 1010 Korb 5 Venn Diagrams Figure 1: P (U) = 1 X Figure 2: P (X) 0 X Y Figure 3: If X " Y = ;; P (X [ Y ) = P (X) + P (Y ) PHL 1010 Korb 6 Conditional Probability Y X Figure 4: P (XjY ) = P (X"Y ) P (Y ) Examples ffl Wherever Mary went, her lamb was sure to go. ffl Wherever Mary went, her brother was sure to avoid. ffl Mary and Tom pay no attention to each other. PHL 1010 Korb 7<F41.13

Towards a rational theory of human information acquisition