An explanatory relation is a binary relation where the intended meaning of α γ is "γ is a preferred explanation of α". In [37], a set of postulates that should be satisfied by preferred explanatory relations was proposed and discussed. The aim of this section is threefold: first, to propose very natural explanatory relations using morphologic that in some cases are computationally tractable; secondly, to examine the adequacy of logical postulates proposed in [37], and thirdly, the discovery of new logical properties for explanatory reasoning. Morphologic allows us to define the most central part of a formula, according to the fundamental principles of this theory (see e.g.

We define a consensus postulate in the propositional belief merging setting. In a nutshell, this postulate imposes the merged base to be consistent with the pieces of information provided by each agent involved in the merging process. The interplay of this new postulate with the IC postulates for belief merging is studied, and an incompatibility result is proved. The maximal sets of IC postulates which are consistent with the consensus postulate are exhibited. When satisfying some of the remaining IC postulates, consensus operators are shown to suffer from a weak inferential power. We then introduce two families of consensus operators having a better inferential power by setting aside some of these postulates.

Recent approaches to goal recognition have progressively relaxed the assumptions about the amount and correctness of domain knowledge and available observations, yielding accurate and efficient algorithms. These approaches, however, assume completeness and correctness of the domain theory against which their algorithms match observations: this is too strong for most real-world domains. In this work, we develop a goal recognition technique capable of recognizing goals using incomplete (and possibly incorrect) domain theories.

Many applications infer the structure of a probabilistic graphical model from data to elucidate the relationships between variables. But how can we train graphical models on a massive data set? In this paper, we show how to construct coresets---compressed data sets which can be used as proxy for the original data and have provably bounded worst case error---for Gaussian dependency networks (DNs), i.e., cyclic directed graphical models over Gaussians, where the parents of each variable are its Markov blanket. Specifically, we prove that Gaussian DNs admit coresets of size independent of the size of the data set. Unfortunately, this does not extend to DNs over members of the exponential family in general. As we will prove, Poisson DNs do not admit small coresets. Despite this worst-case result, we will provide an argument why our coreset construction for DNs can still work well in practice on count data.To corroborate our theoretical results, we empirically evaluated the resulting Core DNs on real data sets. The results demonstrate significant gains over no or naive sub-sampling, even in the case of count data.

We introduce a new semantics for a logic of explicit and implicit beliefs based on the concept of multi-agent belief base. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and doxastic/epistemic alternative are primitive, in our semantics they are non-primitive but are defined from the concept of belief base. We provide a complete axiomatization and a decidability result for our logic.

Dependence is an important concept for many tasks in artificial intelligence. A task can be executed more efficiently by discarding something independent from the task. In this paper, we propose two novel notions of dependence in propositional logic: formula-formula dependence and formula forgetting. The first is a relation between formulas capturing whether a formula depends on another one, while the second is an operation that returns the strongest consequence independent of a formula. We also apply these two notions in two well-known issues: belief update and conservative extension. Firstly, we define a new update operator based on formula-formula dependence. Furthermore, we reduce conservative extension to formula forgetting.

Conceptual Spaces--The Geometry of Thought is a book by Peter Gärdenfors, professor of cognitive science at Lund University, Sweden. Gärdenfors has authored another book in this series (based on work with Carlos Alchourron and David Makinson), Knowledge in Flux, a definitive account of the widely examined AGM (after Alchourron, Gärdenfors, and Makinson) theory of belief revision. The AGM theory is firmly based on classical logic and its model theory, and by his founding participation in developing it, Gärdenfors has earned the right to critique knowledge representation. His new book is not primarily about logic, but it is certainly not an apostasy either. If I may be permitted a minor irreverence, I would say that this book came not to destroy logic but to fulfill.

The idea is that although an AI system without the frame problem might, say, read an echocardiogram and diagnose a heart defect, a really smart autonomous robot will arrive only if, like us humans, it can handle the frame problem. The highlight … is an entertaining go-round between two pugilists trading blows in civil but gloves-off style, reminiscent of a net discussion. We're still confronted by a difficult question: Is there a solution to it? If not, then R2D2 might forever be but a creature of fiction. If, however, the frame problem is solvable, we must confront yet another question: Is there a general solution to the frame problem, or is the best that can be mustered a so-called domain-dependent solution?

Haussler's paper was therefore important in linking the new PAC learning theory work with the ongoing work on machine learning within AI. Twenty years later that link is firmly established, and the two research communities have largely merged into one. In fact, much of the dramatic progress in machine learning over the past two decades has come from a fruitful marriage between research on learning theory and design of practical learning algorithms for particular problem classes. Mitchell and Levesque provide commentary on the two AAAI Classic Paper awards, given at the AAAI-05 conference in Pittsburgh, Pennsylvania. The two winning papers were "Quantifying the Inductive Bias in Concept Learning," by David Haussler, and "Default Reasoning, Nonmonotonic Logics, and the Frame Problem," by Steve Hanks and Drew Mc-Dermott.

This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean vector, and message passing between neighbors. Under broad conditions, it is shown that the message information matrix converges to a unique positive definite limit matrix for arbitrary positive semidefinite initialization, and it approaches an arbitrarily small neighborhood of this limit matrix at a doubly exponential rate. A necessary and sufficient convergence condition for the belief mean vector to converge to the optimal centralized estimator is provided under the assumption that the message information matrix is initialized as a positive semidefinite matrix. Further, it is shown that Gaussian BP always converges when the underlying factor graph is given by the union of a forest and a single loop. The proposed convergence condition in the setup of distributed linear Gaussian models is shown to be strictly weaker than other existing convergence conditions and requirements, including the Gaussian Markov random field based walk-summability condition, and applicable to a large class of scenarios.