Belief Revision

Morphologic for knowledge dynamics: revision, fusion, abduction Artificial Intelligence

Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical morphology in the context of propositional logic, and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based on a semantic approach, that have an intuitive interpretation and that are formally well behaved, to perform revision, fusion and abduction. Computation and tractability are addressed, and simple examples illustrate the typical results that can be obtained.

Book Reviews

AI Magazine

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.

Book Review

AI Magazine

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?

The 2005 AAAI Classic Paper Awards

AI Magazine

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.

Preorder-Based Triangle: A Modified Version of Bilattice-Based Triangle for Belief Revision in Nonmonotonic Reasoning Artificial Intelligence

Bilattice-based triangle provides an elegant algebraic structure for reasoning with vague and uncertain information. But the truth and knowledge ordering of intervals in bilattice-based triangle can not handle repetitive belief revisions which is an essential characteristic of nonmonotonic reasoning. Moreover the ordering induced over the intervals by the bilattice-based triangle is not sometimes intuitive. In this work, we construct an alternative algebraic structure, namely preorder-based triangle and we formulate proper logical connectives for this. It is also demonstrated that Preorder-based triangle serves to be a better alternative to the bilattice-based triangle for reasoning in application areas, that involve nonmonotonic fuzzy reasoning with uncertain information.

Belief Revision with Bridging Axioms

AAAI Conferences

Belief revision deals with the problem of changing a declaratively specified repository under potentially conflicting information. Usually, the problem is approached by providing postulates that specify intended constraints for the revision and constructing concrete revision operators fulfilling them. In the last 30 years since the start of formal belief revision with the work of AGM (Alchourron, Gaerdenfors, and Makinson) roughly four construction principles were investigated and mutually interrelated: partial-meet, epistemic entrenchment, safe/kernel, and the possible worlds (model based) construction. The aim of this paper is to raise into the focus another construction principle relying on the idea of reinterpretation: Conflicts are explained by different use of symbols and conflict resolution is handled by choosing appropriate bridging axioms that relate the different readings. The main purpose of the paper is to argue that the reinterpretation-based approach is sufficiently general by showing how to equivalently formulate classical revision operators such as the operators of Weber, a natural variant of Weber, the operator of Satoh (skeptical operator of Delgrande and Schaub) and the operator of Borgida with reinterpretation operators.

The Linearization of Belief Propagation on Pairwise Markov Networks Artificial Intelligence

Belief Propagation (BP) is a widely used approximation for exact probabilistic inference in graphical models, such as Markov Random Fields (MRFs). In graphs with cycles, however, no exact convergence guarantees for BP are known, in general. For the case when all edges in the MRF carry the same symmetric, doubly stochastic potential, recent works have proposed to approximate BP by linearizing the update equations around default values, which was shown to work well for the problem of node classification. The present paper generalizes all prior work and derives an approach that approximates loopy BP on any pairwise MRF with the problem of solving a linear equation system. This approach combines exact convergence guarantees and a fast matrix implementation with the ability to model heterogenous networks. Experiments on synthetic graphs with planted edge potentials show that the linearization has comparable labeling accuracy as BP for graphs with weak potentials, while speeding-up inference by orders of magnitude.

The "Your Actual Belief" Edition


Next week we're going to discuss the very controversial awards season contender, Nate Parker's The Birth of a Nation. Are you planning to see it in theaters? Record and send us a voice memo at or leave us a message at 646-580-1748 and your thoughts might get shared on next week's episode.

A Generalized Multidimensional Evaluation Framework for Player Goal Recognition

AAAI Conferences

Recent years have seen a growing interest in player modeling, which supports the creation of player-adaptive digital games. A central problem of player modeling is goal recognition, which aims to recognize players’ intentions from observable gameplay behaviors. Player goal recognition offers the promise of enabling games to dynamically adjust challenge levels, perform procedural content generation, and create believable NPC interactions. A growing body of work is investigating a wide range of machine learning-based goal recognition models. In this paper, we introduce GOALIE, a multidimensional framework for evaluating player goal recognition models. The framework integrates multiple metrics for player goal recognition models, including two novel metrics, n-early convergence rate and standardized convergence point . We demonstrate the application of the GOALIE framework with the evaluation of several player goal recognition models, including Markov logic network-based, deep feedforward neural network-based, and long short-term memory network-based goal recognizers on two different educational games. The results suggest that GOALIE effectively captures goal recognition behaviors that are key to next-generation player modeling.

Beliefs propagation in log domain: a neural inspired algorithm for machine learning


Unlike the min-product algorithm, our goal is not limited to estimating the mode of the marginal distribution. We would like to obtain the entire marginal distribution as the sum-product algorithm does. Threads are widely used in the implementation of parallelism in shared memory multiprocessor architectures. We will illustrate it by implementing the shared memory parallel version of Jacobi iteration algorithm.