Evidence and Belief

AAAI Conferences

We discuss the representation of knowledge and of belief from the viewpoint of decision theory. While the Bayesian approach enjoys general-purpose applicability and axiomatic foundations, it suffers from several drawbacks. In particular, it does not model the belief formation process, and does not relate beliefs to evidence. We survey alternative approaches, and focus on formal model of casebased prediction and case-based decisions. A formal model of belief and knowledge representation needs to address several questions. The most basic ones are: (i) how do we represent knowledge?


Using More Reasoning to Improve #SAT Solving

AAAI Conferences

Many real-world problems, including inference in Bayes Nets, can be reduced to #SAT, the problem of counting the number of models of a propositional theory. This has motivated the need for efficient #SAT solvers. Currently, such solvers utilize a modified version of DPLL that employs decomposition and caching, techniques that significantly increase the time it takes to process each node in the search space. In addition, the search space is significantly larger than when solving SAT since we must continue searching even after the first solution has been found. It has previously been demonstrated that the size of a DPLL search tree can be significantly reduced by doing more reasoning at each node. However, for SAT the reductions gained are often not worth the extra time required. In this paper we verify the hypothesis that for #SAT this balance changes. In particular, we show that additional reasoning can reduce the size of a #SAT solver's search space, that this reduction cannot always be achieved by the already utilized technique of clause learning, and that this additional reasoning can be cost effective.


Towards Diagnosing Hybrid Systems

AAAI Conferences

This paper reports on the findings of an ongoing project to investigate techniques to diagnose complex dynamical systems that are modeled as hybrid systems. In particular, we examine continuous systems with embedded supervisory controllers which experience abrupt, partial or full failure of component devices. The problem we address is: given a hybrid model of system behavior, a history of executed controller actions, and a history of observations, including an observation of behavior that is aberrant relative to the model of expected behavior, determine what fault occurred to have caused the aberrant behavior. Determining a diagnosis can be cast as a search problem to find the most likely model for the data. Unfortunately, the search space is extremely large. To reduce search space size and to identify an initial set of candidate diagnoses, we propose to exploit techniques originally applied to qualitative diagnosis of continuous systems. We refine these diagnoses using parameter estimation and model fitting techniques. As a motivating case study, we have examined the problem of diagnosing NASA's Sprint AERCam, a small spherical robotic camera unit with 12 thrusters that enable both linear and rotational motion.


Characterizing neural dependencies with copula models

Neural Information Processing Systems

The coding of information by neural populations depends critically on the statistical dependencies between neuronal responses. However, there is no simple model that combines the observations that (1) marginal distributions over single-neuron spike counts are often approximately Poisson; and (2) joint distributions over the responses of multiple neurons are often strongly dependent. Here, we show that both marginal and joint properties of neural responses can be captured using Poisson copula models. Copulas are joint distributions that allow random variables with arbitrary marginals to be combined while incorporating arbitrary dependencies between them. Different copulas capture different kinds of dependencies, allowing for a richer and more detailed description of dependencies than traditional summary statistics, such as correlation coefficients. We explore a variety of Poisson copula models for joint neural response distributions, and derive an efficient maximum likelihood procedure for estimating them. We apply these models to neuronal data collected in and macaque motor cortex, and quantify the improvement in coding accuracy afforded by incorporating the dependency structure between pairs of neurons.


Christian Freksa

AAAI Conferences

Spatial Cognition is an interdisciplinary research area that - among other things - serves as a testbed for numerous approaches to knowledge representation and for results from artificial intelligence, cognitive psychology, soft computing, geography, biological cybernetics, and robotics. Spatial and temporal granularity are of particular relevance in spatial cognition for at least two different reasons: (1) the granulation of information determines the ease or difficulty of matching representational descriptions with real world situations, and (2) the ability to transform representations between different spatial and temporal granularity levels determines the usability (flexibility and adaptivity) of representations for identification, reasoning, and communication purposes. The contribution presents current knowledge representation research carried out in the framework of the German Spatial Cognition Priority Program. Cognitive agents (in particular people and robots) must represent certain knowledge about their spatial environment to identify objects and to find their way. We distinguish general world knowledge (in particular about general structures of space and time) and specific situation knowledge. The two types of knowledge have rather different properties that necessitate different representational structures: while the general world knowledge enables certain inferences that always hold in spatiotemporal environments, the specific situation knowledge is incomplete, imprecise, fuzzy, and possibly conflicting. This requires special forms of representation and inference.