Approximate Databases and Query Techniques for Agents with Heterogeneous Perceptual Capabilities Patrick Doherty Witold Lukaszewicz Andrzej Szalas Department of Computer Science Department of Computer Science University of Link¨ oping University of Economics and Computer Science Link¨ oping, Sweden Olsztyn, Poland patdo@ida.liu.se and University of Link¨ oping, Link ¨ oping, Sweden witlu@ida.liu.se andsz@ida.liu.se Abstract – In this paper, we propose a framework that provides software and robotic agents with the ability to ask approximate questions to each other in the context of heterogeneous and con- textually limited perceptual capabilities. The framework focuses on situations where agents have varying ability to perceive their environments. These limitations on perceptual capability are for- malized using the idea of tolerance spaces. It is assumed that each agent has one or more approximate databases where approximate relations are represented using intuitions from rough set theory. It is shown how sensory and other limitations can be taken into account when constructing approximate databases for each re- spective agent. Complex relations inherit the approximativeness inherent in the sensors and primitive relations used in their def- initions. Agents then query these databases and receive answers through the filters of their perceptual limitations as represented by tolerance spaces and approximate queries. The techniques used are all tractable. Keywords: Rough sets, database and sensor fusion, approximate reasoning, intelligent agents, cognitive robotics, software agents. 1 Introduction Research in cognitive robotics is concerned with endow- ing robots and software agents with higher level cognitive functions that enable them to reason, act and perceive in changing, incompletely known, and unpredictable environ- ments. Research in robotics has traditionally emphasized low-level sensing, sensor processing and control tasks. One of the open challenges in cognitive robotics is to integrate techniques from both disciplines and develop architectures which seamlessly combine low-level sensing and sensor processing with the generation and maintenance of higher level knowledge structures. This implies signal-to-symbol transformations at many levels of abstraction. One partic- ularly difficult issue involves the quantitative to qualitative transformations which are implied by the need for qualita- tive knowledge structures in high-level reasoning tasks. Low-level sensor data is quantitative in nature, yet higher-level reasoning tasks require the use of properties and relations among individuals in specific domains of dis- course and the associated inference mechanisms which use combinations of base properties and relations in reasoning processes. To add to the difficulty, sensors, by their very nature introduce uncertainty and noise in the data. In or- der to provide an accurate representation of a robotic en- vironment, some of this uncertainty, or lack of knowledge, should be translated into the higher-level knowledge struc- tures. In other words, some of the high-level knowledge struc- tures will be approximate in nature, having both quanti- tative and qualitative characteristics. Such structures are useful in bridging the gap between purely quantitative data generated by sensors and purely qualitative data used in symbolic reasoning tasks. In addition, the perceptual limitations of a robotic agent induced by its sensor suite should be taken into account not only when the robotics agent reasons about its external and internal environments, but also when one or more robotic agents communicate with each other by asking questions about each others knowledge about the world or them- selves. In this case, two robotic agents communicating with each other can only ever ask queries of an approximative nature and receive answers of an approximative nature as seen through their respective filters of perceptual limitation. In this paper, we propose a technique that can provide software and robotic agents with the ability to ask approx- imate questions to each other in the context of heteroge- neous perceptual capabilities and approximate knowledge derived through uncertain sensor data. Even though they may have concepts in common, their ability to perceive in- dividuals as having specific properties or relations can be distinct. The question then is how this affects the questions that can be asked and the replies that can be generated by agents with perception functions limited to varying degrees. In order to provide the proper level of detail for the spe- cific framework in question, the following set of abstrac- tions will be used in the paper. Each robotic agent will have access to the following functionalities and representations: • An abstraction called a tolerance space which is used to represent similarity of data points for both basic and complex data domains. 1 • A set of sensors and a sensor model for each sensor. The sensor models will take into account the contex- tual indiscernibility of signal data by using tolerance spaces to represent that indiscernibility. 1 Of course, similarity has been studied in many contexts. For a discussion of a similarity-based measures that can be applied in defining tolerance functions of tolerance spaces, see, e.g., [1]).