Journal of Logic, Language and Information
, Volume 18, Issue 1, pp 97129
First online:
Developing Bounded Reasoning
 Michał WalickiAffiliated withDepartment of Informatics, University of Bergen Email author
 , Marc BezemAffiliated withDepartment of Informatics, University of Bergen
 , Wojtek SzajnkenigAffiliated withDepartment of Informatics, University of Bergen
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We introduce a threetiered framework for modelling and reasoning about agents who (i) can use possibly complete reasoning systems without any restrictions but who nevertheless are (ii) bounded in the sense that they never reach infinitely many results and, finally, who (iii) perform their reasoning in time. This last aspect does not concern so much the time it takes for agents to actually carry out their reasoning, as the time which can bring about external changes in the agents’ states such as arriving of new information or discarding previously available information due to bounds of the agent’s resources. These three aspects are treated with the maximal possible degree of independence from each other. The treatment of layer (iii) can be combined with arbitrary logic at level (ii) which, in turn, can be combined with arbitrary agent logic at level (i). At the level (iii), we discuss briefly the duality (or rather, complementarity) of system descriptions based on actions and transitions, on the one hand, and states and their changes, on the other. We settle for the latter and present a simple language, for describing state changes, which is parameterized by an arbitrary language for describing properties of the states. The language can be viewed as a simple fragment of step logic, admitting however various extensions by appropriate choices of the underlying logic. Alternatively, it can be seen as a very specific fragment of temporal logic (with a variant of ‘until’ or ‘chop’ operator), and is interpreted over dense linear time. The reasoning system presented here is sound, as well as strongly complete and decidable (provided that so is the parameter logic for reasoning about single states). We give the main idea of the completeness proof and suggest a wide range of possible applications, which is a simple consequence of the parametric character of both the language and the reasoning system. We address then in more detail the case of nonomniscient rational agents, (ii). Their models are syntactic structures (sets of available formulae) similar in spirit, though not in the technical formulation, to the models used in other syntax oriented approaches and in active logic. We give a new sound, complete and decidable system for reasoning about such agents. Finally, we illustrate its extensions with the internal reasoning of agents, (i), by equipping them with some example logics.
Keywords
Agents Bounded resources Temporal reasoning Title
 Developing Bounded Reasoning
 Journal

Journal of Logic, Language and Information
Volume 18, Issue 1 , pp 97129
 Cover Date
 200901
 DOI
 10.1007/s1084900890709
 Print ISSN
 09258531
 Online ISSN
 15729583
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Agents
 Bounded resources
 Temporal reasoning
 Authors

 Michał Walicki ^{(1)}
 Marc Bezem ^{(1)}
 Wojtek Szajnkenig ^{(1)}
 Author Affiliations

 1. Department of Informatics, University of Bergen, P.O. Box 7800, 5020, Bergen, Norway