Merging operators try to define the beliefs of a group of agents according to the beliefs of each member of the group. Several model-based propositional belief merging operators have been proposed which use distance measures and aggregation functions. This paper introduces the notion of Partial Satisfiability which is an alternative way of measuring the satisfaction of a formula since this notion lets us have satisfaction values in the interval [0,1]. Partial Satisfiability allows us to define model-based merging operator. The proposal produces similar results to other merging approaches, but while other approaches require many merging operators in order to achieve satisfactory results for different scenarios this proposal obtains similar results for all these different scenarios with a unique operator. Moreover, unlike most of model-based approaches, this approach considers the case where the belief bases are inconsistent. The framework presented is in a preliminary state and further analysis of its properties is needed in order to characterize the proposed merging operator in terms of postulates. 625 978-81-904262-7-5 (RPS) c 2007 IFAAMAS
The ramification problem concerns the characterisation of indirect effects of actions. This problem arises when a theory of action is integrated with a set of state constraints. So integrating state constraints to a solution of the frame problem must deal with the ramification problem. In the situation calculus a general solution to both the frame and ramification problems has been proposed. This solution includes the indirect effects of actions in the successor state axioms. On the other hand, in the situation calculus, the notion of belief fluents has been introduced in order to distinguish between facts that hold in a situation and facts that are believed to hold in a situation. So apart from the traditional frame and ramification problems, a belief counterpart of these problems is considered. The successor belief state axioms were proposed to address the belief frame problem. Inspired in the mentioned approaches, we propose a general solution to the belief frame and ramification problems. We consider two sorts of constraints: the believed state constraints relating to physical laws and the believed mental constraints relating to social laws. Constraints imposed by social laws are well know in literature as obligations. Automated reasoning based on the proposal could easily be implemented in Prolog.
Abstract. The Situation Calculus has been used by Scherl and Levesque to represent beliefs and belief change without modal operators thanks to a predicate plays the role of an accessibility relation. Their approach has been extended by Shapiro et al. to support belief revision. In this extension plausibility levels are assigned to each situation, and the believed propositions are the propositions that are true in all the most plausible accessible situations. Their solution is quite elegant from a theoretical point of view but the definition of the plausibility assignment, for a given application domain, raises practical problems. This paper presents a new proposal that does not make use of plausibilities. The idea is to include the knowledge producing actions into the successor state axioms. In this framework each agent may have a different successor state axiom for a given fluent. Then, each agent may have his subjective view of the evolution of the world. Also, agents may know or may not know that a given action has been performed. That is, the actions are not necessarily public.
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