Among the many approaches for reasoning about degrees of belief in the presence of noisy sensing and acting, the logical account proposed by Bacchus, Halpern, and Levesque is perhaps the most expressive. While their formalism is quite general, it is restricted to fluents whose values are drawn from discrete finite domains, as opposed to the continuous domains seen in many robotic applications. In this work, we show how this limitation in that approach can be lifted. By dealing seamlessly with both discrete distributions and continuous densities within a rich theory of action, we provide a very general logical specification of how belief should change after acting and sensing in complex noisy domains.
In a similar vein, from a modal logical perspective, the interaction between categorical knowledge, on the one hand, and degrees of belief, on the other, is further discussed in @cite_6 @cite_2 @cite_8 . While these are essentially propositional, there are first-order variants @cite_3 . Actions are not explicitly addressed, however.
@cite_8 @cite_3 @cite_6 @cite_2
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Reasoning about capabilities, strategies and knowledge is important in the analysis of multiagent systems. Alternating-time Temporal Epistemic Logic (ATEL) was designed with this aim. Nevertheless, the original interpretation of the language suffered from some counterintuitive properties. These are due to the fact that the strategies the agent applies in worlds that he cannot distinguish may not be uniform, in the sense that the same action is applied in all indistinguishable worlds. Several refinements of the original ATEL semantics were proposed since then. In this paper we argue that the STIT framework can easily account for uniform strategies. STIT is a logic of agency that has been proposed in the 90ies in the domain of philosophy of action. It is the logic of constructions of the form "agent a sees to it that φ". To support our claim, we first present a straightforward solution in STIT logic augmented by a modal operator of knowledge. Then we offer a simplification, by introducing a modal logic of knowledge-based uniform agency, for one-step strategies, alias choices. We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms of belief revision, based on compositional reduction axioms. Next, we show how various abstract postulates for belief revision can be analyzed by standard modal frame correspondences for model-changing operations. Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics. We present a modal logic of belief and announcements in a multi-agent setting. This logic allows to express not only that Ψ holds after the announcement of Φ as in standard public announcement logic (PAL), but also that the announcement of Φ occurs. We use the logic to provide a formal analysis of several concepts that are relevant for multi-agent systems (MAS) theory and applications: the notions of communicative action (an agent informs another agent about something) and communicative intention (an agent has the intention to inform another agent about something), and the notion of information source.