Belief Revision in the Situation Calculus Without Plausibility Levels

Abstract

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.

Projection in the Epistemic Situation Calculus with Belief Conditionals

“…While progression may be preferable over regression for long sequences of action, it has the disadvantage that the resulting knowledge base is not always first-order representable. Besides (Shapiro et al 2011;Schwering and Lakemeyer 2014), a number of other proposals such as (Demolombe and Pozos Parra 2006;Delgrande and Levesque 2012;Fang and Liu 2013) have dealt with extending action formalisms with belief revision in the spirit of AGM (Alchourron, Gärdenfors, and Makinson 1985). In (Pagnucco et al 2013) a limited solution to the projection problem in action theories derived from (Shapiro et al 2011) is proposed by a translation to Default Logic extended with preferences (Baumann et al 2010), together with an implementation using Answer Set Programming (Gelfond 2008).…”

From Situation Calculus to Dynamic Epistemic Logic

“…• Up to now there was not too much work on the integration of belief revision into SitCalc [Shapiro et al, 2000;Shapiro and Pagnucco, 2004;Demolombe and Pozos Parra, 2006]. Work in this area could cross-fertilize with recent work on the DEL side by Baltag and Smets [2007, 2008 and others Aucher, 2008].…”