Proceedings of the 16th International Workshop on Non-Monotonic Reasoning (NMR), 22-24 April 2016, Cape Town, South Africa
@cite_0 propose a probabilistic revision operation for imprecise probabilistic beliefs in the framework of Probabilistic Logic Programming (PLP). New evidence may be a probabilistic (conditional) formula and needs not be consistent with the original beliefs. Revision via imaging (e.g., @math ) also overcomes this consistency issue.
@cite_0
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Probabilistic logic programming is a powerful technique to represent and reason with imprecise probabilistic knowledge. A probabilistic logic program (PLP) is a knowledge base which contains a set of conditional events with probability intervals. In this paper, we investigate the issue of revising such a PLP in light of receiving new information. We propose postulates for revising PLPs when a new piece of evidence is also a probabilistic conditional event. Our postulates lead to Jeffrey's rule and Bayesian conditioning when the original PLP defines a single probability distribution. Furthermore, we prove that our postulates are extensions to Darwiche and Pearl (DP) postulates when new evidence is a propositional formula. We also give the representation theorem for the postulates and provide an instantiation of revision operators satisfying the proposed postulates. 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. In real-world applications, knowledge bases consisting of all the available information for a specific domain, along with the current state of affairs, will typically contain contradictory data, coming from different sources, as well as data with varying degrees of uncertainty attached. An important aspect of the effort associated with maintaining such knowledge bases is deciding what information is no longer useful; pieces of information may be outdated; may come from sources that have recently been discovered to be of low quality; or abundant evidence may be available that contradicts them. In this paper, we propose a probabilistic structured argumentation framework that arises from the extension of Presumptive Defeasible Logic Programming (PreDeLP) with probabilistic models, and argue that this formalism is capable of addressing these basic issues. The formalism is capable of handling contradictory and uncertain data, and we study non-prioritized belief revision over probabilistic PreDeLP programs that can help with knowledge-base maintenance. For belief revision, we propose a set of rationality postulates -- based on well-known ones developed for classical knowledge bases -- that characterize how these belief revision operations should behave, and study classes of operators along with theoretical relationships with the proposed postulates, including representation theorems stating the equivalence between classes of operators and their associated postulates. We then demonstrate how our framework can be used to address the attribution problem in cyber security cyber warfare. In this paper, we present a semantical approach to multi-agent belief revision and belief update. For this, we introduce relational structures called conditional doxastic models (CDM's, for short). We show this setting to be equivalent to an epistemic version of the classical AGM Belief Revision theory. We present a logic of conditional beliefs that is complete w.r.t. CDM's. Moving then to belief updates (sometimes called ''dynamic'' belief revision) induced by epistemic actions, we consider two particular cases: public announcements and private announcements to subgroups of agents. We show how the standard semantics for these types of updates can be appropriately modified in order to apply it to CDM's, thus incorporating belief revision into our notion of update. We provide a complete axiomatization of the corresponding dynamic doxastic logics. As an application, we solve a ''cheating version'' of the Muddy Children Puzzle.