Christoph Schwering

A semantic account of iterated belief revision in the situation calculus

Recently Shapiro et al. explored the notion of iterated belief revision within Reiters version of the situation calculus. In particular, they consider a notion of belief defined as truth in the most plausible situations. To specify what an agent is willing to believe at different levels of plausibility they make use of so-called belief conditionals, which themselves neither refer to situations or plausibilities explicitly. Reasoning about such belief conditionals turns out to be complex because there may be too many models satisfying them and negative belief conditionals are also needed to obtain the desired conclusions. In this paper we show that, by adopting a notion of only-believing, these problems can be overcome. The work is carried out within a modal variant of the situation calculus with a possible-world semantics which features levels of plausibility. Among other things, we show that only-believing a knowledge base together with belief conditionals always leads to a unique model, which allows characterizing the beliefs of an agent, after any number of revisions, in terms of entailments within the logic.

Belief revision and projection in the epistemic situation calculus

Abstract This article considers defeasible beliefs in dynamic settings. In particular, we examine the belief projection problem: what is believed after performing an action and/or receiving new information? The approach is based on an epistemic variant of Reiters situation calculus, where actions not only have physical effects but may also provide new information to the agent. The preferential belief structure is initially determined using conditional statements. New information is then incorporated using two popular belief revision schemes, namely natural and lexicographic revision. The projection problem is solved twofold in this formalism: by goal regression and by knowledge base progression.

A Reasoning System for a First-Order Logic of Limited Belief.

Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning decidable or even tractable. While a number of such logics have been proposed in the past, they tend to remain for theoretical analysis only and their practical relevance is very limited. In this paper, we aim to go beyond the theory. Building on earlier work by Liu, Lakemeyer, and Levesque, we develop a logic of limited belief that is highly expressive while remaining decidable in the first-order and tractable in the propositional case and exhibits some characteristics that make it attractive for an implementation. We introduce a reasoning system that employs this logic as representation language and present experimental results that showcase the benefit of limited belief.

Decidable Reasoning in a First-Order Logic of Limited Conditional Belief.

In a series of papers, Liu, Lakemeyer, and Levesque address the problem of decidable reasoning in expressive first-order knowledge bases. Here, we extend their ideas to accommodate conditional beliefs, as in “if she is Australian, then she presumably eats Kangaroo meat.” Perhaps the most prevalent semantics of a conditional belief is to evaluate the consequent in the most-plausible worlds consistent with the premise. In this paper, we devise a technique to approximate this notion of plausibility, and complement it with Liu, Lakemeyer, and Levesque’s weak inference. Based on these ideas, we develop a logic of limited conditional belief, and provide soundness, decidability, and (for the propositional case) tractability results.

Sensor fusion in the epistemic situation calculus

Robot sensors are usually subject to error. Since in many practical scenarios a probabilistic error model is not available, sensor readings are often dealt with in a hard-coded, heuristic fashion. In this paper, we propose a logic to address the problem from a KR perspective. In this logic, the epistemic effect of sensing actions is deferred to so-called fusion actions, which may resolve discrepancies and inconsistencies of recent sensing results. Moreover, a local closed-world assumption can be applied dynamically. When needed, this assumption can be revoked and fusions can be undone using a form of forgetting.