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1

Consistency-based Revision of Structured Belief Bases

Korpusik M., Łukaszewicz W., Madalińska-Bugaj E.

Fundamenta Informaticae

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2015

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Vol. 136, nr 4

381--404

EN

In this paper we extend a consistency-based approach (originally introduced by Delgrande and Schaub) to belief revision for structured belief bases. We explicitly distinguish between observations, i.e., facts that an epistemic agent observes or is being told, and rules representing general knowledge about the considered world. When new information becomes available respective sets are being altered in a different way to preserve parts of knowledge during the revision process. Such an approach allows us to deal with difficult and complex scenarios, involving defeasible information and derivation filtering, with common-sense results.

2

First-order Generalization of the MPMA Belief Update Operator

Madalińska-Bugaj E., Łukaszewicz W.

Fundamenta Informaticae

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2009

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Vol. 94, nr 1

49-61

EN

In this paper we generalize the MPMA belief update operator by admitting first-order knowledge bases and restricted first-order update formulae. This allows us to consider scenarios which cannot be properly formalized either in the originalMPMA or in other existing approaches to belief update.

3

Formalizing Defeasible Logic in CAKE

Madalińska-Bugaj E., Łukaszewicz W.

Fundamenta Informaticae

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2003

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Vol. 57, nr 2-4

193--213

EN

Due to its efficiency, defeasible logic is one of the most interesting non-monotonic formalisms. Unfortunately, the logic has one major limitation: it does not properly deal with cyclic defeasible rules. In this paper, we provide a new variant of defeasible logic, using CAKE method. The resulting formalism is tractable and properly deals with circular defeasible rules.

4

The PMA and relativizing minimal change for action update

Doherty P., Łukaszewicz W., Madalińska-Bugaj E.

Fundamenta Informaticae

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2000

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Vol. 44, Nr 1,2

95-131

EN

Recently, a great deal of progress has been made using nonmonotonic temporal logics to formalize reasoning about action and change. In particular, much focus has been placed on the proper representation of non-deterministic actions and the indirect effects of actions. For the latter the use of causal or fluent dependency rule approaches has been dominant. Although much recent effort has also been spent applying the belief revision/update (BR/U) approach to the action and change domain, there has been less progress in dealing with nondeterministic update and indirect effects represented as integrity constraints. We demonstrate that much is to be gained by cross-fertilization between the two paradigms and we show this in the following manner. We first propose a generalization of the PMA, called the modified MPMA which uses intuitions from the TL paradigm to permit representation of nondeterministic update and the use of integrity constraints interpreted as causal or fluent dependency rules. We provide several syntactic characterizations of MPMA, one of which is in terms of a simple temporal logic and provide a representation theorem showing equivalence between the two. In constructing the MPMA, we discovered a syntactic anomaly which we call the redundant atom anomaly that many TL approaches suffer from. We provide a method for avoiding the problem which is equally applicable across paradigms. We also describe a syntactic characterization of MPMA in terms of Dijkstra semantics. We set up a framework for future generalization of the BR/U approach and conclude with a formal comparison of related approaches.