## Institut für Informatik und Computational Science

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- Answer set programming (1)
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In recent years, there has been a large amount of disparate work concerning the representation and reasoning with qualitative preferential information by means of approaches to nonmonotonic reasoning. Given the variety of underlying systems, assumptions, motivations, and intuitions, it is difficult to compare or relate one approach with another. Here, we present an overview and classification for approaches to dealing with preference. A set of criteria for classifying approaches is given, followed by a set of desiderata that an approach might be expected to satisfy. A comprehensive set of approaches is subsequently given and classified with respect to these sets of underlying principles

We consider the problem of representing arbitrary preferences in causal reasoning and planning systems. In planning, a preference may be seen as a goal or constraint that is desirable, but not necessary, to satisfy. To begin, we define a very general query language for histories, or interleaved sequences of world states and actions. Based on this, we specify a second language in which preferences are defined. A single preference defines a binary relation on histories, indicating that one history is preferred to the other. From this, one can define global preference orderings on the set of histories, the maximal elements of which are the preferred histories. The approach is very general and flexible; thus it constitutes a base language in terms of which higher-level preferences may be defined. To this end, we investigate two fundamental types of preferences that we call choice and temporal preferences. We consider concrete strategies for these types of preferences and encode them in terms of our framework. We suggest how to express aggregates in the approach, allowing, e.g. the expression of a preference for histories with lowest total action costs. Last, our approach can be used to express other approaches and so serves as a common framework in which such approaches can be expressed and compared. We illustrate this by indicating how an approach due to Son and Pontelli can be encoded in our approach, as well as the language PDDL3.

We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Our formal techniques are analogous to those of distance-based belief revision in propositional logic. In particular, we build upon the model theory of logic programs furnished by SE interpretations, where an SE interpretation is a model of a logic program in the same way that a classical interpretation is a model of a propositional formula. Hence we extend techniques from the area of belief revision based on distance between models to belief change in logic programs.
We first consider belief revision: for logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P * Q. We investigate several operators, including (logic program) expansion and two revision operators based on the distance between the SE models of logic programs. It proves to be the case that expansion is an interesting operator in its own right, unlike in classical belief revision where it is relatively uninteresting. Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy all or nearly all of the AGM postulates for revision.
We next consider approaches for merging a set of logic programs, P-1,...,P-n. Again, our formal techniques are based on notions of relative distance between the SE models of the logic programs. Two approaches are examined. The first informally selects for each program P-i those models of P-i that vary the least from models of the other programs. The second approach informally selects those models of a program P-0 that are closest to the models of programs P-1,...,P-n. In this case, P-0 can be thought of as a set of database integrity constraints. We examine these operators with regards to how they satisfy relevant postulate sets.
Last, we present encodings for computing the revision as well as the merging of logic programs within the same logic programming framework. This gives rise to a direct implementation of our approach in terms of off-the-shelf answer set solvers. These encodings also reflect the fact that our change operators do not increase the complexity of the base formalism.

A polynomial translation of logic programs with nested expressions into disjunctive logic programs
(2002)

An Extended Query language for action languages (and its application to aggregates and preferences)
(2006)

In this paper, we show how an approach to belief revision and belief contraction can be axiomatized by means of quantified Boolean formulas. Specifically, we consider the approach of belief change scenarios, a general framework that has been introduced for expressing different forms of belief change. The essential idea is that for a belief change scenario (K, R, C), the set of formulas K, representing the knowledge base, is modified so that the sets of formulas R and C are respectively true in, and consistent with the result. By restricting the form of a belief change scenario, one obtains specific belief change operators including belief revision, contraction, update, and merging. For both the general approach and for specific operators, we give a quantified Boolean formula such that satisfying truth assignments to the free variables correspond to belief change extensions in the original approach. Hence, we reduce the problem of determining the results of a belief change operation to that of satisfiability. This approach has several benefits. First, it furnishes an axiomatic specification of belief change with respect to belief change scenarios. This then leads to further insight into the belief change framework. Second, this axiomatization allows us to identify strict complexity bounds for the considered reasoning tasks. Third, we have implemented these different forms of belief change by means of existing solvers for quantified Boolean formulas. As well, it appears that this approach may be straightforwardly applied to other specific approaches to belief change