AGM contraction and revision assume an underlying logic that contains propositional logic. Consequently, this assumption excludes many useful logics such as the Horn fragment of propositional logic and most description logics. Our goal in this paper is to generalise AGM contraction and revision to (near-)arbitrary fragments of classical first-order logic. To this end, we first define a very general logic that captures these fragments. In so doing, we make the modest assumptions that a logic contains conjunction and that information is expressed by closed formulas or sentences. The resulting logic is called first-order conjunctive logic or FC logic for short. We then take as the point of departure the AGM approach of constructing contraction functions through epistemic entrenchment, that is the entrenchment-based contraction. We redefine entrenchment-based contraction in ways that apply to any FC logic, which we call FC contraction. We prove a representation theorem showing its compliance with all the AGM contraction postulates except for the controversial recovery postulate. We also give methods for constructing revision functions through epistemic entrenchment which we call FC revision; which also apply to any FC logic. We show that if the underlying FC logic contains tautologies then FC revision complies with all the AGM revision postulates. Finally, in the context of FC logic, we provide three methods for generating revision functions via a variant of the Levi Identity, which we call contraction, withdrawal and cut generated revision, and explore the notion of revision equivalence. We show that withdrawal and cut generated revision coincide with FC revision and so does contraction generated revision under a finiteness condition.

A Forgetting is an operation for eliminating variables from a semantic theory of forgetting for normal logic programs knowledge base (Lin and Reiter 1994; Lang, Liberatore, and under answer set semantics is introduced in (Wang, Sattar, Marquis 2003). It constitutes a reduction in an agent's language and Su 2005), in which a sound and complete algorithm or, more accurately, the agent's signature. It has also is developed based on a series of program transformations; been studied under different names, such as variable elimination, this theory is further developed and extended uniform interpolation and relevance (Subramanian, to disjunctive logic programs in (Eiter and Wang 2006; Greiner, and Pearl 1997). Forgetting has various possible 2008). However, this theory of forgetting is defined in terms applications in a reasoning system. For example, in query of answer sets rather than SE models, and so again is not answering, if one can determine what is relevant to a query, syntax-independent.

In this paper we describe asprin, a general, flexible, and extensible framework for handling preferences among the stable models of a logic program. We show how complex preference relations can be specified through user-defined preference types and their arguments. We describe how preference specifications are handled internally by so-called preference programs, which are used for dominance testing. We also give algorithms for computing one, or all, optimal stable models of a logic program. Notably, our algorithms depend on the complexity of the dominance tests and make use of multi-shot answer set solving technology.

In this paper we explore a class of belief update operators, in which the definition of the operator is compositional with respect to the sentence to be added. The goal is to provide an update operator that is intuitive, in that its definition is based on a recursive decomposition of the update sentences structure, and that may be reasonably implemented. In addressing update, we first provide a definition phrased in terms of the models of a knowledge base. While this operator satisfies a core group of the benchmark Katsuno-Mendelzon update postulates, not all of the postulates are satisfied. Other Katsuno-Mendelzon postulates can be obtained by suitably restricting the syntactic form of the sentence for update, as we show. In restricting the syntactic form of the sentence for update, we also obtain a hierarchy of update operators with Winsletts standard semantics as the most basic interesting approach captured. We subsequently give an algorithm which captures this approach; in the general case the algorithm is exponential, but with some not-unreasonable assumptions we obtain an algorithm that is linear in the size of the knowledge base. Hence the resulting approach has much better complexity characteristics than other operators in some situations. We also explore other compositional belief change operators: erasure is developed as a dual operator to update; we show that a forget operator is definable in terms of update; and we give a definition of the compositional revision operator. We obtain that compositional revision, under the most natural definition, yields the Satoh revision operator.

We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Unlike previous approaches to belief change in logic programming, our formal techniques are analogous to those of distance-based belief revision in propositional logic. In developing our results, we build upon the model theory of logic programs furnished by SE models. Since SE models provide a formal, monotonic characterisation of logic programs, we can adapt techniques from the area of belief revision to belief change in logic programs. We introduce methods for revising and merging logic programs, respectively. For the former, we study both subset-based revision as well as cardinality-based revision, and we show that they satisfy the majority of the AGM postulates for revision. For merging, we consider operators following arbitration merging and IC merging, respectively. We also present encodings for computing the revision as well as the merging of logic programs within the same logic programming framework, giving rise to a direct implementation of our approach in terms of off-the-shelf answer set solvers. These encodings reflect in turn the fact that our change operators do not increase the complexity of the base formalism.