Abstract Over the last couple of decades, there has been a considerable effort devoted to the problem of updating logic programs under the stable model semantics (a.k.a. answer-set programs) or, in other words, the problem of characterising the result of bringing up-to-date a logic program when the world it describes changes. Whereas the state-of-the-art approaches are guided by the same basic intuitions and aspirations as belief updates in the context of classical logic, they build upon fundamentally different principles and methods, which have prevented a unifying framework that could embrace both belief and rule updates. In this paper, we will overview some of the main approaches and results related to answer-set programming updates, while pointing out some of the main challenges that research in this topic has faced.

In open environments, agents need to reason with knowledge from various sources, represented in different languages. Multi-Context Systems (MCSs) allow for the integration of knowledge from different heterogeneous sources in an effective and modular way. Whereas most knowledge bases (contexts) typically considered within an MCS are written in some description logic or some non-monotonic rule-based language, sometimes more expressive languages that combine the features of both these paradigms are necessary, such as Hybrid MKNF. However, since agents may not have access to specialized reasoners for contexts using all these languages, it proves useful to have tools that equivalently simplify or transform a given MCS into another MCS that only uses the reasoners that are available. In this article, we thoroughly investigate the relation between MCSs and Hybrid MKNF. We provide a number of transformations that show that Hybrid MKNF knowledge bases can be embedded into MCSs without the need for specific MKNF reasoners. To complete the picture, we also show that when an MKNF reasoner is available, it can be used to handle several description logic and rule contexts joined into a single MKNF context. Furthermore, we show that we can encapsulate the non-monotonic transfer of information between different contexts in one rule language context, allowing e.g. the use of external non-monotonic reasoners.

Abstract Logic programs under the stable model semantics, or answer-set programs, provide an expressive rule-based knowledge representation framework, featuring a formal, declarative and well-understood semantics. However, handling the evolution of rule bases is still a largely open problem. The Alchourrón, Gärdenfors and Makinson (AGM) framework for belief change was shown to give inappropriate results when directly applied to logic programs under a non-monotonic semantics such as the stable models. The approaches to address this issue, developed so far, proposed update semantics based on manipulating the syntactic structure of programs and rules. More recently, AGM revision has been successfully applied to a significantly more expressive semantic characterisation of logic programs based onSE-models. This is an important step, as it changes the focus from the evolution of a syntactic representation of a rule base to the evolution of its semantic content. In this paper, we borrow results from the area of belief update to tackle the problem of updating (instead of revising) answer-set programs. We prove a representation theorem which makes it possible to constructively define any operator satisfying a set of postulates derived from Katsuno and Mendelzon's postulates for belief update. We define a specific operator based on this theorem, examine its computational complexity and compare the behaviour of this operator with syntactic rule update semantics from the literature. Perhaps surprisingly, we uncover a serious drawback of all rule update operators based on Katsuno and Mendelzon's approach to update and onSE-models.

Abstract Over the years, nonmonotonic rules have proven to be a very expressive and useful knowledge representation paradigm. They have recently been used to complement the expressive power of Description Logics (DLs), leading to the study of integrative formal frameworks, generally referred to ashybrid knowledge bases, where both DL axioms and rules can be used to represent knowledge. The need to use these hybrid knowledge bases in dynamic domains has called for the development of update operators, which, given the substantially different way DLs and rules are usually updated, has turned out to be an extremely difficult task. In Slota and Leite (2010b Towards Closed World Reasoning in Dynamic Open Worlds.Theory and Practice of Logic Programming, 26th Int'l. Conference on Logic Programming (ICLP'10) Special Issue10(4–6) (July), 547–564.), a first step towards addressing this problem was taken, and an update operator for hybrid knowledge bases was proposed. Despite its significance—not only for being the first update operator for hybrid knowledge bases in the literature, but also because it has some applications—this operator was defined for a restricted class of problems where only the ABox was allowed to change, which considerably diminished its applicability. Many applications that use hybrid knowledge bases in dynamic scenarios require both DL axioms and rules to be updated. In this paper, motivated by real world applications, we introduce an update operator for a large class of hybrid knowledge bases where both the DL component as well as the rule component are allowed to dynamically change. We introduce splitting sequences and splitting theorem for hybrid knowledge bases, use them to define a modular update semantics, investigate its basic properties, and illustrate its use on a realistic example about cargo imports.

Logic programs under the stable models semantics, or answer-set programs, provide an expressive rule based knowledge representation framework, featuring formal, declarative and well-understood semantics. However, handling the evolution of rule bases is still a largely open problem. The AGM framework for belief change was shown to give inappropriate results when directly applied to logic programs under a nonmonotonic semantics such as the stable models. Most approaches to address this issue, developed so far, proposed update operators based on syntactic conditions for rule rejection.

Abstract The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics forhybrid knowledge basescomposed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve. In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties. To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.

User modeling and personalization are the key aspects of recommender systems in terms of recommendation quality. ERASP is an add-on to existing recommender systems which uses dynamic logic programming -- an extension of answer set programming -- as a means for users to specify and update their models and preferences, with the purpose of enhancing recommendations. While being an excellent solution in recommender systems limited to a few thousand products, ERASP does not scale well beyond that point. In this paper we present a major theoretical redesign of ERASP which entails a significant improvement in the performance of its implementation, making it usable in domains with hundreds of thousands of products.