Forgetting in Modular Answer Set Programming

Authors R. Goncalves, M. Knorr, and J. Leite were partially supported by FCT project FORGET (PTDC/CCI-INF/32219/2017). T. Janhunen was partially supported by the Academy of Finland project 251170. R. Goncalves was partially supported by FCT grant SFRH/BPD/100906/2014. S. Woltran was supported by the Austrian Science Fund (FWF): Y698, P25521.Modular programming facilitates the creation and reuse of large software, and has recently gathered considerable interest in the context of Answer Set Programming (ASP). In this setting, forgetting, or the elimination of middle variables no longer deemed relevant, is of importance as it allows one to, e.g., simplify a program, make it more declarative, or even hide some of its parts without affecting the consequences for those parts that are relevant. While forgetting in the context of ASP has been extensively studied, its known limitations make it unsuitable to be used in Modular ASP. In this paper, we present a novel class of forgetting operators and show that such operators can always be successfully applied in Modular ASP to forget all kinds of atoms - input, output and hidden -overcoming the impossibility results that exist for general ASP. Additionally, we investigate conditions under which this class of operators preserves the module theorem in Modular ASP, thus ensuring that answer sets of modules can still be composed, and how the module theorem can always be preserved if we further allow the reconfiguration of modules.authorsversionpublishe

On Syntactic Forgetting Under Uniform Equivalence

Forgetting in Answer Set Programming (ASP) aims at reducing the language of a logic program without affecting the consequences over the remaining language. It has recently gained interest in the context of modular ASP where it allows simplifying a program of a module, making it more declarative, by omitting auxiliary atoms or hiding certain atoms/parts of the program not to be disclosed. Unlike for arbitrary programs, it has been shown that forgetting for modular ASP can always be applied, for input, output and hidden atoms, and preserve all dependencies over the remaining language (in line with uniform equivalence). However, the definition of the result is based solely on a semantic characterization in terms of HT-models. Thus, computing an actual result is a complicated process and the result commonly bears no resemblance to the original program, i.e., we are lacking a corresponding syntactic operator. In this paper, we show that there is no forgetting operator that preserves uniform equivalence (modulo the forgotten atoms) between the given program and its forgetting result by only manipulating the rules of the original program that contain the atoms to be forgotten. We then present a forgetting operator that preserves uniform equivalence and is syntactic whenever this is suitable. We also introduce a special class of programs, where syntactic forgetting is always possible, and as a complementary result, establish it as the largest known class where forgetting while preserving all dependencies is always possible.acceptedVersionPeer reviewe

Asynchronous Multi-Context Systems

In this work, we present asynchronous multi-context systems (aMCSs), which provide a framework for loosely coupling different knowledge representation formalisms that allows for online reasoning in a dynamic environment. Systems of this kind may interact with the outside world via input and output streams and may therefore react to a continuous flow of external information. In contrast to recent proposals, contexts in an aMCS communicate with each other in an asynchronous way which fits the needs of many application domains and is beneficial for scalability. The federal semantics of aMCSs renders our framework an integration approach rather than a knowledge representation formalism itself. We illustrate the introduced concepts by means of an example scenario dealing with rescue services. In addition, we compare aMCSs to reactive multi-context systems and describe how to simulate the latter with our novel approach.Comment: International Workshop on Reactive Concepts in Knowledge Representation (ReactKnow 2014), co-located with the 21st European Conference on Artificial Intelligence (ECAI 2014). Proceedings of the International Workshop on Reactive Concepts in Knowledge Representation (ReactKnow 2014), pages 31-37, technical report, ISSN 1430-3701, Leipzig University, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-15056

05171 Abstracts Collection -- Nonmonotonic Reasoning, Answer Set Programming and Constraints

From 24.04.05 to 29.04.05, the Dagstuhl Seminar 05171 ``Nonmonotonic Reasoning, Answer Set Programming and Constraints\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Some Thoughts on the Teaching of Mathematics -- ten years later

I describe some deep-seated problems in higher mathematical education, and give some ideas for their solution -- I advocate a move away from the traditional introduction of mathematics through calculus, and towards computation and discrete mathematics.Comment: 10 pages, to appear in Notices of the AM