A Brief History of Updates of Answer-Set Programs

Funding Information: The authors would like to thank José Alferes, Martin Baláz, Federico Banti, Antonio Brogi, Martin Homola, Luís Moniz Pereira, Halina Przymusinska, Teodor C. Przymusinski, and Theresa Swift, with whom they worked on the topic of this paper over the years, as well as Ricardo Gonçalves and Matthias Knorr for valuable comments on an earlier draft of this paper. The authors would also like to thank the anonymous reviewers for their insightful comments and suggestions, which greatly helped us improve this paper. The authors were partially supported by Fundação para a Ciência e Tecnologia through projects FORGET (PTDC/CCI-INF/32219/2017) and RIVER (PTDC/CCI-COM/30952/2017), and strategic project NOVA LINCS (UIDB/04516/2020). Publisher Copyright: © The Author(s), 2022. Published by Cambridge University Press.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.publishersversionpublishe

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

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

Forgetting in Answer Set Programming with Anonymous Cycles

FORGET (PTDC/CCI-INF/32219/2017). NOVA LINCS (UID/CEC/04516/2019).It is now widely accepted that the operation of forgetting in the context of Answer Set Programming [10, 18] is best characterized by the so-called strong persistence, a property that requires that all existing relations between the atoms not to be forgotten be preserved. However, it has been shown that strong persistence cannot always be satisfied. What happens if we must nevertheless forget? One possibility that has been explored before is to consider weaker versions of strong persistence, although not without a cost: some relations between the atoms not to be forgotten are broken in the process. A different alternative is to enhance the logical language so that all such relations can be maintained after the forgetting operation. In this paper, we borrow from the recently introduced notion of fork [1] – a conservative extension of Equilibrium Logic and its monotonic basis, the logic of Here-and-There – which has been shown to be sufficient to overcome the problems related to satisfying strong persistence. We map this notion into the language of logic programs, enhancing it with so-called anonymous cycles, and we introduce a concrete syntactical forgetting operator over this enhanced language that we show to always obey strong persistence.publishe