Forgetting in Modular Answer Set Programming

Abstract

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