Abstract
In this paper, we present a syntactic transformation, called the unfolding operator, that allows forgetting an atom in a logic program (under ASP semantics). The main advantage of unfolding is that, unlike other syntactic operators, it is always applicable and guarantees strong persistence, that is, the result preserves the same stable models with respect to any context where the forgotten atom does not occur. The price for its completeness is that the result is an expression that may contain the fork operator. Yet, we illustrate how, in some cases, the application of fork properties may allow us to reduce the fork to a logic program, even in conditions that could not be treated before using the syntactic methods in the literature.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Most ASP solvers allow hiding the extension of some chosen predicates.
- 2.
As we will see, the cut operator support is a conjunction built from a finite set of rules that is sometimes negated. Generalising to infinite theories would require infinitary Boolean connectives.
- 3.
This is, therefore, equivalent to not satisfying the \(\varOmega \) condition from [10].
- 4.
In fact, [2] presented a more limited forgetting operator \({\texttt{f}}_{es}\) based on the external support.
- 5.
In most cases, after unfolding \({\texttt{f}}_{c}\) as a logic program, we usually obtain not only a result strongly equivalent to \({\texttt{f}}_{sp}\) but also the same or a very close syntactic representation.
- 6.
- 7.
Truth constants can be removed using trivial HT simplifications.
References
Aguado, F., Cabalar, P., Fandinno, J., Pearce, D., Pérez, G., Vidal, C.: Forgetting auxiliary atoms in forks. Artif. Intell. 275, 575–601 (2019)
Aguado, F., Cabalar, P., Fandinno, J., Pérez, G., Vidal, C.: A logic program transformation for strongly persistent forgetting - extended abstract. In: Proc. of the 37th International Conference on Logic Programming (ICLP 2021), Porto, Portugal (virtual event). Electronic Proceedings in Theoretical Computer Science (EPTCS), vol. 345, pp. 11–13 (2021)
Aguado, F., Cabalar, P., Pearce, D., Pérez, G., Vidal, C.: A denotational semantics for equilibrium logic. Theory Pract. Logic Program. 15(4–5), 620–634 (2015)
Berthold, M., Gonçalves, R., Knorr, M., Leite, J.: A syntactic operator for forgetting that satisfies strong persistence. Theory Pract. Logic Program. 19(5–6), 1038–1055 (2019)
Cabalar, P., Ferraris, P.: Propositional theories are strongly equivalent to logic programs. Theory Pract. Logic Program. 7(6), 745–759 (2007)
Cabalar, P., Pearce, D., Valverde, A.: Reducing propositional theories in equilibrium logic to logic programs. In: Bento, C., Cardoso, A., Dias, G. (eds.) EPIA 2005. LNCS (LNAI), vol. 3808, pp. 4–17. Springer, Heidelberg (2005). https://doi.org/10.1007/11595014_2
Cabalar, P., Pearce, D., Valverde, A.: Minimal logic programs. In: Dahl, V., Niemelä, I. (eds.) ICLP 2007. LNCS, vol. 4670, pp. 104–118. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74610-2_8
Ferraris, P., Lee, J., Lifschitz, V.: A generalization of the Lin-Zhao theorem. Ann. Math. Artif. Intell. 47(1–2), 79–101 (2006)
Gonçalves, R., Knorr, M., Leite, J.: The ultimate guide to forgetting in answer set programming. In: KR, pp. 135–144. AAAI Press (2016)
Gonçalves, R., Knorr, M., Leite, J.: You can’t always forget what you want: on the limits of forgetting in answer set programming. In: Kaminka, G.A., et al. (eds.) Proceedings of 22nd European Conference on Artificial Intelligence (ECAI 2016). Frontiers in Artificial Intelligence and Applications, vol. 285, pp. 957–965. IOS Press (2016)
Heyting, A.: Die formalen Regeln der intuitionistischen Logik. In: Sitzungsberichte der Preussischen Akademie der Wissenschaften, pp. 42–56. Deutsche Akademie der Wissenschaften zu Berlin (1930), reprint in Logik-Texte: Kommentierte Auswahl zur Geschichte der Modernen Logik, Akademie-Verlag (1986)
Knorr, M., Alferes, J.J.: Preserving strong equivalence while forgetting. In: Fermé, E., Leite, J. (eds.) JELIA 2014. LNCS (LNAI), vol. 8761, pp. 412–425. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11558-0_29
Marek, V., Truszczyński, M.: Stable models and an alternative logic programming paradigm. In: The Logic Programming Paradigm: a 25-Year Perspective, pp. 169–181. Springer-Verlag (1999). https://doi.org/10.1007/978-3-642-60085-2_17
Mints, G.: Cut-free formulations for a quantified logic of here and there. Ann. Pure Appl. Logic 162(3), 237–242 (2010)
Niemelä, I.: Logic programs with stable model semantics as a constraint programming paradigm. Ann. Math. Artif. Intell. 25, 241–273 (1999)
Pearce, D.: A new logical characterisation of stable models and answer sets. In: Dix, J., Pereira, L.M., Przymusinski, T.C. (eds.) NMELP 1996. LNCS, vol. 1216, pp. 57–70. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0023801
Acknowledgements
We want to thank the anonymous reviewers for their suggestions that helped to improve this paper. Partially funded by Xunta de Galicia and the European Union, grants CITIC (ED431G 2019/01) and GPC ED431B 2022/33, and by the Spanish Ministry of Science and Innovation (grant PID2020-116201GB-I00).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Aguado, F., Cabalar, P., Fandinno, J., Pearce, D., Pérez, G., Vidal, C. (2022). Syntactic ASP Forgetting with Forks. In: Gottlob, G., Inclezan, D., Maratea, M. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2022. Lecture Notes in Computer Science(), vol 13416. Springer, Cham. https://doi.org/10.1007/978-3-031-15707-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-031-15707-3_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-15706-6
Online ISBN: 978-3-031-15707-3
eBook Packages: Computer ScienceComputer Science (R0)