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2022 | OriginalPaper | Buchkapitel

Syntactic ASP Forgetting with Forks

verfasst von : Felicidad Aguado, Pedro Cabalar, Jorge Fandinno, David Pearce, Gilberto Pérez, Concepción Vidal

Erschienen in: Logic Programming and Nonmonotonic Reasoning

Verlag: Springer International Publishing

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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.

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Vorheriges Kapitel Correction to: Logic Programming and Nonmonotonic Reasoning

Nächstes Kapitel Modal Logic S5 in Answer Set Programming with Lazy Creation of Worlds

Most ASP solvers allow hiding the extension of some chosen predicates.

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.

This is, therefore, equivalent to not satisfying the \(\varOmega \) condition from [10].

In fact, [2] presented a more limited forgetting operator \({\texttt{f}}_{es}\) based on the external support.

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.

In fact, the as-dual set from [4] can be seen as an effect of the (CUT) rule. Moreover, our use of the latter was inspired by this as-dual construction.

Truth constants can be removed using trivial HT simplifications.

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Titel: Syntactic ASP Forgetting with Forks
verfasst von: Felicidad Aguado
Pedro Cabalar
Jorge Fandinno
David Pearce
Gilberto Pérez
Concepción Vidal
Verlag: Springer International Publishing
Buch: Logic Programming and Nonmonotonic Reasoning
Print ISBN: 978-3-031-15706-6

Electronic ISBN: 978-3-031-15707-3

Copyright-Jahr: 2022
DOI: https://doi.org/10.1007/978-3-031-15707-3_1

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