Parametric Connectives in Disjunctive Logic Programming
<|reference_start|>Parametric Connectives in Disjunctive Logic Programming: Disjunctive Logic Programming (\DLP) is an advanced formalism for Knowledge Representation and Reasoning (KRR). \DLP is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class $\SigmaP{2}$ ($\NP^{\NP}$). Importantly, the \DLP encodings are often simple and natural.   In this paper, we single out some limitations of \DLP for KRR, which cannot naturally express problems where the size of the disjunction is not known ``a priori'' (like N-Coloring), but it is part of the input. To overcome these limitations, we further enhance the knowledge modelling abilities of \DLP, by extending this language by {\em Parametric Connectives (OR and AND)}. These connectives allow us to represent compactly the disjunction/conjunction of a set of atoms having a given property. We formally define the semantics of the new language, named $DLP^{\bigvee,\bigwedge}$ and we show the usefulness of the new constructs on relevant knowledge-based problems. We address implementation issues and discuss related works.<|reference_end|>
@article{perri2003parametric,
    title={Parametric Connectives in Disjunctive Logic Programming},
    author={Simona Perri, Nicola Leone},
    journal={arXiv preprint arXiv:cs/0311007},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0311007},
    primaryClass={cs.AI}
}