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Nonground Abductive Logic Programming with Probabilistic Integrity Constraints

Published online by Cambridge University Press:  27 September 2021

ELENA BELLODI Open the ORCID record for ELENA BELLODI [Opens in a new window] ,
MARCO GAVANELLI ,
RICCARDO ZESE Open the ORCID record for RICCARDO ZESE [Opens in a new window] ,
EVELINA LAMMA  and
FABRIZIO RIGUZZI Open the ORCID record for FABRIZIO RIGUZZI [Opens in a new window]
ELENA BELLODI
Affiliation:
Department of Engineering - University of Ferrara, Ferrara, Italy (e-mails: elena.bellodi@unife.it, marco.gavanelli@unife.it, riccardo.zese@unife.it, lme@unife.it)
MARCO GAVANELLI
Affiliation:
Department of Engineering - University of Ferrara, Ferrara, Italy (e-mails: elena.bellodi@unife.it, marco.gavanelli@unife.it, riccardo.zese@unife.it, lme@unife.it)
RICCARDO ZESE
Affiliation:
Department of Engineering - University of Ferrara, Ferrara, Italy (e-mails: elena.bellodi@unife.it, marco.gavanelli@unife.it, riccardo.zese@unife.it, lme@unife.it)
EVELINA LAMMA
Affiliation:
Department of Engineering - University of Ferrara, Ferrara, Italy (e-mails: elena.bellodi@unife.it, marco.gavanelli@unife.it, riccardo.zese@unife.it, lme@unife.it)
FABRIZIO RIGUZZI
Affiliation:
Department of Mathematics and Computer Science - University of Ferrara, Ferrara, Italy (e-mail: fabrizio.riguzzi@unife.it)
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Abstract

Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical models are a suitable framework to handle uncertain information, and in the last decade many probabilistic logical languages have been proposed, as well as inference and learning systems for them. In the realm of Abductive Logic Programming (ALP), a variety of proof procedures have been defined as well. In this paper, we consider a richer logic language, coping with probabilistic abduction with variables. In particular, we consider an ALP program enriched with integrity constraints à la IFF, possibly annotated with a probability value. We first present the overall abductive language and its semantics according to the Distribution Semantics. We then introduce a proof procedure, obtained by extending one previously presented, and prove its soundness and completeness.

Keywords

abductionintegrity constraintsdistribution semanticsprobabilistic IFF
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 21 , Issue 5: 37th International Conference on Logic Programming Special Issue I , September 2021 , pp. 557 - 574
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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