---
title: "Well-Supported Semantics for Description Logic Programs"
authors:
  - "Yi-Dong Shen"
doi: "10.5591/978-1-57735-516-8/IJCAI11-185"
url: "https://ijcai.org/proceedings/2011/185"
pdf: "https://ijcai.org/proceedings/2011/0185.pdf"
venue: "Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence"
year: 2011
pages: "1081-1085"
track: ""
keywords:
---

# Well-Supported Semantics for Description Logic Programs

Yi-Dong Shen

*Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence*, pages 1081-1085. DOI: [10.5591/978-1-57735-516-8/IJCAI11-185](https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-185)

## Abstract

Fages [1994] introduces the notion of well-supportedness as a key requirement for the semantics of normal logic programs and characterizes the standard answer set semantics in terms of the well-supportedness condition. With the property of well-supportedness, answer sets are guaranteed to be free of circular justifications. In this paper, we extend Fages’ work to description logic programs (or DL-programs). We introduce two forms of well-supportedness for DL-programs. The first one defines weakly well-supported models that are free of circular justifications caused by positive literals in rule bodies. The second one defines strongly well-supported models that are free of circular justifications caused by either positive or negative literals. We then define two new answer set semantics for DL-programs and characterize them in terms of the weakly and strongly well-supported models, respectively. The first semantics is based on an extended Gelfond-Lifschitz transformation and defines weakly well-supported answer sets that are free of circular justifications for the class of DL-programs without negative dl-atoms. The second semantics defines strongly well-supported answer sets which are free of circular justifications for all DL-programs. We show that the existing answer set semantics for DL-programs, such as the weak answer set semantics, the strong answer set semantics, and the FLP-based answer set semantics, satisfy neither the weak nor the strong well-supportedness condition, even for DL-programs without negative dl-atoms. This explains why their answer sets incur circular justifications.