TY - JOUR
T1 - Vicious circle principle, aggregates, and formation of sets in ASP based languages
AU - Gelfond, Michael
AU - Zhang, Yuanlin
N1 - Funding Information:
We would like to thank Evgenii Balai, Amelia Harrison, Patrick Kahl, Vladimir Lifschitz, Tran Cao Son, Mirek Truszczynski and the anonymous reviewers for useful comments which helped to improve the quality of the paper. The authors’ work was partially supported by NSF grant IIS-1018031 and CNS-1359359.
Funding Information:
We would like to thank Evgenii Balai, Amelia Harrison, Patrick Kahl, Vladimir Lifschitz, Tran Cao Son, Mirek Truszczynski and the anonymous reviewers for useful comments which helped to improve the quality of the paper. The authors' work was partially supported by NSF grant IIS-1018031 and CNS-1359359 .
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/10
Y1 - 2019/10
N2 - The paper introduces an extension of the original Answer Set Prolog (ASP) by several set constructs including aggregates, defined as functions on sets. The new language, called Alog allows creating sets based on the Vicious Circle Principle by Poincaré and Russell which eliminates a number of problems found in existing extensions of ASP by aggregates. We argue that, despite the fact that Alog is not as expressive as other extensions of ASP by aggregates, clarity of its syntax and semantics, addition of several new set-based constructs, and simplicity and the ease of use make it a viable competitor to these languages. We also study a number of important properties of the language and show how ideas used in its design can be utilized to generalize and simplify the definition of another important extension of ASP by aggregates.
AB - The paper introduces an extension of the original Answer Set Prolog (ASP) by several set constructs including aggregates, defined as functions on sets. The new language, called Alog allows creating sets based on the Vicious Circle Principle by Poincaré and Russell which eliminates a number of problems found in existing extensions of ASP by aggregates. We argue that, despite the fact that Alog is not as expressive as other extensions of ASP by aggregates, clarity of its syntax and semantics, addition of several new set-based constructs, and simplicity and the ease of use make it a viable competitor to these languages. We also study a number of important properties of the language and show how ideas used in its design can be utilized to generalize and simplify the definition of another important extension of ASP by aggregates.
KW - Aggregates
KW - Answer set programming
KW - Knowledge representation
KW - Language design
KW - Logic programming
UR - http://www.scopus.com/inward/record.url?scp=85065478094&partnerID=8YFLogxK
U2 - 10.1016/j.artint.2019.04.004
DO - 10.1016/j.artint.2019.04.004
M3 - Article
AN - SCOPUS:85065478094
SN - 0004-3702
VL - 275
SP - 28
EP - 77
JO - Artificial Intelligence
JF - Artificial Intelligence
ER -