On the Foundations of Grounding in Answer Set Programming

• URL: http://arxiv.org/abs/2108.04769v1
• Date: Tue, 10 Aug 2021 16:23:49 GMT
• Title: On the Foundations of Grounding in Answer Set Programming
• Authors: Roland Kaminski and Torsten Schaub
• Abstract summary: We provide a comprehensive elaboration of the theoretical foundations of variable instantiation, or grounding, in Answer Set Programming (ASP) We introduce a formal characterization of grounding algorithms in terms of (fixed point) operators. A major role is played by dedicated well-founded operators whose associated models provide semantic guidance for delineating the result of grounding.
• Score: 4.389457090443418
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We provide a comprehensive elaboration of the theoretical foundations of variable instantiation, or grounding, in Answer Set Programming (ASP). Building on the semantics of ASP's modeling language, we introduce a formal characterization of grounding algorithms in terms of (fixed point) operators. A major role is played by dedicated well-founded operators whose associated models provide semantic guidance for delineating the result of grounding along with on-the-fly simplifications. We address an expressive class of logic programs that incorporates recursive aggregates and thus amounts to the scope of existing ASP modeling languages. This is accompanied with a plain algorithmic framework detailing the grounding of recursive aggregates. The given algorithms correspond essentially to the ones used in the ASP grounder gringo.

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