A transfer of Boolean network results to Datalog^neg yields structural conditions for existence, uniqueness, and counting bounds of stable, stable partial, and regular models, plus a characterization of regular models as minimal stable trap spaces.
Static Analysis of Logic Programs via Boolean Networks
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abstract
Answer Set Programming (ASP) is a declarative problem solving paradigm that can be used to encode a combinatorial problem as a logic program whose stable models correspond to the solutions of the considered problem. ASP has been widely applied to various domains in AI and beyond. The question "What can be said about stable models of a logic program from its static information?" has been investigated and proved useful in many circumstances. In this work, we dive into this direction more deeply by making the connection between a logic program and a Boolean network, which is a prominent modeling framework with applications to various areas. The proposed connection can bring the existing results in the rich history on static analysis of Boolean networks to explore and prove more theoretical results on ASP, making it become a unified and powerful tool to further study the static analysis of ASP. In particular, the newly obtained insights have the potential to benefit many problems in the field of ASP.
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On the Boolean Network Theory of Datalog$^\neg$
A transfer of Boolean network results to Datalog^neg yields structural conditions for existence, uniqueness, and counting bounds of stable, stable partial, and regular models, plus a characterization of regular models as minimal stable trap spaces.