Graphical Conditions for the Existence, Unicity and Number of Regular Models

The regular models of a normal logic program are a particular type of partial (i.e. 3-valued) models which correspond to stable partial models with minimal undefinedness. In this paper, we explore graphical conditions on the dependency graph of a finite ground normal logic program to analyze the existence, unicity and number of regular models for the program. We show three main results: 1) a necessary condition for the existence of non-trivial (i.e. non-2-valued) regular models, 2) a sufficient condition for the unicity of regular models, and 3) two upper bounds for the number of regular models based on positive feedback vertex sets. The first two conditions generalize the finite cases of the two existing results obtained by You and Yuan (1994) for normal logic programs with well-founded stratification. The third result is also new to the best of our knowledge. Key to our proofs is a connection that we establish between finite ground normal logic programs and Boolean network theory.

Static Analysis of Logic Programs via Boolean Networks

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.