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An abstract view on optimizations in propositional frameworks

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Abstract

Search/optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared toward solving and modeling search/optimization problems. Automated reasoning and knowledge representation are the subfields of AI that are particularly vested in these developments. Many popular automated reasoning paradigms provide users with languages supporting optimization statements: answer set programming or MaxSAT or min-one, to name a few. These paradigms vary significantly in their languages and in the ways they express quality conditions on computed solutions. Here we propose a unifying framework of so-called weight systems that eliminates syntactic distinctions between paradigms and allows us to see essential similarities and differences between optimization statements provided by paradigms. This unifying outlook has significant simplifying and explanatory potential in the studies of optimization and modularity in automated reasoning and knowledge representation. It also supplies researchers with a convenient tool for proving the formal properties of distinct frameworks; bridging these frameworks; and facilitating the development of translational solvers.

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Acknowledgements

We would like to acknowledge Mario Alviano, Martin Gebser, Jorge Fandinno, Torsten Schaub, Miroslaw Truszczynski, and Da Shen for valuable discussions related to this work. We are also grateful for anonymous reviewers for helping to make this paper more accessible. The project was partially supported by NSF grant 1707371

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  1. Department of Computer Science, University of Nebraska Omaha, 6001 Dodge St, Omaha, NE, 68182, USA

    Yuliya Lierler

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Lierler, Y. An abstract view on optimizations in propositional frameworks. Ann Math Artif Intell 92, 355–391 (2024). https://doi.org/10.1007/s10472-023-09914-6

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