{"ID":2871838,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.10326","arxiv_id":"2509.10326","title":"State Algebra for Propositional Logic","abstract":"This paper presents State Algebra, a novel framework designed to represent and manipulate propositional logic using algebraic methods. The framework is structured as a hierarchy of three representations: Set, Coordinate, and Row Decomposition. These representations anchor the system in well-known semantics while facilitating the computation using a powerful algebraic engine. A key aspect of State Algebra is its flexibility in representation. We show that although the default reduction of a state vector is not canonical, a unique canonical form can be obtained by applying a fixed variable order during the reduction process. This highlights a trade-off: by foregoing guaranteed canonicity, the framework gains increased flexibility, potentially leading to more compact representations of certain classes of problems. We explore how this framework provides tools to articulate both search-based and knowledge compilation algorithms and discuss its natural extension to probabilistic logic and Weighted Model Counting.","short_abstract":"This paper presents State Algebra, a novel framework designed to represent and manipulate propositional logic using algebraic methods. The framework is structured as a hierarchy of three representations: Set, Coordinate, and Row Decomposition. These representations anchor the system in well-known semantics while facili...","url_abs":"https://arxiv.org/abs/2509.10326","url_pdf":"https://arxiv.org/pdf/2509.10326v1","authors":"[\"Dmitry Lesnik\",\"Tobias Schäfer\"]","published":"2025-09-12T15:05:52Z","proceeding":"cs.AI","tasks":"[\"cs.AI\",\"cs.LO\"]","methods":"[]","has_code":false}