State Algebra for Propositional Logic

• URL: http://arxiv.org/abs/2509.10326v1
• Date: Fri, 12 Sep 2025 15:05:52 GMT
• Title: State Algebra for Propositional Logic
• Authors: Dmitry Lesnik, Tobias Schäfer,
• Abstract summary: State Algebra is a framework to represent and manipulate propositional logic.<n>It is structured as a hierarchy of three representations: Set, Coordinate, and Row Decomposition.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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