A novel EGs-based framework for systematic propositional-formula simplification
Abstract
This paper presents a novel simplification calculus for propositional logic derived from Peirce’s Existential Graphs’ rules of inference and implication graphs. Our rules can be applied to arbitrary propositional logic formulae (not only in CNF), are equivalence-preserving, guarantee a monotonically decreasing number of clauses and literals, and maximise the preservation of structural problem information. Our techniques can also be seen as higher-level SAT preprocessing, and we show how one of our rules (TWSR) generalises and streamlines most of the known equivalence-preserving SAT preprocessing methods. We further show how this rule can be extended with a novel n-ary implication graph to capture all known equivalence-preserving preprocessing procedures. Finally, we discuss the complexity and implementation of our framework as a solver-agnostic algorithm to simplify Boolean satisfiability problems and arbitrary propositional formula.
Citation
Francès de Mas , J & Kuster Filipe Bowles , J 2023 , A novel EGs-based framework for systematic propositional-formula simplification . in R Glück & B Kafle (eds) , Logic-Based Program Synthesis and Transformation : 33rd International Symposium, LOPSTR 2023, Cascais, Portugal, October 23-24, 2023, Proceedings . vol. 14330 , Lecture Notes in Computer Science , vol. 14330 , Springer , pp. 169-187 , 33rd International Symposium on Logic-based Program Synthesis and Transformation (LOPSTR 2023) , Lisbon , Portugal , 23/10/23 . https://doi.org/10.1007/978-3-031-45784-5_11 conference
Publication
Logic-Based Program Synthesis and Transformation
ISSN
0302-9743Type
Conference item
Description
Funding: Bowles is partially supported by Austrian FWF Meitner Fellowship M-3338 N.Collections
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