Abstract
Although it is believed that there is no efficient algorithm for the decidability of satisfiability in propositional logic, many algorithms are efficient in practice. This is particularly true when a formula is satisfiable; for example, when you build a truth table for an unsatisfiable formula of size n you will have to generate all 2n rows, but if the formula is satisfiable you might get lucky and find a model after generating only a few rows. Even an incomplete algorithm—one that can find a model if one exists but may not be able to detect if a formula is unsatisfiable—can be useful in practice.
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Ben-Ari, M. (2012). Propositional Logic: SAT Solvers. In: Mathematical Logic for Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-4129-7_6
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DOI: https://doi.org/10.1007/978-1-4471-4129-7_6
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