Abstract
We prove constructively that for any propositional formula φ in Conjunctive Normal Form, we can either find a satisfying assignment of true and false to its variables, or a refutation of φ showing that it is unsatisfiable. This refutation is a resolution proof of ¬φ. From the formalization of our proof in Coq, we extract Robinson’s famous resolution algorithm as a Haskell program correct by construction. The account is an example of the genre of highly readable formalized mathematics.
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Constable, R., Moczydłowski, W. (2007). Extracting the Resolution Algorithm from a Completeness Proof for the Propositional Calculus. In: Artemov, S.N., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2007. Lecture Notes in Computer Science, vol 4514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72734-7_11
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DOI: https://doi.org/10.1007/978-3-540-72734-7_11
Publisher Name: Springer, Berlin, Heidelberg
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