Abstract
We address the problem of proof-search in the natural deduction calculus for Classical propositional logic. Our aim is to improve the usual naïve proof-search procedure where introduction rules are applied upwards and elimination rules downwards. In particular, we introduce NCR, a variant of the usual natural deduction calculus for Classical propositional logic, and we show that it can be used as a base for a proof-search procedure which does not require backtracking nor loop-checking.
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References
Bolotov, A., Bocharov, V., Gorchakov, A., Shangin, V.: Automated first order natural deduction. In: Prasad, B. (ed.) IICAI, pp. 1292–1311. IICAI (2005)
D’Agostino, M.: Classical natural deduction. In: Artëmov, S.N., et al. (eds.) We Will Show Them!, pp. 429–468. College Publications (2005)
Dyckhoff, R., Pinto, L.: Cut-elimination and a permutation-free sequent calculus for intuitionistic logic. Studia Logica 60(1), 107–118 (1998)
Ferrari, M., Fiorentini, C., Fiorino, G.: A terminating evaluation-driven variant of g3i. In: Galmiche, D., Larchey-Wendling, D. (eds.) TABLEAUX 2013. LNCS, vol. 8123, pp. 104–118. Springer, Heidelberg (2013)
Ferrari, M., Fiorentini, C., Fiorino, G.: An evaluation-driven decision procedure for G3i. ACM Transactions on Computational Logic (TOCL), 6(1), 8:1–8:37 (2015)
Gabbay, D.M., Olivetti, N.: Goal-Directed Proof Theory. Springer (2000)
Girard, J.Y., Taylor, P., Lafont, Y.: Proofs and types. Camb. Univ. Press (1989)
Indrzejczak, A.: Natural Deduction, Hybrid Systems and Modal Logics. Trends in Logic, vol. 30. Springer (2010)
Jaśkowski, S.: On the rules of suppositions in formal logic. Studia Logica 1, 5–32 (1934)
Liang, C., Miller, D.: Focusing and polarization in linear, intuitionistic, and classical logics. Theoretical Computer Science 410(46), 4747–4768 (2009)
Pastre, D.: Strong and weak points of the MUSCADET theorem prover - examples from CASC-JC. AI Commun. 15(2-3), 147–160 (2002)
Pfenning, F.: Automated theorem proving. Lecture notes. CMU (2004)
Prawitz, D.: Natural Deduction. Almquist and Winksell (1965)
Sieg, W., Byrnes, J.: Normal natural deduction proofs (in classical logic). Studia Logica 60(1), 67–106 (1998)
Sieg, W., Cittadini, S.: Normal natural deduction proofs (in non-classical logics). In: Hutter, D., Stephan, W. (eds.) Mechanizing Mathematical Reasoning. LNCS (LNAI), vol. 2605, pp. 169–191. Springer, Heidelberg (2005)
Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory, 2nd edn. Cambridge Tracts in Theoretical Computer Science, vol. 43. Camb. Univ. Press (2000)
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Ferrari, M., Fiorentini, C. (2015). Proof-Search in Natural Deduction Calculus for Classical Propositional Logic. In: De Nivelle, H. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2015. Lecture Notes in Computer Science(), vol 9323. Springer, Cham. https://doi.org/10.1007/978-3-319-24312-2_17
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DOI: https://doi.org/10.1007/978-3-319-24312-2_17
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