Abstract
The paper introduces a free variable, labelled proof system for intuitionistic propositional logic with variable splitting. In this system proofs can be found without backtracking over rules by generating a single, uniform derivation. We prove soundness, introduce a construction that extracts finite countermodels from unprovable sequents, and formulate a branchwise termination condition. This is the first proof system for intuitionistic propositional logic that admits goal-directed search procedures without compromising proof lengths, compared to corresponding tableau calculi.
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Antonsen, R., Waaler, A.: Consistency of variable splitting in free variable systems of first-order logic. In: Beckert, B. (ed.) TABLEAUX 2005. LNCS (LNAI), vol. 3702, pp. 33–47. Springer, Heidelberg (2005)
Antonsen, R., Waaler, A.: Liberalized variable splitting. Journal of Automated Reasoning 38, 3–30 (2007)
Bibel, W.: Automated Theorem Proving. 2. edn. Vieweg Verlag (1987)
Dyckhoff, R.: Contraction-free sequent calculi for intuitionistic logic. Journal of Symbolic Logic 57, 795–807 (1992)
Giese, M.: Proof Search without Backtracking for Free Variable Tableaux. PhD thesis, Fakultät für Informatik, Universität Karlsruhe (July 2002)
Hansen, C.M., Antonsen, R., Waaler, A.: Incremental closure of variable splitting tableaux, position paper. In: Olivetti, N. (ed.) TABLEAUX 2007, Aix en Provence, France. LNCS, vol. 4548, Springer, Heidelberg (2007)
Hudelmaier, J.: Bounds on cut-elimination in intuitionistic propositional logic. Archive for Mathematical Logic 31, 331–353 (1992)
Kreitz, C., Otten, J.: Connection-based theorem proving in classical and non-classical logics. Journal of Universal Computer Science 5(3), 88–112 (1999)
Otten, J.: Clausal connection-based theorem proving in intuitionistic first-order logic. In: Beckert, B. (ed.) TABLEAUX 2005. LNCS (LNAI), vol. 3702, pp. 245–261. Springer, Heidelberg (2005)
Raths, T., Otten, J., Kreitz, C.: The ILTP library: Benchmarking automated theorem provers for intuitionistic logic. In: Beckert, B. (ed.) TABLEAUX 2005. LNCS (LNAI), vol. 3702, pp. 333–337. Springer, Heidelberg (2005)
Sahlin, D., Franzén, T., Haridi, S.: An intuitionistic predicate logic theorem prover. Journal of Logic and Computation 2(5), 619–656 (1992)
Smullyan, R.M.: First-Order Logic. In: Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 43, Springer, New York (1968)
Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory, 2nd edn. Cambridge University Press, Cambridge (2000)
Waaler, A.: Connections in nonclassical logics. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 22, vol. II, pp. 1487–1578. Elsevier, Amsterdam (2001)
Waaler, A., Wallen, L.: Tableaux for intuitionistic logics. In: D’Agostino, M., Gabbay, D.M., Hähnle, R., Posegga, J. (eds.) Handbook of Tableaux Methods, pp. 255–296. Kluwer Academic Publishers, Dordrecht (1999)
Wallen, L.A.: Automated deduction in nonclassical logics. MIT Press, Cambridge (1990)
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Antonsen, R., Waaler, A. (2007). A Labelled System for IPL with Variable Splitting. In: Pfenning, F. (eds) Automated Deduction – CADE-21. CADE 2007. Lecture Notes in Computer Science(), vol 4603. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73595-3_10
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DOI: https://doi.org/10.1007/978-3-540-73595-3_10
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