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Abstract: Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux. (Update)
Context of citations to this paper: More
.... Massacci, 1998b, Massacci, 1998a, Gore, 1999] or primarily concerns algorithms for proof search [Otten and Kreitz, 1996, Beckert and Gore, 1997, Schmidt, 1998] is dominated by the study of the propositional logic of a single modal operator (or accessibility relation)...
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BibTeX entry: (Update)
B. Beckert and R. Gor'e. Free variable tableaux for propositional modal logics. In these proceedings, 1997. http://citeseer.ist.psu.edu/beckert97freevariable.html More
@inproceedings{ beckert97free,
author = "Bernhard Beckert and Rajeev Gor\'e",
title = "Free Variable Tableaux for Propositional Modal Logics",
booktitle = "Proc.\ International Conference on Theorem Proving with Analytic Tableaux and Related Methods, Pont-a-Mousson, France",
volume = "1227",
publisher = "Springer-Verlag",
pages = "91--106",
year = "1997",
url = "citeseer.ist.psu.edu/beckert97freevariable.html" }
Citations (may not include all citations):322 First-Order Logic and Automated Theorem Proving (context) - Fitting - 1996
242 Proof Methods for Modal and Intuitionistic Logics (context) - Fitting - 1983
134 Labelled Deductive Systems (context) - Gabbay - 1996
131 SETHEO: A highperformance theorem prover (context) - Letz, Schumann et al. - 1992
53 Strongly analytic tableaux for normal modal logics - Massacci - 1994
44 Tableau methods for modal and temporal logics (context) - Gor - 1999
27 Free variable tableaux for propositional modal logics - Beckert, Gor - 1997
25 Journal of Logic and Computation (context) - Fitting - 1998
22 Lean tableau-based deduction (context) - Beckert, Posegga - 1995
20 A general framework for modal deduction - Frisch, Scherl - 1991
16 Efficient loop-check for backward proof search in some non-c.. - Heuerding, Seyfried et al. - 1996
16 ileanTAP: An intuitionistic theorem prover - Otten - 1997
15 A Short Introduction to Modal Logic (context) - Mints - 1992
14 Free logic (context) - Bencivenga - 1986
10 Semantic tableaux as a framework for automated theorem-provi.. (context) - Reeves - 1987
8 Generalising propositional modal logic using labelled deduct.. (context) - Russo - 1996
8 Grafting modalities onto substructural implication systems - D'Agostino, Gabbay et al. - 1997
7 A general proof method for first-order modal logic (context) - Jackson, Reichgelt - 1987
6 Distributed modal theorem proving with KE (context) - Pitt, Cunningham - 1996
6 Simplification: A general constraint propagation technique f.. (context) - Massaci - 1998
6 Stockholm Studies in Philosophy (context) - Kanger, Logic - 1957
4 Analytic tableaux (context) - Beckert, Hhnle - 1998
3 Comparison of theorem provers for modal logics: Introduction.. (context) - Balsinger, Heuerding - 1998
2 The tableau-based theorem prover 3 T A P (context) - Beckert, Hhnle et al. - 1996
1 Description for the comparison of theorem provers for modal .. (context) - Beckert, Gor
1 A reduplication and loop checking free proof system for S (context) - Governatori - 1996
1 A free variable sequent system for tense logic Kt (context) - Bonnette, FV - 2000
1 System description: leanK (context) - Beckert, Gor - 1998
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