Socratic Trees
Studia Logica 101 (5):959-986 (2013)
| Abstract |
The method of Socratic proofs (SP-method) simulates the solving of logical problem by pure questioning. An outcome of an application of the SP-method is a sequence of questions, called a Socratic transformation. Our aim is to give a method of translation of Socratic transformations into trees. We address this issue both conceptually and by providing certain algorithms. We show that the trees which correspond to successful Socratic transformations—that is, to Socratic proofs—may be regarded, after a slight modification, as Gentzen-style proofs. Thus proof-search for some Gentzen-style calculi can be performed by means of the SP-method. At the same time the method seems promising as a foundation for automated deduction.
|
| Keywords | Socratic transformations Socratic proofs Sequent calculi Proof search Automated deduction |
| Categories | (categorize this paper) |
| DOI | 10.1007/s11225-012-9404-0 |
| Options |
Edit this record
Mark as duplicate
Export citation
Request removal from index
|
Download options
References found in this work BETA
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
The Posing of Questions. Logical Foundations of Erotetic Inferences.Andrzej Wi'sniewski - 1995 - Kluwer Academic Publishers.
View all 11 references / Add more references
Citations of this work BETA
A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences.Jared Millson - 2019 - Studia Logica:1-34.
Automatic Proof Generation in an Axiomatic System for $\Mathsf{CPL}$ by Means of the Method of Socratic Proofs.Aleksandra Grzelak & Dorota Leszczyńska-Jasion - 2018 - Logic Journal of the IGPL 26 (1):109-148.
Dual Erotetic Calculi and the Minimal $${\Mathsf{LFI}}$$ LFI.Dorota Leszczyńska-Jasion & Szymon Chlebowski - 2015 - Studia Logica 103 (6):1245-1278.
Inferential Erotetic Logic Meets Inquisitive Semantics.Andrzej Wiśniewski & Dorota Leszczyńska-Jasion - 2015 - Synthese 192 (6):1585-1608.
A Survey of Nonstandard Sequent Calculi.Andrzej Indrzejczak - 2014 - Studia Logica 102 (6):1295-1322.
Similar books and articles
The Method of Socratic Proofs for Normal Modal Propositional Logics.Dorota Leszczynska-Jasion - 2007 - Wydawn. Naukowe Uniwersytetu Im. Adama Mickiewicza.
The Method of Socratic Proofs for Normal Modal Propositional Logics.Dorota Leszczynska - 2007 - Wydawn. Naukowe Uniwersytetu Im. Adama Mickiewicza.
On Scott and Karp Trees of Uncountable Models.Tapani Hyttinen & Jouko Väänänen - 1990 - Journal of Symbolic Logic 55 (3):897-908.
Computable Trees of Scott Rank $\Omega _{1}^{\Mathit{CK}}$ , and Computable Approximation.Wesley Calvert, Julia F. Knight & Jessica Millar - 2006 - Journal of Symbolic Logic 71 (1):283 - 298.
Uniformization, Choice Functions and Well Orders in the Class of Trees.Shmuel Lifsches & Saharon Shelah - 1996 - Journal of Symbolic Logic 61 (4):1206-1227.
Congruence of Morphological and Molecular Phylogenies.Davide Pisani, Michael J. Benton & Mark Wilkinson - 2007 - Acta Biotheoretica 55 (3):269-281.
A Loop-Free Decision Procedure for Modal Propositional Logics K4, S4 and S.Dorota Leszczyńska-Jasion - 2009 - Journal of Philosophical Logic 38 (2):151 - 177.
Analytics
Added to PP index
2012-09-05
Total views
28 ( #273,919 of 2,327,914 )
Recent downloads (6 months)
3 ( #542,080 of 2,327,914 )
2012-09-05
Total views
28 ( #273,919 of 2,327,914 )
Recent downloads (6 months)
3 ( #542,080 of 2,327,914 )
How can I increase my downloads?
Downloads
