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Proof Search Optimizations for Non-Clausal Connection Calculi

Jens Otten
2018 Conference on Automated Deduction  
The paper presents several proof search optimization techniques for non-clausal connection calculi. These techniques are implemented and integrated into the non-clausal connection prover nanoCoP.  ...  Their effectiveness is evaluated on the problems in the TPTP library. Together with a fixed strategy scheduling, these techniques are the basis of the new version 1.1 of nanoCoP.  ...  Hence, reordering clauses is a crucial technique for connection calculi using restricted backtracking.  ... 
dblp:conf/cade/Otten18 fatcat:ii443mkjofdavl3dgsucq4wohy

randoCoP: Randomizing the Proof Search Order in the Connection Calculus

Thomas Raths, Jens Otten
2008 Conference on Automated Deduction  
We present randoCoP, a theorem prover for classical firstorder logic, which integrates randomized search techniques into the connection prover leanCoP 2.0.  ...  Introduction Connection calculi, such as the connection calculus [1, 2] , the connection tableau calculus [8] , or the model elimination calculus [9] , are in contrast to standard tableau or saturation-based  ...  The effect of reordering axioms (or clauses) and literals is limited when a complete search in connection calculi is done. In this case the performance can even get worse.  ... 
dblp:conf/cade/RathsO08 fatcat:n732hqkxt5g55ccf6hxxzy76yu

Page 2189 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
Although restrictions on the proof search (preserving completeness) are given in the pa- per and most of them are theoretically appealing, the use of those calculi for mechanization is however doubtful  ...  The calculi are based on d’Agostino and Mondadori’s calculus KE and therefore they admit a restricted cut-rule that is not eliminable.  ... 

Machine Learning Guidance for Connection Tableaux

Michael Färber, Cezary Kaliszyk, Josef Urban
2020 Journal of automated reasoning  
Connection calculi allow for very compact implementations of goal-directed proof search.  ...  We give an overview of our work related to connection tableaux calculi: first, we show optimised functional implementations of connection tableaux proof search, including a consistent Skolemisation procedure  ...  Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long  ... 
doi:10.1007/s10817-020-09576-7 pmid:33678931 pmcid:PMC7900060 fatcat:ipgat65s4rfivp4myeuyhqvk4u

A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality [chapter]

Jasmin Christian Blanchette, Mathias Fleury, Christoph Weidenbach
2016 Lecture Notes in Computer Science  
Through a chain of refinements, an abstract CDCL calculus is connected to a SAT solver expressed in a functional programming language, with total correctness guarantees.  ...  We developed a formal framework for CDCL (conflict-driven clause learning) in Isabelle/HOL.  ...  Andrei Popescu gave us his permission to reuse, in a slightly adapted form, the succinct description of locales he cowrote on a different occasion [7] .  ... 
doi:10.1007/978-3-319-40229-1_4 fatcat:5xhbugmxdbazpnnszokuyovxou

Machine Learning Guidance and Proof Certification for Connection Tableaux [article]

Michael Färber, Cezary Kaliszyk, Josef Urban
2018 arXiv   pre-print
Connection calculi allow for very compact implementations of goal-directed proof search.  ...  Finally, we give a translation of connection proofs to LK, enabling proof certification and automatic proof search in interactive theorem provers.  ...  The principal implementations of the connection tableaux calculi, leanCoP and nanoCoP, use a number of optimisation techniques, such as regularity, lemmata, and restricted backtracking (Otten 2010) .  ... 
arXiv:1805.03107v3 fatcat:6aaytx66ujd7djk423fowfwcfe

A Model Generation Style Completeness Proof for Constraint Tableaux with Superposition [chapter]

Martin Giese
2002 Lecture Notes in Computer Science  
The calculi and the completeness proof are compared to earlier results of Degtyarev and Voronkov [7] .  ...  We prove completeness of this calculus by an adaptation of the model generation [1, 15] technique commonly used for completeness proofs of resolution calculi.  ...  Acknowledgements I thank Bernhard Beckert, Reiner Hähnle and Peter Schmitt for many fruitful discussions which led to the results presented in this paper.  ... 
doi:10.1007/3-540-45616-3_10 fatcat:ponooefvkbdoxakfudxvjpkqra

Two loop detection mechanisms: A comparison [chapter]

Jacob M. Howe
1997 Lecture Notes in Computer Science  
In order to compare two loop detection mechanisms we describe two calculi for theorem proving in intuitionistic propositional logic.  ...  These calculi combine in different ways the ideas on focused proof search of Herbelin and Dyckhoff & Pinto with the work of Heuerding et al on loop detection.  ...  This was done in the Swiss MJ Hist -the history mechanism operates in one place only and other restrictions for loop prevention involve no storage.  ... 
doi:10.1007/bfb0027414 fatcat:fwcz5lyrkjbnhgwqoez25e7fa4

nanoCoP: A Non-clausal Connection Prover [chapter]

Jens Otten
2016 Lecture Notes in Computer Science  
Most of the popular efficient proof search calculi work on formulae that are in clausal form, i.e. in disjunctive or conjunctive normal form.  ...  It is based on a non-clausal connection calculus and implemented with a few lines of Prolog code.  ...  The author would like to thank Wolfgang Bibel for his helpful comments on a preliminary version of this paper. nanoCoP: A Non-clausal Connection Prover  ... 
doi:10.1007/978-3-319-40229-1_21 fatcat:rhrl3tvvnrhfhloiwuz245wuxu

nanoCoP: Natural Non-clausal Theorem Proving

Jens Otten
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
Most efficient fully automated theorem provers implement proof search calculi that require the input formula to be in a clausal form, i.e. disjunctive or conjunctive normal form.  ...  It is based on a non-clausal connection calculus and implemented with a few lines of Prolog code.  ...  Set is a list of options used to control the restricted backtracking technique [Otten, 2010] and may contain "cut" and "comp(I)" for I ∈ IN .  ... 
doi:10.24963/ijcai.2017/695 dblp:conf/ijcai/Otten17 fatcat:e7twk7ckbnhjvee46egwmol7km

A Non-clausal Connection Calculus [chapter]

Jens Otten
2011 Lecture Notes in Computer Science  
Thus, the calculus combines the advantage of a non-clausal proof search in tableau calculi with the more efficient goal-oriented proof search of clausal connection calculi.  ...  Copying of appropriate (sub-)clauses in a dynamic way, i.e. during the actual proof search, is realized by a generalized extension rule.  ...  Restricted Backtracking. Proof search in the (clausal and non-clausal) connection calculus is not confluent, i.e. it might end up in dead ends.  ... 
doi:10.1007/978-3-642-22119-4_18 fatcat:n5o5knrq7nbvjeufz4bd5ezw6i

Page 4522 of Mathematical Reviews Vol. , Issue 97G [page]

1997 Mathematical Reviews  
; Bloomington, IN) Backtrack searching in the presence of symmetry.  ...  Petunin (Kiev) 97g:68199 68T15 03B35 68Q42 Briining, Stefan (D-DARM-II; Darmstadt) Exploiting equivalences in connection calculi. (English summary) J.IGPL 3 (1995), no. 6, 857-886.  ... 

A Curiously Effective Backtracking Strategy for Connection Tableaux [article]

Michael Färber
2021 arXiv   pre-print
Automated proof search with connection tableaux, such as implemented by Otten's leanCoP prover, depends on backtracking for completeness.  ...  I introduce a new, less restricted backtracking strategy based on the notion of exclusive cuts.  ...  implements restricted backtracking using Prolog's built-in cut operator [19] .  ... 
arXiv:2106.13722v1 fatcat:rb26upii3fdync7nplceor24he

Termination of Derivations in a Fragment of Transitive Distributed Knowledge Logic

Regimantas Pliuškevičius, Aida Pliuškevičienė
2008 Informatica  
Formulas are defined in traditional way from propositional symbols using logical connectives, knowledge operators K i , i ∈ {1, . . . , n}, and distributed knowledge operator D.  ...  Hilbert-Style and Gentzen-Style Calculi for the Logic S4 n D The logic S4 n D is obtained from the multi-modal logic S4 n by adding distributed knowledge operator D (see, e.g., (Fagin and Vardi, 1986;  ...  Lemma 15 allows us to restrict backtracking in backward proof search in G 3 S4 n D.  ... 
doi:10.15388/informatica.2008.232 fatcat:tbpew6tncbcwvf6i2qcrt6pm6m

Certified Connection Tableaux Proofs for HOL Light and TPTP [article]

Cezary Kaliszyk, Josef Urban, Jiri Vyskocil
2014 arXiv   pre-print
In the annual CASC competition, the leanCoP system based on connection tableaux has however performed better than Metis.  ...  This plays a crucial role in extending the MESON proof reconstruction mechanism to connection tableaux proofs, providing an implementation of leanCoP that certifies its proofs.  ...  In contrast to saturation-based calculi used in most of the stateof-the-art ATPs (E, Vampire, etc.), connection calculi implement goal-oriented proof search.  ... 
arXiv:1410.5476v1 fatcat:t252orhdznfqdmuiw2vllggsey
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