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On the Relation of Resolution and Tableaux Proof Systems for Description Logics

Ullrich Hustadt, Renate A. Schmidt
1999 International Joint Conference on Artificial Intelligence  
Our resolution proof system is based on a selection refinement and utilises standard redundancy elimination criteria to ensure termination.  ...  This paper investigates the relationship between resolution and tableaux proof system for the satisfiability of general knowledge bases in the description logic We show that resolution proof systems can  ...  Ordered Resolution: where (i) is the most general unifier of A1 and A2, (ii) no literal is selected in C and is strictlymaximal with respect to and (iii) -A 2 is either selected, or is maximal in and no  ... 
dblp:conf/ijcai/HustadtS99 fatcat:5ktpmhsdqzaedl2vh2awqt44du

Rewrite-based Equational Theorem Proving with Selection and Simplification

1994 Journal of Logic and Computation  
It is often possible to compute the closure of nontrivial sets of clauses under application of non-redundant inferences.  ...  We present various refutationally complete calculi for first-order clauses with equality that allow for arbitrary selection of negative atoms in clauses.  ...  Acknowledgements Marianne Haberstrau and Robert Nieuwenhuis have found two errors in a preliminary version of the paper. We are very grateful for their careful reading.  ... 
doi:10.1093/logcom/4.3.217 fatcat:unag3wwpmzdgzcqdjx7dklezhq

Superposition with equivalence reasoning and delayed clause normal form transformation

Harald Ganzinger, Jürgen Stuber
2005 Information and Computation  
The paper presents a completeness proof and reports on practical experience obtained with the Saturate system.  ...  Superposition and simplification inferences may employ equivalences that have arbitrary formulas at their smaller side.  ...  This refinement is complete, since any minimal counterexample with a selected atom can be reduced in a similar way as by Reflexivity Resolution and Negative Superposition in the proof above.  ... 
doi:10.1016/j.ic.2004.10.010 fatcat:cwg2mgcmrzgl7k5fgzyj5oy7qy

Positive deduction modulo regular theories [chapter]

Laurent Vigneron
1996 Lecture Notes in Computer Science  
We propose a new technique for dealing with an equational theory E in the clausal framework.  ...  This consists of the de nition of two inference rules called contextual superposition and extended superposition, and of an algorithm for computing the only needed applications of these last inference  ...  I would like to dedicate this paper to the memory of my colleague Valentin Antimirov of INRIA Lorraine (France), with whom I had very interesting discussions while preparing a rst version of this paper  ... 
doi:10.1007/3-540-61377-3_54 fatcat:clszw5f3yzfhvgw5sijhuoktrq

First-Order Resolution Methods for Modal Logics [chapter]

Renate A. Schmidt, Ullrich Hustadt
2013 Lecture Notes in Computer Science  
In this paper we give an overview of results for modal logic which can be shown using techniques and methods from first-order logic and resolution.  ...  Because of the breadth of the area and the many applications we focus on the use of first-order resolution methods for modal logics.  ...  In other words, unrestricted use and fine-tuning of ordering restrictions, selection functions and redundancy criteria is possible. This implies that e.g.  ... 
doi:10.1007/978-3-642-37651-1_15 fatcat:pta3fxqsnfal3cigcnryyxjcba

An overview of Rewrite Rule Laboratory (RRL)

D. Kapur, H. Zhang
1995 Computers and Mathematics with Applications  
We provide a brief historical account of development of RRL and its descendants, give an overview of the main capabilities of RRL and conclude with a discussion of applications of RRL.  ...  the use of formal methods in hardware and software design.  ...  Compared with other methods, the clausal superposition method works particularly well if tile input involves non-Horn clauses with equality.  ... 
doi:10.1016/0898-1221(94)00218-a fatcat:mqgk7ygjerd3poaldoyq3qbcpu

An overview of Rewrite Rule Laboratory (RRL) [chapter]

Deepak Kapur, Hantao Zhang
1989 Lecture Notes in Computer Science  
We provide a brief historical account of development of RRL and its descendants, give an overview of the main capabilities of RRL and conclude with a discussion of applications of RRL.  ...  the use of formal methods in hardware and software design.  ...  Compared with other methods, the clausal superposition method works particularly well if tile input involves non-Horn clauses with equality.  ... 
doi:10.1007/3-540-51081-8_138 fatcat:qwdmeuudbrhzjklqdzzgcxcp24

A Taxonomy of Theorem-Proving Strategies [chapter]

Maria Paola Bonacina
1999 Lecture Notes in Computer Science  
For each class, the form of derivation is specified, and it is shown how inference system and search plan cooperate to generate it.  ...  For this purpose, a formal notion of search plan is given and shown to apply to all classes of strategies.  ...  Redundancy depends on the well-founded ordering on clauses: like selecting different orderings may yield different contraction rules, selecting different orderings may yield different redundancy criteria  ... 
doi:10.1007/3-540-48317-9_3 fatcat:kax5uhmf5ne2zeyzbu4g4ykxbu

From Search to Computation: Redundancy Criteria and Simplification at Work [chapter]

Thomas Hillenbrand, Ruzica Piskac, Uwe Waldmann, Christoph Weidenbach
2013 Lecture Notes in Computer Science  
Hence, the key to successfully applying first-order theorem proving to a problem domain is to find those simplifications and redundancy criteria that fit this domain and can be effectively implemented.  ...  For a number of subclasses of firstorder logic appropriate redundancy and simplification concepts even turn the superposition calculus into a decision procedure.  ...  The resulting inference system is the basis of the superposition calculus; it consists of the rules superposition, equality resolution (i. e., ordered resolution with the reflexivity axiom), and either  ... 
doi:10.1007/978-3-642-37651-1_7 fatcat:fr4uqtwvubbtvgjepamaamojeu

First-Order Theorem Proving and Vampire [chapter]

Laura Kovács, Andrei Voronkov
2013 Lecture Notes in Computer Science  
We discuss the superposition calculus and explain the key concepts of saturation and redundancy elimination, present saturation algorithms and preprocessing, and demonstrate how these concepts are implemented  ...  Further, we also cover more recent topics and features of VAMPIRE designed for advanced applications, including satisfiability checking, theory reasoning, interpolation, consequence elimination, and program  ...  This work was partially done while the first author was affiliated with the TU Vienna.  ... 
doi:10.1007/978-3-642-39799-8_1 fatcat:bhabf63t35h3fdvmqb23d3w2jq

A Combined Superposition and Model Evolution Calculus

Peter Baumgartner, Uwe Waldmann
2010 Journal of automated reasoning  
inference rules and redundancy criteria in a non-trivial way.  ...  It integrates the inference rules of Superposition and of Model Evolution in a non-trivial way while preserving the individual semantically-based redundancy criteria of the two calculi.  ...  We thank the reviewers for their critical and helpful remarks, which helped a lot to improve the presentation of this paper.  ... 
doi:10.1007/s10817-010-9214-x fatcat:7jreirdnfvecbdbfxkrdvxon4e

Superposition and Model Evolution Combined [chapter]

Peter Baumgartner, Uwe Waldmann
2009 Lecture Notes in Computer Science  
inference rules and redundancy criteria in a non-trivial way.  ...  We present a new calculus for first-order theorem proving with equality, ME+Sup, which generalizes both the Superposition calculus and the Model Evolution calculus (with equality) by integrating their  ...  We thank the reviewers of an earlier version of this paper and Cesare Tinelli for their helpful comments.  ... 
doi:10.1007/978-3-642-02959-2_2 fatcat:yrbih5lqjbhjpaq4dnr4m6g5bi

Associative-commutative superposition [chapter]

Leo Bachmair, Harald Ganzinger
1995 Lecture Notes in Computer Science  
It is compatible with an abstract notion of redundancy that covers such simpli cation techniques as tautology deletion, subsumption, and simpli cation by (associative-commutative) rewriting.  ...  The calculus is parametrized by a selection function (on negative literals) and a well-founded ordering on terms.  ...  Recently, associativecommutative calculi have been combined with the basic strategy, or more generally, with constraint-based deduction, and completeness results have been proved by Nieuwenhuis and Rubio  ... 
doi:10.1007/3-540-60381-6_1 fatcat:5e5ihgzlhfhvvbo266oruhs4ky

Detection of First Order Axiomatic Theories [chapter]

Guillaume Burel, Simon Cruanes
2013 Lecture Notes in Computer Science  
We present here a generic way of describing and recognizing axiomatic theories in clausal form first-order logic with equality.  ...  Automated theorem provers for first-order logic with equality have become very powerful and useful, thanks to both advanced calculisuch as superposition and its refinements -and mature implementation techniques  ...  Acknowledgements We would like to thank Gilles Dowek for his help, and the anonymous reviewers for their detailed and helpful comments.  ... 
doi:10.1007/978-3-642-40885-4_16 fatcat:j2wxzydcnvaw3pc2a2fnxgme6i

The Model Evolution Calculus with Equality [chapter]

Peter Baumgartner, Cesare Tinelli
2005 Lecture Notes in Computer Science  
Our main result is the correctness of the ME E calculus in the presence of very general redundancy elimination criteria.  ...  The calculus also features a generic, semantically justified simplification rule which covers many simplification techniques known from superposition-style theorem proving.  ...  Given that our model construction and the "induced" redundancy criteria are adapted from the superposition calculus, it is not too surprising that comparable simplification techniques can be obtained with  ... 
doi:10.1007/11532231_29 fatcat:4zmryafkqzct5g3kskjhn2ja4y
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