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129
Incremental closure of free variable tableaux
 Proc. Intl. Joint Conf. on Automated Reasoning IJCAR
, 2001
"... Abstract. This paper presents a technique for automated theorem proving with free variable tableaux that does not require backtracking. Most existing automated proof procedures using free variable tableaux require iterative deepening and backtracking over applied instantiations to guarantee complete ..."
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Cited by 35 (6 self)
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Abstract. This paper presents a technique for automated theorem proving with free variable tableaux that does not require backtracking. Most existing automated proof procedures using free variable tableaux require iterative deepening and backtracking over applied instantiations to guarantee completeness. If the correct instantiation is hard to find, this can lead to a significant amount of duplicated work. Incremental Closure is a way of organizing the search for closing instantiations that avoids this inefficiency. 1
Using Vampire to reason with OWL
 In Proc. of the 2004 International Semantic Web Conference (ISWC
, 2004
"... Abstract. OWL DL corresponds to a Description Logic (DL) that is a fragment of classical firstorder predicate logic (FOL). Therefore, the standard methods of automated reasoning for full FOL can potentially be used instead of dedicated DL reasoners to solve OWL DL reasoning tasks. In this paper we ..."
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Cited by 32 (1 self)
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Abstract. OWL DL corresponds to a Description Logic (DL) that is a fragment of classical firstorder predicate logic (FOL). Therefore, the standard methods of automated reasoning for full FOL can potentially be used instead of dedicated DL reasoners to solve OWL DL reasoning tasks. In this paper we report on some experiments designed to explore the feasibility of using existing generalpurpose FOL provers to reason with OWL DL. We also extend our approach to SWRL, a proposed rule language extension to OWL. 1
2001b, ‘The CADE17 ATP System Competition
 Journal of Automated Reasoning
"... Abstract. The results of the IJCAR ATP System Competition are presented. ..."
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Cited by 31 (7 self)
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Abstract. The results of the IJCAR ATP System Competition are presented.
Blocking and other enhancements for bottomup model generation methods
 Third Int. Joint Conference on Automated Reasoning (IJCAR), Springer LNAI
, 2006
"... In this paper we introduce several new improvements to the bottomup model generation (BUMG) paradigm. Our techniques are based on nontrivial transformations of firstorder problems into a certain implicational form, namely rangerestricted clauses. These refine existing transformations to rangeres ..."
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Cited by 28 (15 self)
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In this paper we introduce several new improvements to the bottomup model generation (BUMG) paradigm. Our techniques are based on nontrivial transformations of firstorder problems into a certain implicational form, namely rangerestricted clauses. These refine existing transformations to rangerestricted form by extending the domain of interpretation with new Skolem terms in a more careful and deliberate way. Our transformations also extend BUMG with a blocking technique for detecting recurrence in models. Blocking is based on a conceptually rather simple encoding together with standard equality theorem proving and redundancy elimination techniques. This provides a generalpurpose method for finding small models. The presented techniques are implemented and have been successfully tested with existing theorem provers on the satisfiable problems from the TPTP library. 1
On a Rewriting Approach to Satisfiability Procedures: Extension, Combination of Theories and an Experimental Appraisal
, 2005
"... The rewriting approach to Tsatisfiability is based on establishing termination of a rewritebased inference system for firstorder logic on the Tsatisfiability problem. Extending previous such results, including the quantifierfree theory of equality and the theory of arrays with or without exte ..."
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Cited by 28 (15 self)
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The rewriting approach to Tsatisfiability is based on establishing termination of a rewritebased inference system for firstorder logic on the Tsatisfiability problem. Extending previous such results, including the quantifierfree theory of equality and the theory of arrays with or without extensionality, we prove termination for the theories of records with or without extensionality, integer offsets and integer offsets modulo. A general theorem for termination on combinations of theories, that covers any combination of the theories above, is given next. For empirical evaluation, the rewritebased theorem prover E is compared with the validity checkers CVC and CVC Lite, on both synthetic and realworld benchmarks, including both valid and invalid instances. Parametric synthetic benchmarks test scalability, while realworld benchmarks test ability to handle huge sets of literals. Contrary to the folklore that a generalpurpose prover cannot compete with specialized reasoners, the experiments are overall favorable to the theorem prover, showing that the rewriting approach is both elegant and practical.
Integrating linear arithmetic into superposition calculus
 In Computer Science Logic (CSL’07
, 2007
"... Abstract. We present a method of integrating linear rational arithmetic into superposition calculus for firstorder logic. One of our main results is completeness of the resulting calculus under some finiteness assumptions. 1 ..."
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Cited by 27 (3 self)
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Abstract. We present a method of integrating linear rational arithmetic into superposition calculus for firstorder logic. One of our main results is completeness of the resulting calculus under some finiteness assumptions. 1
Decision Procedures for Extensions of the Theory of Arrays
 Annals of Mathematics and Artificial Intelligence
"... Abstract The theory of arrays, introduced by McCarthy in his seminal paper “Towards a mathematical science of computation”, is central to Computer Science. Unfortunately, the theory alone is not sufficient for many important verification applications such as program analysis. Motivated by this obser ..."
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Cited by 27 (4 self)
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Abstract The theory of arrays, introduced by McCarthy in his seminal paper “Towards a mathematical science of computation”, is central to Computer Science. Unfortunately, the theory alone is not sufficient for many important verification applications such as program analysis. Motivated by this observation, we study extensions of the theory of arrays whose satisfiability problem (i.e. checking the satisfiability of conjunctions of ground literals) is decidable. In particular, we consider extensions where the indexes of arrays have the algebraic structure of Presburger Arithmetic and the theory of arrays is augmented with axioms characterizing additional symbols such as dimension, sortedness, or the domain of definition of arrays. We provide methods for integrating available decision procedures for the theory of arrays and Presburger Arithmetic with automatic instantiation strategies which allow us to reduce the satisfiability problem for the extension of the theory of arrays to that of the theories decided by the available procedures. Our approach aims to reuse as much as possible existing techniques so as to ease the implementation of the proposed methods. To this end, we show how to use modeltheoretic, rewritingbased theorem proving
Using firstorder theorem provers in the Jahob data structure verification system
 In Byron Cook and Andreas Podelski, editors, Verification, Model Checking, and Abstract Interpretation, LNCS 4349
, 2007
"... Abstract. This paper presents our integration of efficient resolutionbased theorem provers into the Jahob data structure verification system. Our experimental results show that this approach enables Jahob to automatically verify the correctness of a range of complex dynamically instantiable data st ..."
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Cited by 23 (2 self)
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Abstract. This paper presents our integration of efficient resolutionbased theorem provers into the Jahob data structure verification system. Our experimental results show that this approach enables Jahob to automatically verify the correctness of a range of complex dynamically instantiable data structures, including data structures such as hash tables and search trees, without the need for interactive theorem proving or techniques tailored to individual data structures. Our primary technical results include: (1) a translation from higherorder logic to firstorder logic that enables the application of resolutionbased theorem provers and (2) a proof that eliminating type (sort) information in formulas is both sound and complete, even in the presence of a generic equality operator. Moreover, our experimental results show that the elimination of this type information dramatically decreases the time required to prove the resulting formulas. These techniques enabled us to verify complex correctness properties of Java programs such as a mutable set implemented as an imperative linked list, a finite map implemented as a functional ordered tree, a hash table with a mutable array, and a simple library system example that uses these container data structures. Our system verifies (in a matter of minutes) that data structure operations correctly update the finite map, that they preserve data structure invariants (such as ordering of elements, membership in appropriate hash table buckets, or relationships between sets and relations), and that there are no runtime errors such as null dereferences or array out of bounds accesses. 1
Decidability and undecidability results for NelsonOppen and rewritebased decision procedures
 In Proc. IJCAR3, U. Furbach and
, 2006
"... Abstract. In the context of combinations of theories with disjoint signatures, we classify the component theories according to the decidability of constraint satisfiability problems in arbitrary and in infinite models, respectively. We exhibit a theory T1 such that satisfiability is decidable, but s ..."
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Cited by 22 (14 self)
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Abstract. In the context of combinations of theories with disjoint signatures, we classify the component theories according to the decidability of constraint satisfiability problems in arbitrary and in infinite models, respectively. We exhibit a theory T1 such that satisfiability is decidable, but satisfiability in infinite models is undecidable. It follows that satisfiability in T1 ∪ T2 is undecidable, whenever T2 has only infinite models, even if signatures are disjoint and satisfiability in T2 is decidable. In the second part of the paper we strengthen the NelsonOppen decidability transfer result, by showing that it applies to theories over disjoint signatures, whose satisfiability problem, in either arbitrary or infinite models, is decidable. We show that this result covers decision procedures based on rewriting, complementing recent work on combination of theories in the rewritebased approach to satisfiability. 1
System Description: EKRHyper
"... Abstract. The EKRHyper system is a model generator and theorem prover for firstorder logic with equality. It implements the new Ehyper tableau calculus, which integrates a superpositionbased handling of equality into the hyper tableau calculus. EKRHyper extends our previous KRHyper system, whic ..."
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Cited by 21 (4 self)
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Abstract. The EKRHyper system is a model generator and theorem prover for firstorder logic with equality. It implements the new Ehyper tableau calculus, which integrates a superpositionbased handling of equality into the hyper tableau calculus. EKRHyper extends our previous KRHyper system, which has been used in a number of applications in the field of knowledge representation. In contrast to most first order theorem provers, it supports features important for such applications, for example queries with predicate extensions as answers, handling of large sets of uniformly structured input facts, arithmetic evaluation and stratified negation as failure. It is our goal to extend the range of application possibilities of KRHyper by adding equality reasoning. 1