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122
Splitting Without Backtracking
, 2001
"... Integrating the splitting rule into a saturationbased theorem prover may be highly beneficial for solving certain classes of fistorder problems. The use of splitting in the context of saturationbased theorem proving based on explicit case analysis (as implemented in SPASS) employs backtracking wh ..."
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Cited by 37 (2 self)
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Integrating the splitting rule into a saturationbased theorem prover may be highly beneficial for solving certain classes of fistorder problems. The use of splitting in the context of saturationbased theorem proving based on explicit case analysis (as implemented in SPASS) employs backtracking which is difficult to implement as it affects design of the whole system. Here we present a "cheap" and efficient technique for implementing splitting that does not use backtracking.
Modular Data Structure Verification
 EECS DEPARTMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
, 2007
"... This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java ..."
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Cited by 36 (21 self)
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This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higherorder logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to firstorder logic, which enables the use of existing resolutionbased theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables
Concurrent Classification of EL Ontologies
"... Abstract. We describe an optimised consequencebased procedure for classification of ontologies expressed in a polynomial fragment ELH R + of the OWL 2 EL profile. A distinguishing property of our procedure is that it can take advantage of multiple processors/cores, which increasingly prevail in com ..."
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Cited by 35 (6 self)
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Abstract. We describe an optimised consequencebased procedure for classification of ontologies expressed in a polynomial fragment ELH R + of the OWL 2 EL profile. A distinguishing property of our procedure is that it can take advantage of multiple processors/cores, which increasingly prevail in computer systems. Our solution is based on a variant of the ‘given clause ’ saturation algorithm for firstorder theorem proving, where we assign derived axioms to ‘contexts ’ within which they can be used and which can be processed independently. We describe an implementation of our procedure within the Javabased reasoner ELK. Our implementation is lightweight in the sense that an overhead of managing concurrent computations is minimal. This is achieved by employing lockfree data structures and operations such as ‘compareandswap’. We report on preliminary experimental results demonstrating a substantial speedup of ontology classification on multicore systems. In particular, one of the largest and widelyused medical ontologies SNOMED CT can be classified in as little as 5 seconds. 1
Hybrid Logics
"... This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur ..."
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Cited by 34 (10 self)
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This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur
Lightweight relevance filtering for machinegenerated resolution problems
 In ESCoR: Empirically Successful Computerized Reasoning
, 2006
"... Irrelevant clauses in resolution problems increase the search space, making it hard to find proofs in a reasonable time. Simple relevance filtering methods, based on counting function symbols in clauses, improve the success rate for a variety of automatic theorem provers and with various initial set ..."
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Cited by 33 (8 self)
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Irrelevant clauses in resolution problems increase the search space, making it hard to find proofs in a reasonable time. Simple relevance filtering methods, based on counting function symbols in clauses, improve the success rate for a variety of automatic theorem provers and with various initial settings. We have designed these techniques as part of a project to link automatic theorem provers to the interactive theorem prover Isabelle. They should be applicable to other situations where the resolution problems are produced mechanically and where completeness is less important than achieving a high success rate with limited processor time. 1
New Directions in InstantiationBased Theorem Proving
"... We consider instantiationbased theorem proving whereby instances of clauses are generated by certain inferences, and where inconsistency is detected by propositional tests. We give a model construction proof of completeness by which restrictive inference systems as well as admissible simplification ..."
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Cited by 32 (3 self)
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We consider instantiationbased theorem proving whereby instances of clauses are generated by certain inferences, and where inconsistency is detected by propositional tests. We give a model construction proof of completeness by which restrictive inference systems as well as admissible simplification techniques can be justified. Another contribution of the paper are novel inference systems that allow one to also employ decision procedures for firstorder fragments more complex than propositional logic. The decision procedure provides for an approximative consistency test, and the instance generation inference system is a means of successively refining the approximation.
A Decomposition Rule for Decision Procedures by Resolutionbased Calculi
 In: Proc. 11th Int. Conf. on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR
, 2004
"... Abstract. Resolutionbased calculi are among the most widely used calculi for theorem proving in firstorder logic. Numerous refinements of resolution are nowadays available, such as e.g. basic superposition, a calculus highly optimized for theorem proving with equality. However, even such an advanc ..."
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Cited by 31 (10 self)
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Abstract. Resolutionbased calculi are among the most widely used calculi for theorem proving in firstorder logic. Numerous refinements of resolution are nowadays available, such as e.g. basic superposition, a calculus highly optimized for theorem proving with equality. However, even such an advanced calculus does not restrict inferences enough to obtain decision procedures for complex logics, such as SHIQ. In this paper, we present a new decomposition inference rule, which can be combined with any resolutionbased calculus compatible with the standard notion of redundancy. We combine decomposition with basic superposition to obtain three new decision procedures: (i) for the description logic SHIQ, (ii) for the description logic ALCHIQb, and (iii) for answering conjunctive queries over SHIQ knowledge bases. The first two procedures are worstcase optimal and, based on the vast experience in building efficient theorem provers, we expect them to be suitable for practical usage. 1
Towards FirstOrder Temporal Resolution
 In KI 2001, Proceedings
"... In this paper we show how to extend clausal temporal resolution to the ground eventuality fragment of monodic firstorder temporal logic, which has recently been introduced by Hodkinson, Wolter and Zakharyaschev. While a finite Hilbertlike axiomatization of complete monodic first order temporal ..."
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Cited by 27 (13 self)
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In this paper we show how to extend clausal temporal resolution to the ground eventuality fragment of monodic firstorder temporal logic, which has recently been introduced by Hodkinson, Wolter and Zakharyaschev. While a finite Hilbertlike axiomatization of complete monodic first order temporal logic was developed by Wolter and Zakharyaschev, we propose a temporal resolutionbased proof system which reduces the satisfiability problem for ground eventuality monodic firstorder temporal formulae to the satisfiability problem for formulae of classical firstorder logic.
Monodic temporal resolution
 ACM Transactions on Computational Logic
, 2003
"... Until recently, FirstOrder Temporal Logic (FOTL) has been only partially understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However, a breakthrough by Hodkinson et al., identifying a f ..."
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Cited by 27 (15 self)
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Until recently, FirstOrder Temporal Logic (FOTL) has been only partially understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However, a breakthrough by Hodkinson et al., identifying a finitely axiomatisable fragment, termed the monodic fragment, has led to improved understanding of FOTL. Yet, in order to utilise these theoretical advances, it is important to have appropriate proof techniques for this monodic fragment. In this paper, we modify and extend the clausal temporal resolution technique, originally developed for propositional temporal logics, to enable its use in such monodic fragments. We develop a specific normal form for monodic formulae in FOTL, and provide a complete resolution calculus for formulae in this form. Not only is this clausal resolution technique useful as a practical proof technique for certain monodic classes, but the use of this approach provides us with increased understanding of the monodic fragment. In particular, we here show how several features of monodic FOTL can be established as corollaries of the completeness result for the clausal temporal resolution method. These include definitions of new decidable monodic classes, simplification of existing monodic classes by reductions, and completeness of clausal temporal resolution in the case of
A resolutionbased decision procedure for SHOIQ
 Proc. of the 3rd Int. Joint Conf. on Automated Reasoning (IJCAR 2006), volume 4130 of LNAI
, 2006
"... Abstract. We present a resolutionbased decision procedure for the description logic SHOIQ—the logic underlying the Semantic Web ontology language OWLDL. Our procedure is goaloriented, and it naturally extends a similar procedure for SHIQ, which has proven itself in practice. Applying existing tec ..."
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Cited by 24 (6 self)
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Abstract. We present a resolutionbased decision procedure for the description logic SHOIQ—the logic underlying the Semantic Web ontology language OWLDL. Our procedure is goaloriented, and it naturally extends a similar procedure for SHIQ, which has proven itself in practice. Applying existing techniques for deriving saturationbased decision procedures to SHOIQ is not straightforward due to nominals, number restrictions, and inverse roles—a combination known to cause termination problems. We overcome this difficulty by using the basic superposition calculus, extended with custom simplification rules. 1