The Experts below are selected from a list of 213 Experts worldwide ranked by ideXlab platform
Albert Rubio - One of the best experts on this subject based on the ideXlab platform.
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Paramodulation with well-founded orderings
2016Co-Authors: Miquel Bofill, Albert RubioAbstract:Abstract For many years, all existing completeness results for Knuth-Bendix completion and Ordered Paramodulation required the term order-ing ≻ to be well-founded, monotonic and total(izable) on ground terms. Then, it was shown that well-foundedness and the subterm property were enough for ensuring completeness of Ordered Paramodulation. Here we show that the subterm property is not necessary either. By us-ing a new restricted form of rewriting, we obtain a completeness proof of Ordered Paramodulation for Horn clauses with equality, where well-foundedness of the ordering suffices. Apart from the theoretical signifi-cance of this result, some potential applications motivating the interest of dropping the subterm property are given. The proof of the results included in this paper, being still technical in some parts, is pretty much shorter and easier to read than the one we have in the preliminary version of this work presented at the CADE 2002 conference [8]. Key words: term rewriting, equational reasoning, theorem proving, Paramodulation, Knuth-Bendix completion
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Paramodulation with Non-Monotonic Orderings and Simplification
Journal of Automated Reasoning, 2013Co-Authors: Miquel Bofill, Albert RubioAbstract:Ordered Paramodulation and Knuth-Bendix completion are known to remain complete when using non-monotonic orderings. However, these results do not imply the compatibility of the calculus with essential redundancy elimination techniques such as demodulation, i.e., simplification by rewriting, which constitute the primary mode of computation in most successful automated theorem provers. In this paper we present a complete Ordered Paramodulation calculus for non-monotonic orderings which is compatible with powerful redundancy notions including demodulation, hence strictly improving the previous results and making the calculus more likely to be used in practice. As a side effect, we obtain a Knuth-Bendix completion procedure compatible with simplification techniques, which can be used for finding, whenever it exists, a convergent term rewrite system for a given set of equations and a (possibly non-totalizable) reduction ordering.
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Paramodulation with Well-founded Orderings
Journal of Logic and Computation, 2008Co-Authors: Miquel Bofill, Albert RubioAbstract:For many years, all existing completeness results for Knuth–Bendix completion and Ordered Paramodulation required the term ordering ≻ to be well-founded, monotonic and total(izable) on ground terms. Then, it was shown that well-foundedness and the subterm property were enough for ensuring completeness of Ordered Paramodulation. Here we show that the subterm property is not necessary either. By using a new restricted form of rewriting, we obtain a completeness proof of Ordered Paramodulation for Horn clauses with equality, where well-foundedness of the ordering suffices. Apart from the theoretical significance of this result, some potential applications motivating the interest of dropping the subterm property are given. The proof of the results included in this article, being still technical in some parts, is pretty much shorter and easier to read than the one we have in the preliminary version of this work presented at the CADE, 2002 conference (Bofill, and Rubio, 2002, CADE, Vol. 2392 of LNAI, pp. 456–470).
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IJCAR - Redundancy Notions for Paramodulation with Non-monotonic Orderings
Automated Reasoning, 2004Co-Authors: Miquel Bofill, Albert RubioAbstract:Recently, Ordered Paramodulation and Knuth-Bendix completion were shown to remain complete when using non-monotonic orderings. However, these results only implied the compatibility with too weak redundancy notions and, in particular, demodulation could not be applied at all.
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Paramodulation and Knuth–Bendix Completion with Nontotal and Nonmonotonic Orderings
Journal of Automated Reasoning, 2003Co-Authors: Miquel Bofill, Guillem Godoy, Robert Nieuwenhuis, Albert RubioAbstract:Up to now, all existing completeness results for Ordered Paramodulation and Knuth–Bendix completion have required term ordering ≻ to be well founded, monotonic, and total(izable) on ground terms. For several applications, these requirements are too strong, and hence weakening them has been a well-known research challenge. Here we introduce a new completeness proof technique for Ordered Paramodulation where the only properties required on ≻ are well-foundedness and the subterm property. The technique is a relatively simple and elegant application of some fundamental results on the termination and confluence of ground term rewrite systems (TRS). By a careful further analysis of our technique, we obtain the first Knuth–Bendix completion procedure that finds a convergent TRS for a given set of equations E and a (possibly non-totalizable) reduction ordering ≻ whenever it exists. Note that being a reduction ordering is the minimal possible requirement on ≻, since a TRS terminates if, and only if, it is contained in a reduction ordering.
Miquel Bofill - One of the best experts on this subject based on the ideXlab platform.
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Paramodulation with well-founded orderings
2016Co-Authors: Miquel Bofill, Albert RubioAbstract:Abstract For many years, all existing completeness results for Knuth-Bendix completion and Ordered Paramodulation required the term order-ing ≻ to be well-founded, monotonic and total(izable) on ground terms. Then, it was shown that well-foundedness and the subterm property were enough for ensuring completeness of Ordered Paramodulation. Here we show that the subterm property is not necessary either. By us-ing a new restricted form of rewriting, we obtain a completeness proof of Ordered Paramodulation for Horn clauses with equality, where well-foundedness of the ordering suffices. Apart from the theoretical signifi-cance of this result, some potential applications motivating the interest of dropping the subterm property are given. The proof of the results included in this paper, being still technical in some parts, is pretty much shorter and easier to read than the one we have in the preliminary version of this work presented at the CADE 2002 conference [8]. Key words: term rewriting, equational reasoning, theorem proving, Paramodulation, Knuth-Bendix completion
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Paramodulation with Non-Monotonic Orderings and Simplification
Journal of Automated Reasoning, 2013Co-Authors: Miquel Bofill, Albert RubioAbstract:Ordered Paramodulation and Knuth-Bendix completion are known to remain complete when using non-monotonic orderings. However, these results do not imply the compatibility of the calculus with essential redundancy elimination techniques such as demodulation, i.e., simplification by rewriting, which constitute the primary mode of computation in most successful automated theorem provers. In this paper we present a complete Ordered Paramodulation calculus for non-monotonic orderings which is compatible with powerful redundancy notions including demodulation, hence strictly improving the previous results and making the calculus more likely to be used in practice. As a side effect, we obtain a Knuth-Bendix completion procedure compatible with simplification techniques, which can be used for finding, whenever it exists, a convergent term rewrite system for a given set of equations and a (possibly non-totalizable) reduction ordering.
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Paramodulation with Well-founded Orderings
Journal of Logic and Computation, 2008Co-Authors: Miquel Bofill, Albert RubioAbstract:For many years, all existing completeness results for Knuth–Bendix completion and Ordered Paramodulation required the term ordering ≻ to be well-founded, monotonic and total(izable) on ground terms. Then, it was shown that well-foundedness and the subterm property were enough for ensuring completeness of Ordered Paramodulation. Here we show that the subterm property is not necessary either. By using a new restricted form of rewriting, we obtain a completeness proof of Ordered Paramodulation for Horn clauses with equality, where well-foundedness of the ordering suffices. Apart from the theoretical significance of this result, some potential applications motivating the interest of dropping the subterm property are given. The proof of the results included in this article, being still technical in some parts, is pretty much shorter and easier to read than the one we have in the preliminary version of this work presented at the CADE, 2002 conference (Bofill, and Rubio, 2002, CADE, Vol. 2392 of LNAI, pp. 456–470).
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IJCAR - Redundancy Notions for Paramodulation with Non-monotonic Orderings
Automated Reasoning, 2004Co-Authors: Miquel Bofill, Albert RubioAbstract:Recently, Ordered Paramodulation and Knuth-Bendix completion were shown to remain complete when using non-monotonic orderings. However, these results only implied the compatibility with too weak redundancy notions and, in particular, demodulation could not be applied at all.
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Paramodulation and Knuth–Bendix Completion with Nontotal and Nonmonotonic Orderings
Journal of Automated Reasoning, 2003Co-Authors: Miquel Bofill, Guillem Godoy, Robert Nieuwenhuis, Albert RubioAbstract:Up to now, all existing completeness results for Ordered Paramodulation and Knuth–Bendix completion have required term ordering ≻ to be well founded, monotonic, and total(izable) on ground terms. For several applications, these requirements are too strong, and hence weakening them has been a well-known research challenge. Here we introduce a new completeness proof technique for Ordered Paramodulation where the only properties required on ≻ are well-foundedness and the subterm property. The technique is a relatively simple and elegant application of some fundamental results on the termination and confluence of ground term rewrite systems (TRS). By a careful further analysis of our technique, we obtain the first Knuth–Bendix completion procedure that finds a convergent TRS for a given set of equations E and a (possibly non-totalizable) reduction ordering ≻ whenever it exists. Note that being a reduction ordering is the minimal possible requirement on ≻, since a TRS terminates if, and only if, it is contained in a reduction ordering.
Harald Ganzinger - One of the best experts on this subject based on the ideXlab platform.
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Integrating equational reasoning intoinstantiation-based theorem proving
2008Co-Authors: Harald Ganzinger, Konstantin KorovinAbstract:Abstract. In this paper we present a method for integrating equational reason-ing into instantiation-based theorem proving. The method employs a satisfiability solver for ground equational clauses together with an instance generation processbased on an Ordered Paramodulation type calculus for literals. The completeness of the procedure is proved using the the model generation technique, which al-lows us to justify redundancy elimination based on appropriate orderings
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CSL - Integrating Equational Reasoning into Instantiation-Based Theorem Proving
Computer Science Logic, 2004Co-Authors: Harald Ganzinger, Konstantin KorovinAbstract:In this paper we present a method for integrating equational reasoning into instantiation-based theorem proving. The method employs a satisfiability solver for ground equational clauses together with an instance generation process based on an Ordered Paramodulation type calculus for literals. The completeness of the procedure is proved using the the model generation technique, which allows us to justify redundancy elimination based on appropriate orderings.
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Basic Paramodulation
Information and Computation, 1995Co-Authors: Leo Bachmair, Harald Ganzinger, Christopher S. Lynch, Wayne SnyderAbstract:AbstractWe introduce a class of restrictions for the Ordered Paramodulation and superposition calculi (inspired by the basic strategy for narrowing), which forbid Paramodulation inferences at terms introduced by substitutions from previous inference steps. In addition we introduce restrictions based on term selection rules and redex orderings, which are general criteria for delimiting the terms which are available for inferences. These refinements are compatible with standard ordering restrictions and are complete without Paramodulation into variables or using functional reflexivity axioms. We prove refutational completeness in the context of deletion rules, such as simplification by rewriting (demodulation) and subsumption, and of techniques for eliminating redundant inferences
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Basic Paramodulation
1995Co-Authors: Leo Bachmair, Harald Ganzinger, Christopher Lynch, Wayne SnyderAbstract:We introduce a class of restrictions for the Ordered Paramodulation and superposition calculi (inspired by the basic strategy for narrowing), in which Paramodulation inferences are forbidden at terms introduced by substitutions from previous inference steps. In addition we introduce restrictions based on term selection rules and redex orderings, which are general criteria for delimiting the terms which are available for inferences. These refinements are compatible with standard ordering restrictions and are complete without Paramodulation into variables or using functional reflexivity axioms. We prove refutational completeness in the context of deletion rules, such as simplification by rewriting (demodulation) and subsumption, and of techniques for eliminating redundant inferences
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CADE - Basic Paramodulation and Superposition
Automated Deduction—CADE-11, 1992Co-Authors: Leo Bachmair, Harald Ganzinger, Christopher S. Lynch, Wayne SnyderAbstract:We introduce a class of restrictions for the Ordered Paramodulation and superposition calculi (inspired by the basic strategy for narrowing), in which Paramodulation inferences are forbidden at terms introduced by substitutions from previous inference steps. These refinements are compatible with standard ordering restrictions and are complete without Paramodulation into variables or using functional reflexivity axioms. We prove refutational completeness in the context of deletion rules, such as simplification by rewriting (demodulation) and subsumption, and of techniques for eliminating redundant inferences. Finally, we discuss experimental data obtained from a modification of Otter.
Andrei Voronkov - One of the best experts on this subject based on the ideXlab platform.
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CADE - Efficient instance retrieval with standard and relational path indexing
2005Co-Authors: Alexandre Riazanov, Andrei VoronkovAbstract:Backward demodulation is a simplification technique used in saturation-based theorem proving with superposition and Ordered Paramodulation. It requires instance retrieval, i.e., search for instances of some term in a typically large set of terms. Path indexing is a family of indexing techniques that can be used to solve this problem efficiently. We propose a number of powerful optimisations to standard path indexing. We also describe a novel framework that combines path indexing with relational joins. The main advantage of the proposed scheme is flexibility, which we illustrate by sketching how to adapt the scheme to instance retrieval modulo commutativity and backward subsumption on multi-literal clauses.
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Efficient instance retrieval with standard and relational path indexing
Information and Computation, 2005Co-Authors: Alexandre Riazanov, Andrei VoronkovAbstract:AbstractBackward demodulation is a simplification technique used in saturation-based theorem proving with superposition and Ordered Paramodulation. It requires instance retrieval, i.e., search for instances of some term in a typically large set of terms. Path indexing is a family of indexing techniques that can be used to solve this problem efficiently. We propose a number of powerful optimisations to standard path indexing. We also describe a novel framework that combines path indexing with relational joins. The main advantage of the proposed scheme is flexibility, which we illustrate by sketching how to adapt the scheme to instance retrieval modulo commutativity and backward subsumption on multi-literal clauses
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Automated Deduction - CADE-18, 18th International Conference on Automated Deduction, Copenhagen, Denmark, July 27-30, 2002, Proceedings
2002Co-Authors: Andrei VoronkovAbstract:Description Logics and Semantic Web.- Reasoning with Expressive Description Logics: Theory and Practice.- BDD-Based Decision Procedures for .- Proof-Carrying Code and Compiler Verification.- Temporal Logic for Proof-Carrying Code.- A Gradual Approach to a More Trustworthy, Yet Scalable, Proof-Carrying Code.- Formal Verification of a Java Compiler in Isabelle.- Non-classical Logics.- Embedding Lax Logic into Intuitionistic Logic.- Combining Proof-Search and Counter-Model Construction for Deciding Godel-Dummett Logic.- Connection-Based Proof Search in Propositional BI Logic.- System Descriptions.- DDDLIB: A Library for Solving Quantified Difference Inequalities.- An LCF-Style Interface between HOL and First-Order Logic.- System Description: The MathWeb Software Bus for Distributed Mathematical Reasoning.- Proof Development with ?mega.- Learn?matic: System Description.- HyLoRes 1.0: Direct Resolution for Hybrid Logics.- SAT.- Testing Satisfiability of CNF Formulas by Computing a Stable Set of Points.- A Note on Symmetry Heuristics in SEM.- A SAT Based Approach for Solving Formulas over Boolean and Linear Mathematical Propositions.- Model Generation.- Deductive Search for Errors in Free Data Type Specifications Using Model Generation.- Reasoning by Symmetry and Function Ordering in Finite Model Generation.- Algorithmic Aspects of Herbrand Models Represented by Ground Atoms with Ground Equations.- Session 7.- A New Clausal Class Decidable by Hyperresolution.- CASC.- Spass Version 2.0.- System Description: GrAnDe 1.0.- The HR Program for Theorem Generation.- AutoBayes/CC - Combining Program Synthesis with Automatic Code Certification - System Description -.- CADE-CAV Invited Talk.- The Quest for Efficient Boolean Satisfiability Solvers.- Session 9.- Recursive Path Orderings Can Be Context-Sensitive.- Combination of Decision Procedures.- Shostak Light.- Formal Verification of a Combination Decision Procedure.- Combining Multisets with Integers.- Logical Frameworks.- The Reflection Theorem: A Study in Meta-theoretic Reasoning.- Faster Proof Checking in the Edinburgh Logical Framework.- Solving for Set Variables in Higher-Order Theorem Proving.- Model Checking.- The Complexity of the Graded ?-Calculus.- Lazy Theorem Proving for Bounded Model Checking over Infinite Domains.- Equational Reasoning.- Well-Foundedness Is Sufficient for Completeness of Ordered Paramodulation.- Basic Syntactic Mutation.- The Next Waldmeister Loop.- Proof Theory.- Focussing Proof-Net Construction as a Middleware Paradigm.- Proof Analysis by Resolution.
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Logic programming and automated reasoning : 4th International Conference, LPAR '93, St. Petersburg, Russia, July 13-20, 1993 : proceedings
1993Co-Authors: Andrei VoronkovAbstract:Entailment and disentailment of order-sorted feature constraints.- Computing extensions of default logic - Preliminary report.- Prolog with arrays and bounded quantifications.- Linear 0-1 inequalities and extended clauses.- Search space pruning by checking dynamic term growth.- A proof search system for a modal substructural logic based on labelled deductive systems.- Consistency checking of automata functional specifications.- Yet another application for Toupie: Verification of mutual exclusion algorithms.- Parsing with DCG-terms.- A first order resolution calculus with symmetries.- Ordered Paramodulation and resolution as decision procedure.- Static analysis of Prolog with cut.- A new type theory for representing logics.- Verification of Switch-level designs with many-valued logic.- Deciding in HFS-theory via linear integer programming.- The completion of typed logic programs and SLDNF-resolution.- Increasing the versatility of heuristic based theorem provers.- Sequentialization of parallel logic programs with mode analysis.- Refinements and extensions of model elimination.- Executable specifications based on dynamic algebras.- Generic resolution in propositional modal systems.- Optimized translation of multi modal logic into predicate logic.- Default reasoning with a constraint resolution principle.- Non-clausal deductive techniques for computing prime implicants and prime implicates.- Unification under one-sided distributivity with a multiplicative unit.- Unification in Order-Sorted Logic with Term Declarations.- Extracting inheritance hierarchies from Prolog programs: A system based on the inference of type relations.- A comparison of mechanisms for avoiding repetition of subdeductions in chain format linear deduction systems.- Neutralization and preemption in extended logic programs.- MULTLOG: A system for axiomatizing many-valued logics.- SKIL: A system for programming with proofs.- Reasoning about the reals: the marriage of HOL and maple.- System description of LAMBDALG.- Mixing metafor.- A complete axiom system for isomorphism of types in closed categories.- Reasoning, modeling, and component-based technology.
Gernot Salzer - One of the best experts on this subject based on the ideXlab platform.
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Ordered Paramodulation and resolution as decision procedure
International Conference on Logic Programming, 1993Co-Authors: Christian G Fermuller, Gernot SalzerAbstract:In recent years interesting decidability results for syntactically specified classes of clause sets have been achieved by employing resolution as a decision procedure. We extend this line of research by considering also clauses with equality literals. We use a special version of Ordered Paramodulation and resolution to decide a class of clause sets that corresponds to an extension of the Ackermann class with equality (i.e., prenex formulas with prefixes of type ∃*∀∃*). By encoding Turing machines we also show that slight modifications of the defining conditions for this class lead to undecidability.
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LPAR - Ordered Paramodulation and Resolution as Decision Procedure
Logic Programming and Automated Reasoning, 1993Co-Authors: Christian G Fermuller, Gernot SalzerAbstract:In recent years interesting decidability results for syntactically specified classes of clause sets have been achieved by employing resolution as a decision procedure. We extend this line of research by considering also clauses with equality literals. We use a special version of Ordered Paramodulation and resolution to decide a class of clause sets that corresponds to an extension of the Ackermann class with equality (i.e., prenex formulas with prefixes of type ∃*∀∃*). By encoding Turing machines we also show that slight modifications of the defining conditions for this class lead to undecidability.