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Christoph Weidenbach - One of the best experts on this subject based on the ideXlab platform.
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FroCos - On the Expressivity and Applicability of Model Representation Formalisms
Frontiers of Combining Systems, 2019Co-Authors: Andreas Teucke, Marco Voigt, Christoph WeidenbachAbstract:A number of first-order calculi employ an explicit model representation formalism in support of non-Redundant inferences and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) Clauses, is such a formalism used in the approximation refinement calculus (AR). Our first result is a finite model property for MSLH Clause sets. Therefore, MSLH Clause sets cannot represent models of Clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus (ME), to atoms with disequality constraints, the formalisms used in the non-Redundant Clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of Clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For Clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH Clause set formalism.
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On the Expressivity and Applicability of Model Representation Formalisms.
arXiv: Logic in Computer Science, 2019Co-Authors: Andreas Teucke, Marco Voigt, Christoph WeidenbachAbstract:A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) Clauses, is such a formalism used in the approximation refinement calculus. Our first result is a finite model property for MSLH Clause sets. Therefore, MSLH Clause sets cannot represent models of Clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus, to atoms with disequality constraints, the formalisms used in the non-Redundant Clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of Clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For Clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH Clause set formalism.
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On the Expressivity and Applicability of Model Representation Formalisms
2019Co-Authors: Andreas Teucke, Marco Voigt, Christoph WeidenbachAbstract:A number of first-order calculi employ an explicit model representation formalism in support of non-Redundant inferences and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) Clauses, is such a formalism used in the approximation refinement calculus (AR). Our first result is a finite model property for MSLH Clause sets. Therefore, MSLH Clause sets cannot represent models of Clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus (ME), to atoms with disequality constraints, the formalisms used in the non-Redundant Clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of Clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For Clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH Clause set formalism.
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FroCos - NRCL - A Model Building Approach toźthe Bernays-Schönfinkel Fragment
Frontiers of Combining Systems, 2015Co-Authors: Gábor Alagi, Christoph WeidenbachAbstract:We combine constrained literals for model representation with key concepts from first-order superposition and propositional conflict-driven Clause learning CDCL to create the new calculus Non-Redundant Clause Learning NRCL deciding the Bernays-Schonfinkel fragment. We use first-order literals constrained by disequalities between tuples of terms for compact model representation. From superposition, NRCL inherits the abstract redundancy criterion and the monotone model operator. CDCL adds the dynamic, conflict-driven search for a model. As a result, NRCL finds a false Clause modulo the current model candidate effectively. It guides the derivation of a first-order ordered resolvent that is never Redundant. Similar to 1UIP-learning in CDCL, the learned resolvent induces backtracking and, by blocking the previous conflict state via propagation, it enforces progress towards finding a model or a refutation. The non-redundancy result also implies that only finitely many Clauses can be generated by NRCL on the Bernays-Schonfinkel fragment, which proves termination.
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NRCL - A Model Building Approach to the Bernays-Schönfinkel Fragment (Full Paper).
arXiv: Logic in Computer Science, 2015Co-Authors: Gábor Alagi, Christoph WeidenbachAbstract:We combine constrained literals for model representation with key concepts from first-order superposition and propositional conflict-driven Clause learning (CDCL) to create the new calculus Non-Redundant Clause Learning (NRCL) deciding the Bernays-Sch\"onfinkel fragment. Our calculus uses first-order literals constrained by disequations between tuples of terms for compact model representation. From superposition, NRCL inherits the abstract redundancy criterion and the monotone model operator. CDCL adds the dynamic, conflict-driven search for an atom ordering inducing a model. As a result, in NRCL a false Clause can be found effectively modulo the current model candidate. It guides the derivation of a first-order ordered resolvent that is never Redundant. Similar to 1UIP-learning in CDCL, the learned resolvent induces backtracking and, by blocking the previous conflict state via propagation, it enforces progress towards finding a model or a refutation. The non-redundancy result also implies that only finitely many Clauses can be generated by NRCL on the Bernays-Sch\"onfinkel fragment, which serves as an argument for termination.
Weidenbach Christoph - One of the best experts on this subject based on the ideXlab platform.
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On the Expressivity and Applicability of Model Representation Formalisms
2019Co-Authors: Teucke Andreas, Voigt Marco, Weidenbach ChristophAbstract:A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) Clauses, is such a formalism used in the approximation refinement calculus. Our first result is a finite model property for MSLH Clause sets. Therefore, MSLH Clause sets cannot represent models of Clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus, to atoms with disequality constraints, the formalisms used in the non-Redundant Clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of Clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For Clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH Clause set formalism.Comment: 15 page
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On the Expressivity and Applicability of Model Representation Formalisms
Springer, 2019Co-Authors: Teucke Andreas, Voigt Marco, Weidenbach ChristophAbstract:International audienceA number of first-order calculi employ an explicit model representation formalism in support of non-Redundant inferences and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) Clauses, is such a formalism used in the approximation refinement calculus (AR). Our first result is a finite model property for MSLH Clause sets. Therefore, MSLH Clause sets cannot represent models of Clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus (ME), to atoms with disequality constraints, the formalisms used in the non-Redundant Clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of Clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For Clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH Clause set formalism
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{NRCL} - a model building approach to the {Bernays-Schönfinkel} fragment
'Springer Science and Business Media LLC', 2015Co-Authors: Alagi Gábor, Weidenbach ChristophAbstract:International audienceWe combine constrained literals for model representation with key concepts from first-order superposition and propositional conflict-driven Clause learning (CDCL) to create the new calculus Non-Redundant Clause Learning (NRCL) deciding the Bernays-Schönfinkel fragment. We use first-order literals constrained by disequalities between tuples of terms for compact model representation. From superposition, NRCL inherits the abstract redundancy criterion and the monotone model operator. CDCL adds the dynamic, conflict-driven search for a model. As a result, NRCL finds a false Clause modulo the current model candidate effectively. It guides the derivation of a first-order ordered resolvent that is never Redundant. Similar to 1UIP-learning in CDCL, the learned resolvent induces backtracking and, by blocking the previous conflict state via propagation, it enforces progress towards finding a model or a refutation. The non-redundancy result also implies that only finitely many Clauses can be generated by NRCL on the Bernays-Schönfinkel fragment, which proves termination
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NRCL - A Model Building Approach to the Bernays-Sch\"onfinkel Fragment (Full Paper)
2015Co-Authors: Alagi Gábor, Weidenbach ChristophAbstract:We combine constrained literals for model representation with key concepts from first-order superposition and propositional conflict-driven Clause learning (CDCL) to create the new calculus Non-Redundant Clause Learning (NRCL) deciding the Bernays-Sch\"onfinkel fragment. Our calculus uses first-order literals constrained by disequations between tuples of terms for compact model representation. From superposition, NRCL inherits the abstract redundancy criterion and the monotone model operator. CDCL adds the dynamic, conflict-driven search for an atom ordering inducing a model. As a result, in NRCL a false Clause can be found effectively modulo the current model candidate. It guides the derivation of a first-order ordered resolvent that is never Redundant. Similar to 1UIP-learning in CDCL, the learned resolvent induces backtracking and, by blocking the previous conflict state via propagation, it enforces progress towards finding a model or a refutation. The non-redundancy result also implies that only finitely many Clauses can be generated by NRCL on the Bernays-Sch\"onfinkel fragment, which serves as an argument for termination
Joao Marques-silva - One of the best experts on this subject based on the ideXlab platform.
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Algorithms for computing minimal equivalent subformulas
Artificial Intelligence, 2014Co-Authors: Anton Belov, Mikoláš Janota, Inês Lynce, Joao Marques-silvaAbstract:Knowledge representation and reasoning using propositional logic is an important component of AI systems. A propositional formula in Conjunctive Normal Form (CNF) may contain Redundant Clauses — Clauses whose removal from the formula does not affect the set of its models. Identification of Redundant Clauses is important because redundancy often leads to unnecessary computation, wasted storage, and may obscure the structure of the problem. A formula obtained by the removal of all Redundant Clauses from a given CNF formula F is called a Minimal Equivalent Subformula (MES) of F. This paper proposes a number of efficient algorithms and optimization techniques for the computation of MESes. Previous work on MES computation proposes a simple algorithm based on iterative application of the definition of a Redundant Clause, similar to the well-known deletion-based approach for the computation of Minimal Unsatisfiable Subformulas (MUSes). This paper observes that, in fact, most of the existing algorithms for the computation of MUSes can be adapted to the computation of MESes. However, some of the optimization techniques that are crucial for the performance of the state-of-the-art MUS extractors cannot be applied in the context of MES computation, and thus the resulting algorithms are often not efficient in practice. To address the problem of efficient computation of MESes, the paper develops a new class of algorithms that are based on the iterative analysis of subsets of Clauses, and a lightweight pruning technique based on the computation of backbones. The experimental results, obtained on representative problem instances, confirm the effectiveness of the proposed methods. The experimental results also reveal that many CNF instances obtained from the practical applications of SAT exhibit a large degree of redundancy.
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CP - On Computing Minimal Equivalent Subformulas
Lecture Notes in Computer Science, 2012Co-Authors: Anton Belov, Mikoláš Janota, Inês Lynce, Joao Marques-silvaAbstract:A propositional formula in Conjunctive Normal Form (CNF) may contain Redundant Clauses -- Clauses whose removal from the formula does not affect the set of its models. Identification of Redundant Clauses is important because redundancy often leads to unnecessary computation, wasted storage, and may obscure the structure of the problem. A formula obtained by the removal of all Redundant Clauses from a given CNF formula ${\mathcal{F}}$ is called a Minimal Equivalent Subformula (MES) of ${\mathcal{F}}$. This paper proposes a number of efficient algorithms and optimization techniques for the computation of MESes. Previous work on MES computation proposes a simple algorithm based on iterative application of the definition of a Redundant Clause, similar to the well-known deletion-based approach for the computation of Minimal Unsatisfiable Subformulas (MUSes). This paper observes that, in fact, most of the existing algorithms for the computation of MUSes can be adapted to the computation of MESes. However, some of the optimization techniques that are crucial for the performance of the state-of-the-art MUS extractors cannot be applied in the context of MES computation, and thus the resulting algorithms are often not efficient in practice. To address the problem of efficient computation of MESes, the paper develops a new class of algorithms that are based on the iterative analysis of subsets of Clauses. The experimental results, obtained on representative problem instances, confirm the effectiveness of the proposed algorithms. The experimental results also reveal that many CNF instances obtained from the practical applications of SAT exhibit a large degree of redundancy.
Anton Belov - One of the best experts on this subject based on the ideXlab platform.
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Algorithms for computing minimal equivalent subformulas
Artificial Intelligence, 2014Co-Authors: Anton Belov, Mikoláš Janota, Inês Lynce, Joao Marques-silvaAbstract:Knowledge representation and reasoning using propositional logic is an important component of AI systems. A propositional formula in Conjunctive Normal Form (CNF) may contain Redundant Clauses — Clauses whose removal from the formula does not affect the set of its models. Identification of Redundant Clauses is important because redundancy often leads to unnecessary computation, wasted storage, and may obscure the structure of the problem. A formula obtained by the removal of all Redundant Clauses from a given CNF formula F is called a Minimal Equivalent Subformula (MES) of F. This paper proposes a number of efficient algorithms and optimization techniques for the computation of MESes. Previous work on MES computation proposes a simple algorithm based on iterative application of the definition of a Redundant Clause, similar to the well-known deletion-based approach for the computation of Minimal Unsatisfiable Subformulas (MUSes). This paper observes that, in fact, most of the existing algorithms for the computation of MUSes can be adapted to the computation of MESes. However, some of the optimization techniques that are crucial for the performance of the state-of-the-art MUS extractors cannot be applied in the context of MES computation, and thus the resulting algorithms are often not efficient in practice. To address the problem of efficient computation of MESes, the paper develops a new class of algorithms that are based on the iterative analysis of subsets of Clauses, and a lightweight pruning technique based on the computation of backbones. The experimental results, obtained on representative problem instances, confirm the effectiveness of the proposed methods. The experimental results also reveal that many CNF instances obtained from the practical applications of SAT exhibit a large degree of redundancy.
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CP - On Computing Minimal Equivalent Subformulas
Lecture Notes in Computer Science, 2012Co-Authors: Anton Belov, Mikoláš Janota, Inês Lynce, Joao Marques-silvaAbstract:A propositional formula in Conjunctive Normal Form (CNF) may contain Redundant Clauses -- Clauses whose removal from the formula does not affect the set of its models. Identification of Redundant Clauses is important because redundancy often leads to unnecessary computation, wasted storage, and may obscure the structure of the problem. A formula obtained by the removal of all Redundant Clauses from a given CNF formula ${\mathcal{F}}$ is called a Minimal Equivalent Subformula (MES) of ${\mathcal{F}}$. This paper proposes a number of efficient algorithms and optimization techniques for the computation of MESes. Previous work on MES computation proposes a simple algorithm based on iterative application of the definition of a Redundant Clause, similar to the well-known deletion-based approach for the computation of Minimal Unsatisfiable Subformulas (MUSes). This paper observes that, in fact, most of the existing algorithms for the computation of MUSes can be adapted to the computation of MESes. However, some of the optimization techniques that are crucial for the performance of the state-of-the-art MUS extractors cannot be applied in the context of MES computation, and thus the resulting algorithms are often not efficient in practice. To address the problem of efficient computation of MESes, the paper develops a new class of algorithms that are based on the iterative analysis of subsets of Clauses. The experimental results, obtained on representative problem instances, confirm the effectiveness of the proposed algorithms. The experimental results also reveal that many CNF instances obtained from the practical applications of SAT exhibit a large degree of redundancy.
Gábor Alagi - One of the best experts on this subject based on the ideXlab platform.
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FroCos - NRCL - A Model Building Approach toźthe Bernays-Schönfinkel Fragment
Frontiers of Combining Systems, 2015Co-Authors: Gábor Alagi, Christoph WeidenbachAbstract:We combine constrained literals for model representation with key concepts from first-order superposition and propositional conflict-driven Clause learning CDCL to create the new calculus Non-Redundant Clause Learning NRCL deciding the Bernays-Schonfinkel fragment. We use first-order literals constrained by disequalities between tuples of terms for compact model representation. From superposition, NRCL inherits the abstract redundancy criterion and the monotone model operator. CDCL adds the dynamic, conflict-driven search for a model. As a result, NRCL finds a false Clause modulo the current model candidate effectively. It guides the derivation of a first-order ordered resolvent that is never Redundant. Similar to 1UIP-learning in CDCL, the learned resolvent induces backtracking and, by blocking the previous conflict state via propagation, it enforces progress towards finding a model or a refutation. The non-redundancy result also implies that only finitely many Clauses can be generated by NRCL on the Bernays-Schonfinkel fragment, which proves termination.
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NRCL - A Model Building Approach to the Bernays-Schönfinkel Fragment (Full Paper).
arXiv: Logic in Computer Science, 2015Co-Authors: Gábor Alagi, Christoph WeidenbachAbstract:We combine constrained literals for model representation with key concepts from first-order superposition and propositional conflict-driven Clause learning (CDCL) to create the new calculus Non-Redundant Clause Learning (NRCL) deciding the Bernays-Sch\"onfinkel fragment. Our calculus uses first-order literals constrained by disequations between tuples of terms for compact model representation. From superposition, NRCL inherits the abstract redundancy criterion and the monotone model operator. CDCL adds the dynamic, conflict-driven search for an atom ordering inducing a model. As a result, in NRCL a false Clause can be found effectively modulo the current model candidate. It guides the derivation of a first-order ordered resolvent that is never Redundant. Similar to 1UIP-learning in CDCL, the learned resolvent induces backtracking and, by blocking the previous conflict state via propagation, it enforces progress towards finding a model or a refutation. The non-redundancy result also implies that only finitely many Clauses can be generated by NRCL on the Bernays-Sch\"onfinkel fragment, which serves as an argument for termination.
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{NRCL} - a model building approach to the {Bernays-Schönfinkel} fragment
2015Co-Authors: Gábor Alagi, Christoph WeidenbachAbstract:We combine constrained literals for model representation with key concepts from first-order superposition and propositional conflict-driven Clause learning (CDCL) to create the new calculus Non-Redundant Clause Learning (NRCL) deciding the Bernays-Schönfinkel fragment. We use first-order literals constrained by disequalities between tuples of terms for compact model representation. From superposition, NRCL inherits the abstract redundancy criterion and the monotone model operator. CDCL adds the dynamic, conflict-driven search for a model. As a result, NRCL finds a false Clause modulo the current model candidate effectively. It guides the derivation of a first-order ordered resolvent that is never Redundant. Similar to 1UIP-learning in CDCL, the learned resolvent induces backtracking and, by blocking the previous conflict state via propagation, it enforces progress towards finding a model or a refutation. The non-redundancy result also implies that only finitely many Clauses can be generated by NRCL on the Bernays-Schönfinkel fragment, which proves termination.