The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform
Clare Dixon - One of the best experts on this subject based on the ideXlab platform.
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A Resolution-Based Theorem Prover for $${\textsf {K}}_{n}^{}$$Kn: Architecture, Refinements, Strategies and Experiments
Journal of Automated Reasoning, 2020Co-Authors: Cláudia Nalon, Ullrich Hustadt, Clare DixonAbstract:In this paper we describe the implementation of , a resolution-based prover for the basic Multimodal Logic $${\textsf {K}}_{n}^{}$$ K n . The prover implements a resolution-based calculus for both local and global reasoning. The user can choose different normal forms, refinements of the basic resolution calculus, and strategies. We describe these options in detail and discuss their implications. We provide experiments comparing some of these options and comparing the prover with other provers for this Logic.
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A Resolution-Based Theorem Prover for \({\textsf {K}}_{n}^{}\) : Architecture, Refinements, Strategies and Experiments
Journal of Automated Reasoning, 2020Co-Authors: Cláudia Nalon, Ullrich Hustadt, Clare DixonAbstract:In this paper we describe the implementation of , a resolution-based prover for the basic Multimodal Logic $${\textsf {K}}_{n}^{}$$ . The prover implements a resolution-based calculus for both local and global reasoning. The user can choose different normal forms, refinements of the basic resolution calculus, and strategies. We describe these options in detail and discuss their implications. We provide experiments comparing some of these options and comparing the prover with other provers for this Logic.
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Modal Resolution: Proofs, Layers and Refinements
ACM Transactions on Computational Logic, 2019Co-Authors: Cláudia Nalon, Clare Dixon, Ullrich HustadtAbstract:Resolution-based provers for Multimodal normal Logics require pruning of the search space for a proof in order to ameliorate the inherent intractability of the satisfiability problem for such Logics. We present a clausal modal-layered hyper-resolution calculus for the basic Multimodal Logic, which divides the clause set according to the modal level at which clauses occur in order to reduce the number of possible inferences. We show that the calculus is complete for the Logics being considered. We also show that the calculus can be combined with other strategies. In particular, we discuss the completeness of combining modal layering with negative and ordered resolution and provide experimental results comparing the different refinements.
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IJCAI - KSP: A Resolution-based Prover for Multimodal K, Abridged Report
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, 2017Co-Authors: Cláudia Nalon, Ullrich Hustadt, Clare DixonAbstract:We briefly describe an implementation of a hyperresolution-based calculus for the propositional basic Multimodal Logic, Kn. The prover, KSP, which allows for both local and global reasoning, is designed to support experimentation with different combinations of refinements for its basic calculus. We present an experimental evaluation that compares K S P with a range of existing reasoners for Kn.
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Open image in new window: A Resolution-Based Prover for Multimodal K
2016Co-Authors: Cláudia Nalon, Ullrich Hustadt, Clare DixonAbstract:In this paper, we describe an implementation of a hyper-resolution-based calculus for the propositional basic Multimodal Logic, Open image in new window . The prover was designed to support experimentation with different combinations of refinements for its basic calculus: it is primarily based on the set of support strategy, which can then be combined with other refinements, simplification techniques and different choices for the underlying normal form and clause selection. The prover allows for both local and global reasoning. We show experimental results for different combinations of strategies and comparison with existing tools.
Cláudia Nalon - One of the best experts on this subject based on the ideXlab platform.
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A Resolution-Based Theorem Prover for $${\textsf {K}}_{n}^{}$$Kn: Architecture, Refinements, Strategies and Experiments
Journal of Automated Reasoning, 2020Co-Authors: Cláudia Nalon, Ullrich Hustadt, Clare DixonAbstract:In this paper we describe the implementation of , a resolution-based prover for the basic Multimodal Logic $${\textsf {K}}_{n}^{}$$ K n . The prover implements a resolution-based calculus for both local and global reasoning. The user can choose different normal forms, refinements of the basic resolution calculus, and strategies. We describe these options in detail and discuss their implications. We provide experiments comparing some of these options and comparing the prover with other provers for this Logic.
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A Resolution-Based Theorem Prover for \({\textsf {K}}_{n}^{}\) : Architecture, Refinements, Strategies and Experiments
Journal of Automated Reasoning, 2020Co-Authors: Cláudia Nalon, Ullrich Hustadt, Clare DixonAbstract:In this paper we describe the implementation of , a resolution-based prover for the basic Multimodal Logic $${\textsf {K}}_{n}^{}$$ . The prover implements a resolution-based calculus for both local and global reasoning. The user can choose different normal forms, refinements of the basic resolution calculus, and strategies. We describe these options in detail and discuss their implications. We provide experiments comparing some of these options and comparing the prover with other provers for this Logic.
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Modal Resolution: Proofs, Layers and Refinements
ACM Transactions on Computational Logic, 2019Co-Authors: Cláudia Nalon, Clare Dixon, Ullrich HustadtAbstract:Resolution-based provers for Multimodal normal Logics require pruning of the search space for a proof in order to ameliorate the inherent intractability of the satisfiability problem for such Logics. We present a clausal modal-layered hyper-resolution calculus for the basic Multimodal Logic, which divides the clause set according to the modal level at which clauses occur in order to reduce the number of possible inferences. We show that the calculus is complete for the Logics being considered. We also show that the calculus can be combined with other strategies. In particular, we discuss the completeness of combining modal layering with negative and ordered resolution and provide experimental results comparing the different refinements.
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IJCAI - KSP: A Resolution-based Prover for Multimodal K, Abridged Report
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, 2017Co-Authors: Cláudia Nalon, Ullrich Hustadt, Clare DixonAbstract:We briefly describe an implementation of a hyperresolution-based calculus for the propositional basic Multimodal Logic, Kn. The prover, KSP, which allows for both local and global reasoning, is designed to support experimentation with different combinations of refinements for its basic calculus. We present an experimental evaluation that compares K S P with a range of existing reasoners for Kn.
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Open image in new window: A Resolution-Based Prover for Multimodal K
2016Co-Authors: Cláudia Nalon, Ullrich Hustadt, Clare DixonAbstract:In this paper, we describe an implementation of a hyper-resolution-based calculus for the propositional basic Multimodal Logic, Open image in new window . The prover was designed to support experimentation with different combinations of refinements for its basic calculus: it is primarily based on the set of support strategy, which can then be combined with other refinements, simplification techniques and different choices for the underlying normal form and clause selection. The prover allows for both local and global reasoning. We show experimental results for different combinations of strategies and comparison with existing tools.
Alfredo Burrieza - One of the best experts on this subject based on the ideXlab platform.
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Implementing a relational system for order of magnitude reasoning
2020Co-Authors: Alfredo Burrieza, Angel Mora, Manuel Ojeda-aciegoAbstract:This work concentrates on the automated deduction of Logics of order-of-magnitude reasoning. Specifically, a Prolog implementation is presented for the RasiowaSikorski proof system associated to the relational translation Re(OM) of the Multimodal Logic of qualitative order-of-magnitude reasoning OM.
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Theory and Applications of Relational Structures as Knowledge Instruments - Relational approach to order-of-magnitude reasoning
Lecture Notes in Computer Science, 2020Co-Authors: Alfredo Burrieza, Manuel Ojeda-aciego, Ewa OrłowskaAbstract:This work concentrates on the automated deduction of Logics of order-of-magnitude reasoning. Specifically, a translation of the Multimodal Logic of qualitative order-of-magnitude reasoning into relational Logics is provided; then, a sound and complete Rasiowa-Sikorski proof system is presented for the relational version of the language.
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A flexible Logic-based approach to closeness using order of magnitude qualitative reasoning
Logic Journal of the IGPL, 2019Co-Authors: Alfredo Burrieza, Emilio Muñoz-velasco, Manuel Ojeda-aciegoAbstract:Abstract In this paper, we focus on a Logical approach to the important notion of closeness, which has not received much attention in the literature. Our notion of closeness is based on the so-called proximity intervals, which will be used to decide the elements that are close to each other. Some of the intuitions of this definition are explained on the basis of examples. We prove the decidability of the recently introduced Multimodal Logic for closeness and, then, we show some capabilities of the Logic with respect to expressivity in order to denote particular positions of the proximity intervals.
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a Multimodal Logic for closeness
Journal of Applied Non-Classical Logics, 2017Co-Authors: Alfredo Burrieza, Emilio Munozvelasco, Manuel OjedaaciegoAbstract:AbstractWe introduce a Multimodal Logic for order of magnitude reasoning which considers a new Logic-based alternative to the notion of closeness, we provide an axiom system and prove its soundness and completeness.
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CAEPIA - A Logic for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance
Current Topics in Artificial Intelligence, 2007Co-Authors: Alfredo Burrieza, Emilio Muñoz-velasco, Manuel Ojeda-aciegoAbstract:This paper continues the research line on the Multimodal Logic of qualitative reasoning; specifically, it deals with the introduction of the notions non-closeness and distance. These concepts allow us to consider qualitative sum of medium and large numbers. We present a sound and complete axiomatization for this Logic, together with some of its advantages by means of an example.
Ullrich Hustadt - One of the best experts on this subject based on the ideXlab platform.
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A Resolution-Based Theorem Prover for $${\textsf {K}}_{n}^{}$$Kn: Architecture, Refinements, Strategies and Experiments
Journal of Automated Reasoning, 2020Co-Authors: Cláudia Nalon, Ullrich Hustadt, Clare DixonAbstract:In this paper we describe the implementation of , a resolution-based prover for the basic Multimodal Logic $${\textsf {K}}_{n}^{}$$ K n . The prover implements a resolution-based calculus for both local and global reasoning. The user can choose different normal forms, refinements of the basic resolution calculus, and strategies. We describe these options in detail and discuss their implications. We provide experiments comparing some of these options and comparing the prover with other provers for this Logic.
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A Resolution-Based Theorem Prover for \({\textsf {K}}_{n}^{}\) : Architecture, Refinements, Strategies and Experiments
Journal of Automated Reasoning, 2020Co-Authors: Cláudia Nalon, Ullrich Hustadt, Clare DixonAbstract:In this paper we describe the implementation of , a resolution-based prover for the basic Multimodal Logic $${\textsf {K}}_{n}^{}$$ . The prover implements a resolution-based calculus for both local and global reasoning. The user can choose different normal forms, refinements of the basic resolution calculus, and strategies. We describe these options in detail and discuss their implications. We provide experiments comparing some of these options and comparing the prover with other provers for this Logic.
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Modal Resolution: Proofs, Layers and Refinements
ACM Transactions on Computational Logic, 2019Co-Authors: Cláudia Nalon, Clare Dixon, Ullrich HustadtAbstract:Resolution-based provers for Multimodal normal Logics require pruning of the search space for a proof in order to ameliorate the inherent intractability of the satisfiability problem for such Logics. We present a clausal modal-layered hyper-resolution calculus for the basic Multimodal Logic, which divides the clause set according to the modal level at which clauses occur in order to reduce the number of possible inferences. We show that the calculus is complete for the Logics being considered. We also show that the calculus can be combined with other strategies. In particular, we discuss the completeness of combining modal layering with negative and ordered resolution and provide experimental results comparing the different refinements.
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IJCAI - KSP: A Resolution-based Prover for Multimodal K, Abridged Report
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, 2017Co-Authors: Cláudia Nalon, Ullrich Hustadt, Clare DixonAbstract:We briefly describe an implementation of a hyperresolution-based calculus for the propositional basic Multimodal Logic, Kn. The prover, KSP, which allows for both local and global reasoning, is designed to support experimentation with different combinations of refinements for its basic calculus. We present an experimental evaluation that compares K S P with a range of existing reasoners for Kn.
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Open image in new window: A Resolution-Based Prover for Multimodal K
2016Co-Authors: Cláudia Nalon, Ullrich Hustadt, Clare DixonAbstract:In this paper, we describe an implementation of a hyper-resolution-based calculus for the propositional basic Multimodal Logic, Open image in new window . The prover was designed to support experimentation with different combinations of refinements for its basic calculus: it is primarily based on the set of support strategy, which can then be combined with other refinements, simplification techniques and different choices for the underlying normal form and clause selection. The prover allows for both local and global reasoning. We show experimental results for different combinations of strategies and comparison with existing tools.
Lawrence C. Paulson - One of the best experts on this subject based on the ideXlab platform.
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Exploring Properties of Normal Multimodal Logics in Simple Type Theory with LEO-II
2020Co-Authors: Christoph Benzmüller, Lawrence C. PaulsonAbstract:There are two well investigated approaches to automate reasoning in modal Logics: the direct approach and the translational approach. The direct approach [6, 7, 14, 27] develops specific calculi and tools for the task; the translational approach [29, 30] transforms modal Logic formulas into firstorder Logic and applies standard first-order tools. Embeddings of modal Logics into higher-order Logic, however, have not yet been widely studied, although Multimodal Logic can be regarded as a natural fragment of simple type theory. Gallin [15] appears to mention the idea first. He presents an embedding of modal Logic into a 2-sorted type theory. This idea is picked up by Gamut [16] and a related embedding has recently been studied by Hardt and Smolka [17]. Carpenter [12] proposes to use lifted connectives, an idea that is also underlying the embeddings presented by Merz [26], Brown [11], Harrison [18, Chap. 20], and Kaminski and Smolka [22]. In this paper we pick up and extend the embedding of Multimodal Logics in simple type theory as studied by Brown [11]. The starting point is a characterization of Multimodal Logic formulas as particular λ-terms in simple type theory. A distinctive characteristic of the encoding is that the definiens of the 2R operator λ-abstracts over the accessibility relation R. We illustrate that this supports the formulation of meta properties of encoded Multimodal Logics such as the correspondence between certain axioms and properties of the accessibility relation R. We show that some of these meta properties can even be efficiently automated within our higher-order theorem prover Leo-II [9] via cooperation with the first-order automated
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Multimodal and intuitionistic Logics in simple type theory
Logic Journal of The Igpl \ Bulletin of The Igpl, 2010Co-Authors: Christoph Benzmueller, Lawrence C. PaulsonAbstract:We study straightforward embeddings of propositional normal Multimodal Logic and propositional intuitionistic Logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational investigations of various non-classical Logics. We report some experiments using the higher-order automated theorem prover LEO-II.
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Quantified Multimodal Logics in Simple Type Theory
arXiv: Artificial Intelligence, 2009Co-Authors: Christoph Benzmueller, Lawrence C. PaulsonAbstract:We present a straightforward embedding of quantified Multimodal Logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple experiments, using existing higher-order theorem provers, to demonstrate that the embedding allows automated proofs of statements in these Logics, as well as meta properties of them.