Symbolic Logic

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J. N. Hooker - One of the best experts on this subject based on the ideXlab platform.

  • Projection, consistency, and George Boole
    Constraints, 2016
    Co-Authors: J. N. Hooker
    Abstract:

    Although best known for his work in Symbolic Logic, George Boole made seminal contributions in the Logic of probabilities. He solved the probabilistic inference problem with a projection method, leading to the insight that inference (as well as optimization) is essentially a projection problem. This unifying perspective has applications in constraint programming, because consistency maintenance is likewise a form of inference that can be conceived as projection. Viewing consistency in this light suggests a concept of J -consistency, which is achieved by projection onto a subset J of variables. We show how this projection problem can be solved for the satisfiability problem by Logic-based Benders decomposition. We also solve it for among , sequence , regular , and all-different constraints. Maintaining J -consistency for global constraints can be more effective than maintaining traditional domain and bounds consistency when propagating through a richer structure than a domain store, such as a relaxed decision diagram. This paper is written in recognition of Boole’s 200th birthday.

Y Watanabe - One of the best experts on this subject based on the ideXlab platform.

  • new hyper distributed hyper parallel ai approach based on chaotic bifurcations and synchronizations
    International Conference on Multisensor Fusion and Integration for Intelligent Systems, 1994
    Co-Authors: Dianxun Shuai, Y Watanabe
    Abstract:

    For problem solving in the artificial intelligence, this paper presents a new hyper-distributed hyper-parallel approach based on the bifurcations and synchronizations of the hierarchical distributed chaotic dynamic systems. By using Chua's circuits arrays, the realization of the hyper-distributed hyper-parallel heuristic algorithms for real-time search of any implicit AND/OR graph is discussed. The approach not only combines the advantages of both the traditional sequential Symbolic Logic and the conventional neural network approaches, but also overcomes their drawbacks in many respects. >

  • hyper distributed hyper parallel heuristic ai processing based on dynamically clustering competition neural network
    International Symposium on Information Theory and its Applications, 1994
    Co-Authors: Dianxun Shuai, Y Watanabe
    Abstract:

    This paper presents a new approach to the hyper-distributed hyper-parallel implementation of the artificial intelligent (AI) heuristic algorithms for real-time searching, matching and planning. By using the competitive activation mechanism of dynamically clustering neural networks, the concurrent propagations and competitions of concurrent auto waves yielded by distributed parallel heuristic AI algorithms for searching any implicit AND/OR graph are realized. Compared with the AI approaches based on the conventional sequential Symbolic Logic and the conventional neural networks, the approach of this paper has many advantages in many respects, such as high processing speed, always successful obtainment of the optimal solution: local connections between cells, easy utilization of heuristic knowledge, and feasibility of the VLSI implementation.

John C Mitchell - One of the best experts on this subject based on the ideXlab platform.

  • a Symbolic Logic with concrete bounds for cryptographic protocols
    arXiv: Logic in Computer Science, 2015
    Co-Authors: Anupam Datta, John C Mitchell, Joseph Y Halpern, Arnab Roy, Shayak Sen
    Abstract:

    We present a formal Logic for quantitative reasoning about security properties of network protocols. The system allows us to derive concrete security bounds that can be used to choose key lengths and other security parameters. We provide axioms for reasoning about digital signatures and random nonces, with security properties based on the concrete security of signature schemes and pseudorandom number generators (PRG). The formal Logic supports first-order reasoning and reasoning about protocol invariants, taking concrete security bounds into account. Proofs constructed in our Logic also provide conventional asymptotic security guarantees because of the way that concrete bounds accumulate in proofs. As an illustrative example, we use the formal Logic to prove an authentication property with concrete bounds of a signature-based challenge-response protocol.

  • a Symbolic Logic with exact bounds for cryptographic protocols
    Workshop on Logic Language Information and Computation, 2011
    Co-Authors: John C Mitchell
    Abstract:

    This invited talk will describe a formal Logic for reasoning about security properties of network protocols with proof rules indicating exact security bounds that could be used to choose key lengths or other concrete security parameters. The soundness proof for this Logic, a variant of previous versions of Protocol Composition Logic (PCL), shows that derivable properties are guaranteed in a standard cryptographic model of protocol execution and resource-bounded attack.We will discuss the general system and present example axioms for digital signatures and random nonces, with concrete security properties based on concrete security of signature schemes and pseudorandom number generators (PRG). The quantitative formal Logic supports first-order reasoning and reasoning about protocol invariants, taking exact security bounds into account. Proofs constructed in this Logic also provide conventional asymptotic security guarantees because of the way that exact bounds accumulate in proofs. As an illustrative example producing exact bounds, we use the formal Logic to prove an authentication property with exact bounds of a signature-based challenge-response protocol.

  • key exchange protocols security definition proof method and applications
    IACR Cryptology ePrint Archive, 2006
    Co-Authors: Anupam Datta, John C Mitchell, Ante Derek, Bogdan Warinschi
    Abstract:

    We develop a compositional method for proving cryptographically sound security properties of key exchange protocols, based on a Symbolic Logic that is interpreted over conventional runs of a protocol against a probabilistic polynomial-time attacker. Since reasoning about an unbounded number of runs of a protocol involves induction-like arguments about properties preserved by each run, we formulate a specification of secure key exchange that, unlike conventional key indistinguishability, is closed under general composition with steps that use the key. We present formal proof rules based on this game-based condition, and prove that the proof rules are sound over a computational semantics. The proof system is used to establish security of a standard protocol in the computational model.

Fritz Peter - One of the best experts on this subject based on the ideXlab platform.

  • Counterfactuals and Propositional Contingentism
    'Cambridge University Press (CUP)', 2017
    Co-Authors: Fritz Peter, Goodman Jeremy
    Abstract:

    This article explores the connection between two theses: the principle of conditional excluded middle for the counterfactual conditional, and the claim that it is a contingent matter which (coarse grained) propositions there are. Both theses enjoy wide support, and have been defended at length by Robert Stalnaker. We will argue that, given plausible background assumptions, these two principles are incompatible, provided that conditional excluded middle is understood in a certain modalized way. We then show that some (although not all) arguments for conditional excluded middle can in fact be extended to motivate this modalized version of the principle. COPYRIGHT: © Association for Symbolic Logic 201

  • Logics for propositional contingentism
    'Cambridge University Press (CUP)', 2017
    Co-Authors: Fritz Peter
    Abstract:

    Robert Stalnaker has recently advocated propositional contingentism, the claim that it is contingent what propositions there are. He has proposed a philosophical theory of contingency in what propositions there are and sketched a possible worlds model theory for it. In this paper, such models are used to interpret two propositional modal languages: one containing an existential propositional quantifier, and one containing an existential propositional operator. It is shown that the resulting Logic containing an existential quantifier is not recursively axiomatizable, as it is recursively isomorphic to second-order Logic, and a natural candidate axiomatization for the resulting Logic containing an existential operator is shown to be incomplete. COPYRIGHT: © Association for Symbolic Logic 201

Bernd Becker - One of the best experts on this subject based on the ideXlab platform.

  • improving test pattern generation in presence of unknown values beyond restricted Symbolic Logic
    European Test Symposium, 2015
    Co-Authors: Karsten Scheibler, Dominik Erb, Bernd Becker
    Abstract:

    Test generation algorithms considering unknown (X) values are pessimistic if standard n-valued Logic algebras are used. This results in an overestimation of the number of signals with X-values and an underestimation of the fault coverage. In contrast, algorithms based on quantified Boolean formula (QBF), are accurate in presence of X-values but have limits with respect to runtime, scalability and robustness. Recently, an algorithm based on restricted Symbolic Logic (RSL) has been presented which is more accurate than classical three-valued Logic and faster than QBF. Nonetheless, this RSL-based approach is still pessimistic and is unable to detect all testable faults. Additionally, it does not allow the accurate identification of untestable faults. In this paper, we improve test pattern generation based on RSL in two directions in order to reduce the accuracy-gap to QBF further. First, we present techniques to go beyond the accuracy of RSL when generating test patterns. Second, we include a check which is able to accurately identify untestable faults. Experimental results show the high efficiency of the proposed method. It is able to classify almost all faults — either by generating a test pattern or proving untestability.

  • test pattern generation in presence of unknown values based on restricted Symbolic Logic
    International Test Conference, 2014
    Co-Authors: Dominik Erb, Karsten Scheibler, Michael A Kochte, Matthias Sauer, Hansjoachim Wunderlich, Bernd Becker
    Abstract:

    Test generation algorithms based on standard n-valued Logic algebras are pessimistic in presence of unknown (X) values, overestimate the number of signals with X-values and underestimate fault coverage.