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Aruna Chakraborty - One of the best experts on this subject based on the ideXlab platform.

  • extending the Contraposition property of propositional logic for fuzzy abduction
    IEEE Transactions on Fuzzy Systems, 2013
    Co-Authors: Aruna Chakraborty, Amit Konar, Nikhil R Pal, Lakhmi C Jain
    Abstract:

    Abduction deals with assumption-based reasoning to explain an observation. In the context of fuzzy reasoning, abduction attempts to determine the membership function of the fuzzy propositions present in the antecedent of a rule when the membership functions for the propositions in the consequent of the rule are given. Currently available models of fuzzy abduction are capable of inferring the membership function of the antecedent clause accurately when the antecedent includes single fuzzy proposition. However, when the antecedent clause of a rule contains multiple fuzzy propositions, these models fail to determine the independent membership function of the individual propositions present in the antecedent. This paper presents a new formulation to handle the above problem by fuzzy extension of the well-known Contraposition property of propositional logic. Several interesting properties due to the fuzzy extension of the classical Contraposition have been derived. An algorithm for automated abduction using the extended Contraposition property has been developed to demonstrate the principle of abduction with rules containing one or more fuzzy propositions in the antecedent/consequent. The time complexity of the proposed fuzzy abduction for a sequence of n-chained rules, where each rule has m fuzzy propositions, is O (mn), considering a uniform cost for composition operation and t-norm computation of the antecedent.

  • a structured approach to fuzzy abduction based on Contraposition property of propositional logic
    IEEE International Conference on Fuzzy Systems, 2010
    Co-Authors: Aruna Chakraborty, Amit Konar, Atulya K Nagar
    Abstract:

    The paper proposes a new approach to fuzzy abduction by extending the Contraposition rule of propositional logic. The main difficulty of fuzzy abduction is due to the restriction of single antecedent clause in a fuzzy production rule. When more than one antecedent clause occurs jointly in a fuzzy rule, the membership value of the derived antecedent clauses become equal, which should not be the case in general. The paper overcomes this problem and demonstrates a simple but elegant method to compute premises in a multi-chained reasoning system.

De Ronde Christian - One of the best experts on this subject based on the ideXlab platform.

  • The (Quantum) Measurement Problem in Classical Mechanics
    2020
    Co-Authors: De Ronde Christian
    Abstract:

    In this work we analyze the deep link between the 20th Century positivist re-foundation of physics and the famous measurement problem of quantum mechanics. We attempt to show why this is not an “obvious” nor “self evident” problem for the theory of quanta, but rather a direct consequence of the empirical-positivist understanding of physical theories when applied to the orthodox quantum formalism. In Contraposition, we discuss a representational realist account of both physical ‘theories’ and ‘measurement’ which goes back to the works of Einstein, Heisenberg and Pauli. After presenting a critical analysis of Bohr’s definitions of ‘measurement’ we continue to discuss the way in which several contemporary approaches to QM —such as decoherence, modal interpretations and QBism— remain committed to Bohr’s general methodology. Finally, in order to expose the many inconsistencies present within the (empirical-positivist) presuppositions responsible for creating the quantum measurement problem, we show how through these same set of presuppositions it is easy to derive a completely analogous paradox for the case of classical mechanics

  • The (Quantum) Measurement Problem in Classical Mechanics
    2020
    Co-Authors: De Ronde Christian
    Abstract:

    In this work we analyze the deep link between the 20th Century positivist re-foundation of physics and the famous measurement problem of quantum mechanics. We attempt to show why this is not an "obvious" nor "self evident" problem for the theory of quanta, but rather a direct consequence of the empirical-positivist understanding of physical theories when applied to the orthodox quantum formalism. In Contraposition, we discuss a representational realist account of both physical 'theories' and 'measurement' which goes back to the works of Einstein, Heisenberg and Pauli. After presenting a critical analysis of Bohr's definitions of 'measurement' we continue to discuss the way in which several contemporary approaches to QM --such as decoherence, modal interpretations and QBism-- remain committed to Bohr's general methodology. Finally, in order to expose the many inconsistencies present within the (empirical-positivist) presuppositions responsible for creating the quantum measurement problem, we show how through these same set of presuppositions it is easy to derive a completely analogous paradox for the case of classical mechanics.Comment: 24 page

  • Measuring Quantum Superpositions (Or, "It is only the theory which decides what can be observed.")
    2020
    Co-Authors: De Ronde Christian
    Abstract:

    In this work we attempt to confront the orthodox widespread claim present in the foundational literature of Quantum Mechanics (QM) according to which 'superpositions are never actually observed in the lab'. In order to do so, we begin by providing a critical analysis of the famous measurement problem which, we will argue, was originated by the strict application of the empirical-positivist requirements to subsume the quantum formalism under their specific understanding of 'theory'. In this context, the ad hoc introduction of the projection postulate (or measurement rule) can be understood as a necessary requirement coming from a naive empiricist standpoint which presupposes that observations are self evident givens of "common sense" experience --independent of metaphysical (categorical) presuppositions. We then turn our attention to two "non-collapse" interpretations of QM --namely, modal and many worlds-- which even though deny that the "collapse" is a real physical process anyhow retain the measurement rule as a necessary element of the theory. In Contraposition, following Einstein's claim according to which "it is only the theory which decides what can be observed", we propose a return to the realist representational understanding of 'physical theories' in which 'observation' is considered as derived from theoretical presuppositions. It is from this standpoint that we discuss a new non-classical conceptual representation which allows us to understand quantum phenomena in an intuitive (anschaulicht) manner. Leaving behind the projection postulate, we discuss the general physical conditions for measuring and observing quantum superpositions.Comment: 22 page

  • Measuring Quantum Superpositions (Or, “It is only the theory which decides what can be observed.”)
    2020
    Co-Authors: De Ronde Christian
    Abstract:

    In this work we attempt to confront the orthodox widespread claim present in the foundational literature of Quantum Mechanics (QM) according to which ‘superpositions are never actually observed in the lab’. In order to do so, we begin by providing a critical analysis of the famous measurement problem which, we will argue, was originated by the strict application of the empirical-positivist requirements to subsume the quantum formalism under their specific understanding of ‘theory’. In this context, the ad hoc introduction of the projection postulate (or measurement rule) can be understood as a necessary requirement coming from a naive empiricist standpoint which presupposes that observations are self evident givens of “common sense” experience —independent of metaphysical (categorical) presuppositions. We then turn our attention to two “non-collapse” interpretations of QM —namely, modal and many worlds— which even though deny that the “collapse” is a real physical process anyhow retain the measurement rule as a necessary element of the theory. In Contraposition, following Einstein’s claim according to which “it is only the theory which decides what can be observed”, we propose a return to the realist representational understanding of ‘physical theories’ in which ‘observation’ is considered as derived from theoretical presuppositions. It is from this standpoint that we discuss a new non-classical conceptual representation which allows us to understand quantum phenomena in an intuitive (anschaulicht) manner. Leaving behind the projection postulate, we discuss the general physical conditions for measuring and observing quantum superpositions

Lakhmi C Jain - One of the best experts on this subject based on the ideXlab platform.

  • extending the Contraposition property of propositional logic for fuzzy abduction
    IEEE Transactions on Fuzzy Systems, 2013
    Co-Authors: Aruna Chakraborty, Amit Konar, Nikhil R Pal, Lakhmi C Jain
    Abstract:

    Abduction deals with assumption-based reasoning to explain an observation. In the context of fuzzy reasoning, abduction attempts to determine the membership function of the fuzzy propositions present in the antecedent of a rule when the membership functions for the propositions in the consequent of the rule are given. Currently available models of fuzzy abduction are capable of inferring the membership function of the antecedent clause accurately when the antecedent includes single fuzzy proposition. However, when the antecedent clause of a rule contains multiple fuzzy propositions, these models fail to determine the independent membership function of the individual propositions present in the antecedent. This paper presents a new formulation to handle the above problem by fuzzy extension of the well-known Contraposition property of propositional logic. Several interesting properties due to the fuzzy extension of the classical Contraposition have been derived. An algorithm for automated abduction using the extended Contraposition property has been developed to demonstrate the principle of abduction with rules containing one or more fuzzy propositions in the antecedent/consequent. The time complexity of the proposed fuzzy abduction for a sequence of n-chained rules, where each rule has m fuzzy propositions, is O (mn), considering a uniform cost for composition operation and t-norm computation of the antecedent.

Amit Konar - One of the best experts on this subject based on the ideXlab platform.

  • extending the Contraposition property of propositional logic for fuzzy abduction
    IEEE Transactions on Fuzzy Systems, 2013
    Co-Authors: Aruna Chakraborty, Amit Konar, Nikhil R Pal, Lakhmi C Jain
    Abstract:

    Abduction deals with assumption-based reasoning to explain an observation. In the context of fuzzy reasoning, abduction attempts to determine the membership function of the fuzzy propositions present in the antecedent of a rule when the membership functions for the propositions in the consequent of the rule are given. Currently available models of fuzzy abduction are capable of inferring the membership function of the antecedent clause accurately when the antecedent includes single fuzzy proposition. However, when the antecedent clause of a rule contains multiple fuzzy propositions, these models fail to determine the independent membership function of the individual propositions present in the antecedent. This paper presents a new formulation to handle the above problem by fuzzy extension of the well-known Contraposition property of propositional logic. Several interesting properties due to the fuzzy extension of the classical Contraposition have been derived. An algorithm for automated abduction using the extended Contraposition property has been developed to demonstrate the principle of abduction with rules containing one or more fuzzy propositions in the antecedent/consequent. The time complexity of the proposed fuzzy abduction for a sequence of n-chained rules, where each rule has m fuzzy propositions, is O (mn), considering a uniform cost for composition operation and t-norm computation of the antecedent.

  • a structured approach to fuzzy abduction based on Contraposition property of propositional logic
    IEEE International Conference on Fuzzy Systems, 2010
    Co-Authors: Aruna Chakraborty, Amit Konar, Atulya K Nagar
    Abstract:

    The paper proposes a new approach to fuzzy abduction by extending the Contraposition rule of propositional logic. The main difficulty of fuzzy abduction is due to the restriction of single antecedent clause in a fuzzy production rule. When more than one antecedent clause occurs jointly in a fuzzy rule, the membership value of the derived antecedent clauses become equal, which should not be the case in general. The paper overcomes this problem and demonstrates a simple but elegant method to compute premises in a multi-chained reasoning system.

Greg Restall - One of the best experts on this subject based on the ideXlab platform.

  • displaying and deciding substructural logics 1 logics with Contraposition
    Journal of Philosophical Logic, 1998
    Co-Authors: Greg Restall
    Abstract:

    Many logics in the relevant family can be given a proof theory in the style of Belnap's display logic (Belnap, 1982). However, as originally given, the proof theory is essentially more expressive than the logics they seek to model. In this paper, we consider a modified proof theory which more closely models relevant logics. In addition, we use this proof theory to show decidability for a large range of substructural logics.