Galois Connection

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Radhia Cousot - One of the best experts on this subject based on the ideXlab platform.

Patrick Cousot - One of the best experts on this subject based on the ideXlab platform.

Simon Kramer - One of the best experts on this subject based on the ideXlab platform.

  • A Galois-Connection between Cattell's and Szondi's Personality Profiles.
    arXiv: Computational Engineering Finance and Science, 2014
    Co-Authors: Simon Kramer
    Abstract:

    We propose a computable Galois-Connection between, on the one hand, Cattell's 16-Personality-Factor (16PF) Profiles, one of the most comprehensive and widely-used personality measures for non-psychiatric populations and their containing PsychEval Personality Profiles (PPPs) for psychiatric populations, and, on the other hand, Szondi's personality profiles (SPPs), a less well-known but, as we show, finer personality measure for psychiatric as well as non-psychiatric populations (conceived as a unification of the depth psychology of S. Freud, C.G. Jung, and A. Adler). The practical significance of our result is that our Galois-Connection provides a pair of computable, interpreting translations between the two personality spaces of PPPs (containing the 16PFs) and SPPs: one concrete from PPP-space to SPP-space (because SPPs are finer than PPPs) and one abstract from SPP-space to PPP-space (because PPPs are coarser than SPPs). Thus Cattell's and Szondi's personality-test results are mutually interpretable and inter-translatable, even automatically by computers.

  • a Galois Connection between myers briggs type indicators and szondi s personality profiles
    arXiv: Computational Engineering Finance and Science, 2014
    Co-Authors: Simon Kramer
    Abstract:

    We propose a computable Galois-Connection between Myers-Briggs' Type Indicators (MBTIs), the most widely-used personality measure for non-psychiatric populations (based on C.G. Jung's personality types), and Szondi's personality profiles (SPPs), a less well-known but, as we show, finer personality measure for psychiatric as well as non-psychiatric populations (conceived as a unification of the depth psychology of S. Freud, C.G. Jung, and A. Adler). The practical significance of our result is that our Galois-Connection provides a pair of computable, interpreting translations between the two personality spaces of MBTIs and SPPs: one concrete from MBTI-space to SPP-space (because SPPs are finer) and one abstract from SPP-space to MBTI-space (because MBTIs are coarser). Thus Myers-Briggs' and Szondi's personality-test results are mutually interpretable and inter-translatable, even automatically by computers.

Huijie Zhang - One of the best experts on this subject based on the ideXlab platform.

  • a fast pruning redundant rule method using Galois Connection
    Applied Soft Computing, 2011
    Co-Authors: Huawen Liu, Lei Liu, Huijie Zhang
    Abstract:

    Besides preprocessing, post-analysis also plays an important role in knowledge discovery. It can effectively assist users to grasp the obtained knowledge. However, many of data mining algorithms merely take performance into consideration and put the post-analysis of results aside. They generate a modest number of rules for the purpose of improving accuracy. Unfortunately, most induced rules are redundant or insignificant. Their presence not only confuses end-users in post-analysis, but also degrades efficiency in future decision task. Thus, it is necessary to eliminate redundant or irrelevant rules as more as possible. In this paper, we present an efficient post-processing method to prune redundant rules by virtue of the property of Galois Connection, which inherently constrains rules with respect to objects. Its advantage is that information will not be lost greatly during pruning step. The experimental evaluation shows that the proposed method is competent for discarding a large number of superfluous rules effectively and a high compression factor will be achieved. What's more, the computational cost of our method is surprisingly lower than the Apriori method.

Radoslaw Antoni Kycia - One of the best experts on this subject based on the ideXlab platform.

  • Landauer’s Principle as a Special Case of Galois Connection
    Entropy, 2018
    Co-Authors: Radoslaw Antoni Kycia
    Abstract:

    It is demonstrated how to construct a Galois Connection between two related systems with entropy. The construction, called the Landauer's Connection, describes coupling between two systems with entropy. It is straightforward and transfers changes in one system to the other one preserving ordering structure induced by entropy. The Landauer's Connection simplifies the description of the classical Landauer's principle for computational systems. Categorification and generalization of the Landauer's principle opens area of modelling of various systems in presence of entropy in abstract terms.

  • landauer s principle as a special case of Galois Connection
    Entropy, 2018
    Co-Authors: Radoslaw Antoni Kycia
    Abstract:

    It is demonstrated how to construct a Galois Connection between two related systems with entropy. The construction, called the Landauer's Connection, describes coupling between two systems with entropy. It is straightforward and transfers changes in one system to the other one, preserving ordering structure induced by entropy. The Landauer's Connection simplifies the description of the classical Landauer's principle for computational systems. Categorification and generalization of the Landauer's principle opens the area of modeling of various systems in presence of entropy in abstract terms.

  • landauer s principle as a special case of Galois Connection
    arXiv: Mathematical Physics, 2018
    Co-Authors: Radoslaw Antoni Kycia
    Abstract:

    It is demonstrated how to construct a Galois Connection between two related systems with entropy. The construction, called the Landauer's Connection, describes coupling between two systems with entropy. It is straightforward and transfers changes in one system to the other one preserving ordering structure induced by entropy. The Landauer's Connection simplifies the description of the classical Landauer's principle for computational systems. Categorification and generalization of the Landauer's principle opens area of modelling of various systems in presence of entropy in abstract terms.

  • Landauer’s Principle as a Special Case of Galois Connection
    MDPI AG, 2018
    Co-Authors: Radoslaw Antoni Kycia
    Abstract:

    It is demonstrated how to construct a Galois Connection between two related systems with entropy. The construction, called the Landauer’s Connection, describes coupling between two systems with entropy. It is straightforward and transfers changes in one system to the other one, preserving ordering structure induced by entropy. The Landauer’s Connection simplifies the description of the classical Landauer’s principle for computational systems. Categorification and generalization of the Landauer’s principle opens the area of modeling of various systems in presence of entropy in abstract terms

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