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Sebastian Link - One of the best experts on this subject based on the ideXlab platform.

  • Charting the completeness frontier of inference systems for multivalued dependencies
    Acta Informatica, 2008
    Co-Authors: Sebastian Link
    Abstract:

    The implication of multivalued dependencies in relational databases has originally been defined in the context of some fixed Finite Universe. While axiomatisability and implication problems have been intensely studied with respect to this notion almost no research has been devoted towards the alternative notion of implication in which the underlying Universe of attributes is left undetermined. Based on a set of common inference rules we establish all axiomatisations in undetermined Universes, and all axiomatisations in fixed Universes that indicate the role of the complementation rule as a means of database normalisation. This characterises the expressiveness of several incomplete sets of inference rules. We also establish relationships between axiomatisations in fixed and undetermined Universes, and study the time complexity of the implication problem in undetermined Universes. The results of this paper establish a foundation for reasoning about multivalued dependencies without the assumption of a fixed underlying Universe.

  • ON THE IMPLICATION OF MULTIVALUED DEPENDENCIES IN PARTIAL DATABASE RELATIONS
    International Journal of Foundations of Computer Science, 2008
    Co-Authors: Sebastian Link
    Abstract:

    The implication of multivalued dependencies (MVDs) in relational databases has originally and independently been defined in the context of some fixed Finite Universe by Delobel, Fagin, and Zaniolo. Biskup observed that the original axiomatisation for MVD implication does not reflect the fact that the complementation rule is merely a means to achieve database normalisation. He proposed two alternative ways to overcome this deficiency: i) an axiomatisation that does represent the role of the complementation rule adequately, and ii) a notion of MVD implication in which the underlying Universe of attributes is left undetermined together with an axiomatisation of this notion. In this paper we investigate multivalued dependencies with null values (NMVDs) as defined and axiomatised by Lien. We show that Lien's axiomatisation does not adequately reflect the role of the complementation rule, and extend Biskup's findings for MVDs in total database relations to NMVDs in partial database relations. Moreover, a correspondence between (minimal) axiomatisations in fixed Universes that do reflect the property of complementation and (minimal) axiomatisations in undetermined Universes is shown.

  • Full hierarchical dependencies in fixed and undetermined Universes
    Annals of Mathematics and Artificial Intelligence, 2007
    Co-Authors: Sven Hartmann, Henning Köhler, Sebastian Link
    Abstract:

    Full hierarchical dependencies (FHDs) constitute a large class of relational dependencies. A relation exhibits an FHD precisely when it is the natural join over at least two of its projections that all share the same join attributes. Therefore, FHDs generalise multivalued dependencies (MVDs) in which case the number of these projections is precisely two. The implication of FHDs has originally been defined in the context of some fixed Finite Universe. This paper identifies a sound and complete set of inference rules for the implication of FHDs. This axiomatisation is very reminiscent of that for MVDs. Then, an alternative notion of FHD implication is introduced in which the underlying set of attributes is left undetermined. The first main result establishes a Finite axiomatisation for FHD implication in undetermined Universes. It is then formally clarified that the complementation rule is only a mere means for database normalisation. In fact, the second main result establishes a Finite axiomatisation for FHD implication in fixed Universes which allows to infer FHDs either without using the complementation rule at all or only in the very last step of the inference. This also characterises the expressiveness of an incomplete set of inference rules in fixed Universes. The results extend previous work on MVDs by Biskup.

  • FoIKS - On multivalued dependencies in fixed and undetermined Universes
    Lecture Notes in Computer Science, 2006
    Co-Authors: Sebastian Link
    Abstract:

    The implication of multivalued dependencies (MVDs) in relational databases has originally been defined in the context of some fixed Finite Universe. While axiomatisability and implication problem have been intensely studied with respect to this notion, almost no research has been devoted towards the alternative notion of implication in which the underlying Universe of attributes is left undetermined. Based on a set of common inference rules we reveal all axiomatisations in undetermined Universes, and all axiomatisations in fixed Universes that indicate the role of the complementation rule as a means of database normalisation. This characterises the expressiveness of several incomplete sets of inference rules. We also establish relationships between axiomatisations in fixed and undetermined Universes, and study the time complexity of the implication problem in undetermined Universes.

Bill Hibbard - One of the best experts on this subject based on the ideXlab platform.

  • self modeling agents evolving in our Finite Universe
    Artificial General Intelligence, 2014
    Co-Authors: Bill Hibbard
    Abstract:

    This paper proposes that we should avoid inFinite sets in definitions of AI agent and their environments. For agents that evolve to increase their Finite resources it proposes a self-modeling agent definition that avoids assumptions about the agent’s future form. And it proposes a consistent and complete logical theory for reasoning by AI agents in our Finite Universe.

  • AGI - Self-modeling Agents Evolving in Our Finite Universe
    Artificial General Intelligence, 2014
    Co-Authors: Bill Hibbard
    Abstract:

    This paper proposes that we should avoid inFinite sets in definitions of AI agent and their environments. For agents that evolve to increase their Finite resources it proposes a self-modeling agent definition that avoids assumptions about the agent’s future form. And it proposes a consistent and complete logical theory for reasoning by AI agents in our Finite Universe.

Ivo G. Rosenberg - One of the best experts on this subject based on the ideXlab platform.

  • Small clones and the projection property
    Algebra universalis, 2010
    Co-Authors: Maurice Pouzet, Ivo G. Rosenberg
    Abstract:

    In 1986, the second author classified the minimal clones on a Finite Universe into five types. We extend this classification to inFinite Universes and to multiclones. We show that every non-trivial clone contains a “small” clone of one of the five types. From it we deduce, in part, an earlier result, namely that if $${\mathcal{C}}$$ is a clone on a Universe A with at least two elements that contains all constant operations, then all binary idempotent operations are projections and some m -ary idempotent operation is not a projection for some m ≥ 3 if and only if there is a boolean group G on A for which $${\mathcal{C}}$$ is the set of all operations f ( x _1, . . . , x _ n ) of the form $$a + {\sum_{i \in I}x_{i}}$$ for $${a \in A}$$ and $${I \subseteq \{1,\,.\,.\,.\,,n\}}$$ .

  • Small clones and the projection property
    arXiv: Logic, 2007
    Co-Authors: Maurice Pouzet, Ivo G. Rosenberg
    Abstract:

    In 1986, the second author classified the minimal clones on a Finite Universe into five types. We extend this classification to inFinite Universes and to multiclones. We show that every non-trivial clone contains a "small" clone of one of the five types. From it we deduce, in part, an earlier result, namely that if $\mathcal C$ is a clone on a Universe $A$ with at least two elements, that contains all constant operations, then all binary idempotent operations are projections and some $m$-ary idempotent operation is not a projection some $m\geq 3$ if and only if there is a Boolean group $G$ on $A$ for which $\mathcal C$ is the set of all operations $f(x_1,..., x_n)$ of the form $a+\sum_{i\in I}x_i$ for $a\in A$ and $I\subseteq \{1,..., n\}$.

  • Essentially Minimal Groupoids
    Algebras and Orders, 1993
    Co-Authors: Hajime Machida, Ivo G. Rosenberg
    Abstract:

    A clone C is essentially minimal if it contains an essential nonidempotent ope­ ration and every proper subclone of C is essentially unary. For a Finite Universe we determine all essentially minimal clones generated by groupoids of a certain type by means of four varieties and a family of varieties. We narrow the essentially minimal clones generated by groupoids of another type into three families.

  • Completeness theory for Finite partial algebras
    Algebra Universalis, 1992
    Co-Authors: Lucien Haddad, Ivo G. Rosenberg
    Abstract:

    LetA be a Finite Universe of cardinality ¦A¦ >- 3. We characterize the non quasi-diagonai strongly reflexive relations that determine maximal partial clones onA. Combining this with some known results, we deduce a general completeness criterion for Finite partial algebras.

Paul S. Wesson - One of the best experts on this subject based on the ideXlab platform.

  • Mach, the Universe, and foundations of mechanics
    Annalen der Physik, 2012
    Co-Authors: Bahram Mashhoon, Paul S. Wesson
    Abstract:

    Barbour's response to our recent paper on "Mach's principle and higher-dimensional dynamics" describes an approach to Mach's principle in which the Universe as a whole is involved in the definition of inertial frames of reference. Moreover, Barbour's theoretical procedure is in agreement with general relativity for a Finite Universe that is spatially closed. However, we prefer an operational approach that relies ultimately on observational data.

Tommy Wright - One of the best experts on this subject based on the ideXlab platform.

  • Estimation of a Finite Universe total when a stratum is not sampled
    Applied Stochastic Models in Business and Industry, 1999
    Co-Authors: Tommy Wright
    Abstract:

    In the context of a Universe of trucks operating in the United States in 1990, this paper presents statistical methodology for estimating a Finite Universe total on a second occasion when a part of the Universe is sampled and the remainder of the Universe is not sampled. Prediction is used to compensate for the lack of data from the unsampled portion of the Universe. The sample, stratified by age, is from an earlier census without updating the listing (frame). Accounting for births and deaths in the Universe between the two points in time, an estimator is obtained which is a generalization of what an analyst might do in the absence of sample data from a given stratum, the births. Deaths are accounted for through domain estimation, and total updated counts are available from different sources. The approach of the paper is to provide an estimate for births, without actually sampling from the births stratum. With regard to saving resources by not sampling births, it is demonstrated that the analyst who does not sample the births may very well do better than the analyst who does. Copyright © 1999 John Wiley & Sons, Ltd.

  • PREDICTION AND STANDARD ERROR ESTIMATION FOR A Finite Universe TOTAL WHEN A STRATUM IS NOT SAMPLED.
    1994
    Co-Authors: Tommy Wright
    Abstract:

    In the context of a Universe of trucks operating in the United States in 1990, this paper presents statistical methodology for estimating a Finite Universe total on a second occasion when a part of the Universe is sampled and the remainder of the Universe is not sampled. Prediction is used to compensate for the lack of data from the unsampled portion of the Universe. The sample is assumed to be a subsample of an earlier sample where stratification is used on both occasions before sample selection. Accounting for births and deaths in the Universe between the two points in time, the detailed sampling plan, estimator, standard error, and optimal sample allocation, are presented with a focus on the second occasion. If prior auxiliary information is available, the methodology is also applicable to a first occasion.

  • The Development and Theory
    Exact Confidence Bounds when Sampling from Small Finite Universes, 1991
    Co-Authors: Tommy Wright
    Abstract:

    Our objective in this chapter is to provide detailed development and background that completely support the Table in Chapter 4 and its applications described in Chapter 2. Our aim is to make the connection between hypothesis testing and confidence interval estimation visibly clear when selecting simple random samples from a Finite Universe. The development assumes that the reader has had at least an introductory course in statistics and is familiar with conditional probability.