scholarly journals On the implication problem for probabilistic conditional independency

2000 ◽  
Vol 30 (6) ◽  
pp. 785-805 ◽  
Author(s):  
S.K.M. Wong ◽  
C.J. Butz ◽  
D. Wu
Keyword(s):  
Implication Problem ◽  
Conditional Independency

scholarly journals Modules or Mean-Fields?

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 552 ◽  
Author(s):  
Thomas Parr ◽  
Noor Sajid ◽  
Karl J. Friston
Keyword(s):  
Steady State ◽  
Message Passing ◽  
Mean Field Theory ◽  
Functional Anatomy ◽  
Mean Field ◽  
State Density ◽  
Stochastic Dynamical Systems ◽  
Conditional Independency ◽  
The Brain ◽  
Non Equilibrium

The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.

Towards a Normal Form and a Query Language for Extended Relations Defined by Regular Expressions

2016 ◽  
Vol 27 (2) ◽  
pp. 27-48
Author(s):  
András Benczúr ◽  
Gyula I. Szabó
Keyword(s):  
Normal Form ◽  
Data Base ◽  
Data Model ◽  
Query Language ◽  
Xml Schema ◽  
Relational Model ◽  
Regular Expressions ◽  
Functional Dependencies ◽  
Decision Algorithm ◽  
Implication Problem

This paper introduces a generalized data base concept that unites relational and semi structured data models. As an important theoretical result we could find a quadratic decision algorithm for the implication problem of functional and join dependencies defined on the united data model. As practical contribution we presented a normal form for the new data model as a tool for data base design. With our novel representations of regular expressions, a more effective searching method could be developed. XML elements are described by XML schema languages such as a DTD or an XML Schema definition. The instances of these elements are semi-structured tuples. A semi-structured tuple is an ordered list of (attribute: value) pairs. We may think of a semi-structured tuple as a sentence of a formal language, where the values are the terminal symbols and the attribute names are the non-terminal symbols. In the authors' former work (Szabó and Benczúr, 2015) they introduced the notion of the extended tuple as a sentence from a regular language generated by a grammar where the non-terminal symbols of the grammar are the attribute names of the tuple. Sets of extended tuples are the extended relations. The authors then introduced the dual language, which generates the tuple types allowed to occur in extended relations. They defined functional dependencies (regular FD - RFD) over extended relations. In this paper they rephrase the RFD concept by directly using regular expressions over attribute names to define extended tuples. By the help of a special vertex labeled graph associated to regular expressions the specification of substring selection for the projection operation can be defined. The normalization for regular schemas is more complex than it is in the relational model, because the schema of an extended relation can contain an infinite number of tuple types. However, the authors can define selection, projection and join operations on extended relations too, so a lossless-join decomposition can be performed. They extended their previous model to deal with XML schema indicators too, e.g., with numerical constraints. They added line and set constructors too, in order to extend their model with more general projection and selection operators. This model establishes a query language with table join functionality for collected XML element data.

The Implication Problem of Computing Policies

2015 ◽  
pp. 109-123 ◽  
Author(s):  
Rezwana Reaz ◽  
Muqeet Ali ◽  
Mohamed G. Gouda ◽  
Marijn J. H. Heule ◽  
Ehab S. Elmallah
Keyword(s):  
Implication Problem

Inference Rules for XML Strong MVD and XML Weak MVD

2011 ◽  
Vol 268-270 ◽  
pp. 2009-2015
Author(s):  
Li Feng Yin ◽  
Hua Jin ◽  
Hong Tian
Keyword(s):  
Incomplete Information ◽  
Xml Schema ◽  
Inference Rules ◽  
Logical Implication ◽  
Implication Problem ◽  
Xml Document

For solving logical implication problem in the presence of XML strong multi-valued dependency(denoted as XSMVD) and XML weak multi-valued dependency(denoted as XWMVD) under incomplete information circumstances, the inference rules of XSMVD and XWMVD based on XML Schema were discussed. The concepts of XML Schema and incomplete XML document tree according with XML Schema were formalized. Based on the concepts of sub-tree information equivalence and sub-tree information consistent, the definitions of XSMVD and XWMVD were given and their nature was studied. When XSMVD and XWMVD exist at the same time in XML Schema, their inference rules were presented and their soundness was proved. The production in this work lays the foundation for normalization of XML Schema existing XSMVD and XWMVD at the same time under incomplete information circumstances.

scholarly journals A linear-algebraic tool for conditional independence inference

2015 ◽  
Vol 6 (2) ◽  
Author(s):  
Kentaro Tanaka ◽  
Milan Studeny ◽  
Akimichi Takemura ◽  
Tomonari Sei
Keyword(s):  
Computational Result ◽  
Conditional Independence ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Positive Density ◽  
Implication Problem ◽  
Algebraic Tool ◽  
Linear Algebraic Method

In this note, we propose a new linear-algebraic method for the implication problem among conditional independence statements, which is inspired by the factorization characterization of conditional independence. First, we give a criterion in the case of a discrete strictly positive density and relate it to an earlier linear-algebraic approach. Then, we extend the method to the case of a discrete density that need not be strictly positive. Finally, we provide a computational result in the case of six variables. 

scholarly journals Polyteam semantics

2020 ◽  
Vol 30 (8) ◽  
pp. 1541-1566
Author(s):  
Miika Hannula ◽  
Juha Kontinen ◽  
Jonni Virtema
Keyword(s):  
Analogous Result ◽  
Expressive Power ◽  
Order Logic ◽  
Mathematical Framework ◽  
Dependency Theory ◽  
Dependence Logic ◽  
First Order ◽  
Team Semantics ◽  
Implication Problem ◽  
Second Order Logic

Abstract Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define Polyteam Semantics in which formulae are evaluated over a family of teams. We begin by defining a novel polyteam variant of dependence atoms and give a finite axiomatization for the associated implication problem. We relate polyteam semantics to team semantics and investigate in which cases logics over the former can be simulated by logics over the latter. We also characterize the expressive power of poly-dependence logic by properties of polyteams that are downwards closed and definable in existential second-order logic ($\textsf{ESO}$). The analogous result is shown to hold for poly-independence logic and all $\textsf{ESO}$-definable properties. We also relate poly-inclusion logic to greatest fixed point logic.

scholarly journals On the conditional independence implication problem: A lattice-theoretic approach

2013 ◽  
Vol 202 ◽  
pp. 29-51 ◽  
Author(s):  
Mathias Niepert ◽  
Marc Gyssens ◽  
Bassem Sayrafi ◽  
Dirk Van Gucht
Keyword(s):  
Conditional Independence ◽  
Theoretic Approach ◽  
Implication Problem
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