Quantifier-free descriptions for quantifier solutions to interval linear systems of relations

Irene A. Sharaya

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arXiv · 1802.09199

Quantifier-free descriptions for quantifier solutions to interval linear systems of relations

Irene A. Sharaya

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Abstract

We study systems of relations of the form $Ax\,\sigma\,b$, where $\sigma$ is a vector of binary relations with the components "$=$", "$\geq$" and "$\leq$", and the parameters (elements of the matrix $A$ and right-hand side vector $b$) can take values from prescribed intervals. What is considered to be the set of its solutions depends on which logical quantifier is associated with each interval-valued parameter and what is the order of the quantifier prefixes for certain parameters. For solution sets that correspond to the quantifier prefix of a general form, we present equivalent quantifier-free descriptions in the classical interval arithmetic, in Kaucher complete interval arithmetic and in the usual real arithmetic.

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Irene A. Sharaya. 2018-02-26. Quantifier-free descriptions for quantifier solutions to interval linear systems of relations. https://arxiv.org/abs/1802.09199

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