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THE LOGIC OF INFORMATION IN STATE SPACES

Part of: Algebraic logic Philosophical aspects of logic and foundations Theory of computing

Published online by Cambridge University Press:  25 August 2020

LEVIN HORNISCHER
LEVIN HORNISCHER*
Affiliation:
ILLC, UNIVERSITY OF AMSTERDAM SCIENCE PARK 107 1098 XG AMSTERDAMTHE NETHERLANDSE-mail: l.a.hornischer@uva.nl
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Abstract

State spaces are, in the most general sense, sets of entities that contain information. Examples include states of dynamical systems, processes of observations, or possible worlds. We use domain theory to describe the structure of positive and negative information in state spaces. We present examples ranging from the space of trajectories of a dynamical system, over Dunn’s aboutness interpretation of fde, to the space of open sets of a spectral space. We show that these information structures induce so-called hype models which were recently developed by Leitgeb (2019). Conversely, we prove a representation theorem: roughly, hype models can be represented as induced by an information structure. Thus, the well-behaved logic hype is a sound and complete logic for reasoning about information in state spaces.

As application of this framework, we investigate information fusion. We motivate two kinds of fusion. We define a groundedness and a separation property that allow a hype model to be closed under the two kinds of fusion. This involves a Dedekind–MacNeille completion and a fiber-space like construction. The proof-techniques come from pointless topology and universal algebra.

Keywords

State spacedomain theoryHYPEinformation fusion

MSC classification

Primary: 68Q55: Semantics
Secondary: 03G10: Lattices and related structures 03A99: None of the above, but in this section
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 1 , March 2021 , pp. 155 - 186
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Copyright
© Association for Symbolic Logic, 2020

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