Hannula, M. and Virtema, J. (2022) Tractability frontiers in probabilistic team semantics and existential second-order logic over the reals. Annals of Pure and Applied Logic, 173 (10). 103108. ISSN 0168-0072
Abstract
Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus is on the axiomatizability, complexity, and expressivity of probabilistic inclusion logic and its extensions. We identify a natural fragment of existential second-order logic with additive real arithmetic that captures exactly the expressivity of probabilistic inclusion logic. We furthermore relate these formalisms to linear programming, and doing so obtain PTIME data complexity for the logics. Moreover, on finite structures, we show that the full existential second-order logic with additive real arithmetic can only express NP properties. Lastly, we present a sound and complete axiomatization for probabilistic inclusion logic at the atomic level.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | Dependence logic; Team semantics; Metafinite structures; Blum-Shub-Smale machine |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Funding Information: | Funder Grant number DEUTSCHE FORSCHUNGSGEMEINSCHAFT UNSPECIFIED |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 07 Mar 2022 10:12 |
Last Modified: | 24 Feb 2023 12:18 |
Status: | Published |
Publisher: | Elsevier BV |
Refereed: | Yes |
Identification Number: | 10.1016/j.apal.2022.103108 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:184436 |