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  1. 1 Logic and Logical Philosophy

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  1. 1 Benzmüller C.

  2. 1 Steen A.

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  1. 1 2016

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Sweet SIXTEEN: Automation via Embedding into Classical Higher-Order Logic

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Steen A., Benzmüller C.
Logic and Logical Philosophy
|
2016
|
vol. 25
|
issue 4
535-554
EN
An embedding of many-valued logics based on SIXTEEN in classical higher-order logic is presented. SIXTEEN generalizes the four-valued set of truth degrees of Dunn/Belnap’s system to a lattice of sixteen truth degrees with multiple distinct ordering relations between them. The theoretical motivation is to demonstrate that many-valued logics, like other non-classical logics, can be elegantly modeled (and even combined) as fragments of classical higher-order logic. Equally relevant are the pragmatic aspects of the presented approach: interactive and automated reasoning in many-valued logics, which have broad applications in computer science, artificial intelligence, linguistics, philosophy and mathematics, become readily enabled with state of the art reasoning tools for classical higher-order logic.
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