On languages that contain their own ungroundedness predicate (Q2904042)
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scientific article; zbMATH DE number 6063254
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On languages that contain their own ungroundedness predicate |
scientific article; zbMATH DE number 6063254 |
Statements
5 August 2012
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hardest logic problem
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Kripke
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liar
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ungroundedness
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truth-teller
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On languages that contain their own ungroundedness predicate (English)
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In Kripke's fixed-point construction, paradoxical sentences are neither true nor false, but ungrounded. Here, ungroundedness is treated as a third truth value, and the conditions specified under which an interpreted language can contain its own ungroundedness predicate, so that ``\(\sigma\) is ungrounded'' is true just in case \(\sigma\) is ungrounded. The result is then applied to the reasoning of the truth-teller by \textit{B. Rabern} and \textit{L. Rabern} in their paper [Analysis, Oxf. 68, No. 2, 105--112 (2008; Zbl 1143.03317)].
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