PP-2009-45: Yu, Junhua (2009) Prehistoric Phenomena and Self-referentiality in Realization Procedure. [Report]
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Abstract
With terms allowed in types, the Logic of Proofs (LP) has its
polynomials as advanced combinatory terms. As a result, types of the
form t: ϕ(t), which have self-referential meanings, are also
included. If we can fix the class of non-self-referential-realizable
S4-theorems, then we may find some S4 (and hence, intuitionistic)
measure of self-referentiality introduced by the terms-in-types
feature. In this paper, we define and study “prehistoric phenomena”
in G3s, a Gentzen-style formulation of S4. A special prehistoric
phenomenon, i.e., the left-prehistoric-loop, is then shown to be
necessary for self-referentiality in S4-LP realization.
| Item Type: | Report |
|---|---|
| Report Nr: | PP-2009-45 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2009 |
| Uncontrolled Keywords: | Self-reference, Logic of Proofs, Realization |
| Depositing User: | Johan van Benthem |
| Date Deposited: | 12 Oct 2016 14:37 |
| Last Modified: | 12 Oct 2016 14:37 |
| URI: | https://eprints.illc.uva.nl/id/eprint/374 |
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