PP-2009-45: Prehistoric Phenomena and Self-referentiality in Realization Procedure

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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