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2013 The Parallel versus Branching Recurrences in Computability Logic
Wenyan Xu, Sanyang Liu
Notre Dame J. Formal Logic 54(1): 61-78 (2013). DOI: 10.1215/00294527-1731389

Abstract

This paper shows that the basic logic induced by the parallel recurrence \Yup of computability logic (i.e., the one in the signature $\{ ¬, ∧,∨,⅄,\small{𝖸} \}$) is a proper superset of the basic logic induced by the branching recurrence $⫰$ (i.e., the one in the signature $\{ ¬,∧,∨, ⫰, ⫯ \}$). The latter is known to be precisely captured by the cirquent calculus system CL15, conjectured by Japaridze to remain sound—but not complete—with $⅄$ instead of $⫰$. The present result is obtained by positively verifying that conjecture. A secondary result of the paper is showing that $⅄$ is strictly weaker than $⫰$ in the sense that, while $⫰F$ logically implies $⅄F$, the reverse does not hold.

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Wenyan Xu. Sanyang Liu. "The Parallel versus Branching Recurrences in Computability Logic." Notre Dame J. Formal Logic 54 (1) 61 - 78, 2013. https://doi.org/10.1215/00294527-1731389

Information

Published: 2013
First available in Project Euclid: 14 December 2012

zbMATH: 1291.03072
MathSciNet: MR3007962
Digital Object Identifier: 10.1215/00294527-1731389

Subjects:
Primary: 03B47
Secondary: 03B70 , 68Q10 , 68T15 , 68T27

Keywords: cirquent calculus , Computability logic , Game semantics , Interactive computation , resource semantics

Rights: Copyright © 2013 University of Notre Dame

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