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The Parallel versus Branching Recurrences in Computability Logic

作     者:Xu, Wenyan Liu, Sanyang 

作者机构:Xidian Univ Dept Math Xian 710071 Peoples R China 

出 版 物:《NOTRE DAME JOURNAL OF FORMAL LOGIC》 (Notre Dam J. Logic.)

年 卷 期:2013年第54卷第1期

页      面:61-78页

核心收录:

学科分类:01[哲学] 0101[哲学-哲学] 0701[理学-数学] 

基  金:Fundamental Research Funds for the Central Universities [K5051270010] National Natural Science Foundation of China 

主  题:computability logic cirquent calculus interactive computation game semantics resource semantics 

摘      要:This paper shows that the basic logic induced by the parallel recurrence (sic) of computability logic (i.e., the one in the signature {(sic), boolean AND, boolean OR, (sic), gamma}) is a proper superset of the basic logic induced by the branching recurrence (sic) (i.e., the one in the signature {(sic), boolean AND, boolean OR, (sic), (sic)}). The latter is known to be precisely captured by the cirquent calculus system CL15, conjectured by Japaridze to remain sound-but not complete-with (sic) instead of (sic). The present result is obtained by positively verifying that conjecture. A secondary result of the paper is showing that (sic) is strictly weaker than (sic) in the sense that, while (sic) F logically implies (sic)F, the reverse does not hold.

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