The Dual Spatial Connectives of Separation Logic

Authors:
Yuming Shen;Yuefei Sui;Ju Wang
Affiliations:
Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, China 100190 and Graduate University of Chinese Academy of Sciences, China 100 ...;Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, China 100190;School of Computer Science and Information Engineering, Guangxi Normal University, China 541004
Venue:
KSEM '09 Proceedings of the 3rd International Conference on Knowledge Science, Engineering and Management
Year:
2009

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Abstract

Separation logic has two spatial connectives *** and *** *** . It is known that *** and *** *** are not dual each other, like `and' and `or', `for all' and `there exists', `necessarily' and `possibly', etc. To define the dual connectives of *** and *** *** there are two choices: one is to take *** and *** *** as special logical connectives; another is to take *** and *** *** as binary modalities. Correspondingly, the dual modalities of *** and *** *** are represented as the dual connectives of *** and *** *** , and as the dual modalities of *** and *** *** , where the latter can be represented by unary modalities in the case that the formulas are defined in a special form.