2009 Fiscal Year Final Research Report
Semantics for Computational Structures -From Viewpoint of Duality and Noncommutativity-
| Project/Area Number |
19540145
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Okinawa Institute of Science and Technology (2008-2009)
Keio University (2007) |
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Principal Investigator |
HAMANO Masahiro Okinawa Institute of Science and Technology, 大学院・情報理工学系研究科, 客員研究員 (50313705)
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| Project Period (FY) |
2007 – 2009
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| Keywords | linear logic / denotational semantics / polarized category / full completeness / relational category / indexed linear logic / polarity / topological semantics |
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| Research Abstract |
We investigate semantcal structures of computations arising from polarized linear logic. A categorical model is constructed to model computations by employing modules and adjunction between two contravariant categories of dual polarities. To model computability for the second order logic, we accommodate a topological structure for the polarities to a (non-polarized) algebraic semantics. Using the topological semantics, we solve a second order conservation theorem of linear logic over its polarized fragment. To make a relationship between these two kind of semantics of computations and of computability, we present an indexed system for polarized logic and characterize a denotational completeness in terms of the system.
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