2009 Fiscal Year Final Research Report

Semantics for Computational Structures -From Viewpoint of Duality and Noncommutativity-

Research Project

Project/Area Number	19540145
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	General mathematics (including Probability theory/Statistical mathematics)
Research Institution	Okinawa Institute of Science and Technology (2008-2009) Keio University (2007)
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)
Project Period (FY)	2007 – 2009
Keywords	linear logic / denotational semantics / polarized category / full completeness / relational category / indexed linear logic / polarity / topological semantics
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.

(6 results)