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

计算结构的语义-从对偶性和非交换性的角度来看-

• 批准号: 19540145
• 负责人: HAMANO Masahiro
• 金额: $ 2.08万
• 依托单位: Okinawa Institute of Science and Technology (2008-2009)Keio University (2007)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540145/
• 关键词: linear logic; denotational semantics; polarized category; full completeness; relational category; indexed linear logic; polarity; topological semantics; second order linear logic; polarized linear logic; focalization; topological phase space

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.

我们研究由极化线性逻辑引起的计算的语义结构。利用对偶极性的两个逆变范畴之间的模和附加关系，构造了一个范畴模型来模拟计算。为了模拟二阶逻辑的可计算性，我们将极性的拓扑结构容纳到（非极化）代数语义中。利用拓扑语义，我们解决了线性逻辑在其极化片段上的二阶守恒定理。为了建立这两种计算语义和可计算语义之间的关系，我们给出了极化逻辑的一个索引系统，并用该系统表征了一个指称完备性。

项目成果

An Indexed System for Multiplicative Additive Polarized Linear Logic

乘法加法极化线性逻辑的索引系统

• 发表时间: 2008
• 期刊: Proceedings of 17th EACSL Annual Conference on Computer Science Logic, Lecture Notes in Computer Science 5213
• 作者: Masahiro Hamano;Ryo Takemura;Jinping Zhang;板井昌典;T. Arai;Masahiro Hamano
• 通讯作者: Masahiro Hamano

A Categorical Semantics for Polarized MALL

极化购物中心的分类语义

• 发表时间: 2007
• 期刊: Annals of Pure and Applied Logic(Elsevier) 145
• 作者: Masahiro Hamano;Phil Scott
• 通讯作者: Phil Scott

A Phase Semantics for Polarized Linear Logic and Second Order Conservativity

极化线性逻辑和二阶保守性的相位语义

• 发表时间: 2010
• 期刊: Journal of Symbolic Logic 75(1)
• 作者: Masahiro Hamano;Ryo Takemura
• 通讯作者: Ryo Takemura

An Indexed System for Characters of Group Representations

群体表征特征索引系统

• 发表时间: 2008
• 作者: Iacus;S. M.;Uchida;M. and Yoshida;N.;Masahiro Hamano
• 通讯作者: Masahiro Hamano

An Indexed System for Multiplicative Additive Polarized Lineaa Logic

乘法加法极化线性逻辑的索引系统

• 发表时间: 2008
• 期刊: Proc. of 17th EACSL AnnualConference on Computer Science Logic, Lecture Notes in Computer Science(Springer Verlag) 5213
• 作者: Masahiro Hamano;Ryo Takemura
• 通讯作者: Ryo Takemura