Infinitesimal and intensional software

无穷小和内涵软件

• 批准号: 357-2007
• 负责人: Wadge, William
• 金额: $ 1.68万
• 依托单位: University of Victoria
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=362403
• 关键词: Infinitesimal; intensional; software

I will investigate theoretical and practical aspects of a new type of logic I call "infinitesimal logic".Like fuzzy logic, it uses a spectrum of truth values between completely true at one end and completely false at the other. But unlike fuzzy logic, the additional truth values are discrete and separated from each other, not unlike quantum mechanical energy levels. For example, the truth value just below standard truth can be considered as qualitatively less true - in fact, incomparably (even "infinitely") less true.One theoretical use is in the semantics (meaning) of rule based systems with negative conditions - such as Prolog with negation-as-failure. On the practical side, the intermediate truth values can help users express preferences and priorities.For example, suppose you want to fly to Ottawa and prefer an aisle seat. Infinitesimal logic allows you to formulate this so that there are three answers: an unqualified Yes, which means you can; a qualified Yes, which means you can get to Ottawa, but not in an aisle seat; and an unqualified No, which means you can't get to Ottawa.You can therefore make clear the fact that having  an aisle seat is incomparably less important than getting to Ottawa; for instance, that you are not interested in aisle seats to Calgary.

我将研究一种被我称为“无穷小逻辑”的新型逻辑的理论和实践方面。与模糊逻辑一样，它使用介于完全正确和完全错误之间的一系列真值。但与模糊逻辑不同，附加的真值是离散的，彼此分开，与量子力学能级没有什么不同。例如，略低于标准真值的真值可以被认为在质量上不那么真实--事实上，无与伦比(甚至是“无限”)不真实。一种理论用途是在具有否定条件的基于规则的系统的语义(含义)中--例如带有否定即失败的序言。在实用方面，中间真值可以帮助用户表达偏好和优先顺序。例如，假设你想飞往渥太华，更喜欢靠过道的座位。无限小的逻辑允许你这样做，这样就有三个答案：不合格的是，意味着你可以去；合格的是，意味着你可以去渥太华，但不是靠过道的座位；以及不合格的否，这意味着你不能去渥太华。因此，你可以清楚地表明，坐靠过道的座位比去渥太华要重要得多；例如，你对去卡尔加里的过道座位不感兴趣。