Infinitesimal and intensional software

我将研究一种新型逻辑的理论和实践方面，我称之为“无穷小逻辑”。就像模糊逻辑一样，它使用了一组真值，一端是完全真，另一端是完全假。但与模糊逻辑不同的是，附加真值是离散的，彼此分离，与量子力学的能级不同。例如，略低于标准真值的真值可以被认为在性质上较不真实——事实上，是无可比拟的（甚至是“无限”）较不真实。一个理论上的应用是在带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Prolog。在实用方面，中间真值可以帮助用户表达偏好和优先级。例如，假设你想飞往渥太华，想要一个靠过道的座位。无限小的逻辑允许你表述这个问题，所以有三个答案：一个不确定的Yes，这意味着你可以；一个合格的Yes，这意味着你可以去渥太华，但不能坐在靠过道的座位上；和一个不合格的不，这意味着你不能去渥太华。因此，你可以清楚地表明，拥有一个靠过道的座位远没有到达渥太华重要；例如，你对去卡尔加里的靠过道的座位不感兴趣。

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.