用单位圆构建信息度量新框架，解决语义信息悖论问题。
Towards a Measure Theory of Semantic Information
- 基于单位圆与量子概率类比，建立信息度量空间。
- 矛盾与永真命题信息量为零，互斥消息信息量相等。
- 适用于需消除经典悖论的逻辑与语义分析场景。
巴-希尔和卡纳普的经典语义信息量化理论认为，命题的信息量与其概率成反比，但此方法将矛盾句赋予最大信息量，即巴-希尔-卡纳普悖论。弗洛里迪提出基于距离度量和抛物线关系的新理论以消除该悖论，但未能成功。本文在弗洛里迪理论框架内批判性分析其得失，并提出一种基于单位圆的新方法——该关系贯穿三角学至量子理论。通过类比冯·诺依曼量子概率，构造满足弗洛里迪所有要求的信息度量空间，彻底消除悖论。结果表明：矛盾句与重言式信息量为零，相互矛盾的消息具有同等信息量。文中以实例说明其应用价值。
原文摘要 · Abstract (English)
A classic account of the quantification of semantic information is that of Bar-Hiller and Carnap. Their account proposes an inverse relation between the informativeness of a statement and its probability. However, their approach assigns the maximum informativeness to a contradiction: which Floridi refers to as the Bar-Hillel-Carnap paradox. He developed a novel theory founded on a distance metric and parabolic relation, designed to remove this paradox. Unfortunately is approach does not succeed in that aim. In this paper I critique Floridi's theory of strongly semantic information on its own terms and show where it succeeds and fails. I then present a new approach based on the unit circle (a relation that has been the basis of theories from basic trigonometry to quantum theory). This is used, by analogy with von Neumann's quantum probability to construct a measure space for informativeness that meets all the requirements stipulated by Floridi and removes the paradox. In addition, while contradictions and tautologies have zero informativeness, it is found that messages which are contradictory to each other are equally informative. The utility of this is explained by means of an example.
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