The subject generally known as ``information theory'' has nothing to say about how much meaning is conveyed by the information. Accordingly, we fill this gap with the first rigorously justifiable, quantitative definition of ``pragmatic information'' as the amount of information that becomes meaningful because it is used in making a decision. We posit that such information updates a ``state of the world'' random variable, $\omega$, that informs the decision. The pragmatic information of a single message is then defined as the Kulbach-Leibler divergence between the a priori and updated probability distributions of $\omega$, and the pragmatic information of a message ensemble is defined as the expected value of the pragmatic information values of the ensemble's component messages. We justify these definitions by showing, first, that the pragmatic information of a single message is the expected difference between the shortest binary encoding of $\omega$ under the {\it a priori} and updated probability distributions, and, second, that the average of the pragmatic values of individual messages, when sampled a large number of times from the ensemble, approaches its expected value. The resulting pragmatic information formulas have many hoped-for properties, such as non-negativity and additivity for independent decisions and ``pragmatically independent'' messages. We also sketch two applications of these formulas: The first is the single play of a slot machine, a.k.a. a ``one armed bandit'', with an unknown probability of payout; the second being the reformulation of the efficient market hypothesis of financial economics as the claim that the pragmatic information content of all available data about a given security is zero.

翻译：通常被称为"信息论"的学科并未涉及信息所传达的意义量。为此，我们首次提出严格可论证的"实用信息"定量定义，将其定义为因用于决策而变得有意义的信息量。我们假设此类信息更新了一个指导决策的"世界状态"随机变量ω。单条消息的实用信息被定义为ω先验概率分布与更新后概率分布之间的库尔贝克-莱布勒散度，而消息集合的实用信息则被定义为该集合中所有组成消息的实用信息值的期望值。我们通过两方面论证该定义的合理性：首先，单条消息的实用信息等于在先验概率分布与更新后概率分布下对ω的最短二进制编码长度的期望差值；其次，当从集合中大量采样时，各条消息的实用信息均值将趋近其期望值。由此推导出的实用信息公式具有众多理想性质，如非负性、独立决策及"实用独立"消息的可加性。我们还概述了这两个公式的两个应用：其一为单次操作已知赔付概率未知的老虎机（俗称"独臂强盗"）；其二为将金融经济学中的有效市场假说重新表述为：关于某证券的所有可用数据的实用信息含量为零。