Standard information theory says nothing about how much meaning is conveyed by a message. We fill this gap with a rigorously justifiable, quantitative definition of ``pragmatic information'', the amount of meaning in a message relevant to a particular decision. We posit that such a message updates a random variable, $\omega$, that informs the decision. The pragmatic information of a single message is then defined as the Kulbach-Leibler divergence between the apriori and aposteriori probabilities of $\omega$; the pragmatic information of a message ensemble is the expected value of the pragmatic information of the ensemble's component messages. We justify these definitions by proving that the pragmatic information of a single message is the expected difference between the shortest binary encoding of $\omega$ under the a priori and a posteriori distributions, and that the average of the pragmatic values of individual messages, when sampled a large number of times from the ensemble, approaches its expected value. Pragmatic information is non-negative and additive for independent decisions and ``pragmatically independent'' messages. Also, pragmatic information is the information analogue of free energy: just as free energy quantifies the part of a system's total energy available to do useful work, so pragmatic information quantifies the information actually used in making a decision. We sketch 3 applications: the single play of a slot machine, a.k.a. a ``one armed bandit'', with an unknown payout probability; a characterization of the rate of biological evolution in the so-called ``quasi-species'' model; and a reformulation of the efficient market hypothesis of finance. We note the importance of the computational capacity of the receiver in each case.

翻译：标准信息理论未涉及消息传递的意义量。本文通过严格可论证的定量化“实用信息”定义填补这一空白，该定义量化了与特定决策相关的消息意义含量。我们假设此类消息会更新一个为决策提供信息的随机变量$\omega$。单个消息的实用信息定义为$\omega$先验概率与后验概率间的Kullback-Leibler散度；消息集合的实用信息则为集合中各消息实用信息的期望值。我们通过以下证明验证该定义的合理性：单个消息的实用信息是$\omega$在先验分布与后验分布下最短二进制编码长度的期望差，且当从集合中多次采样时，各消息实用信息的平均值趋近于其期望值。实用信息具有非负性，并对独立决策及“实用独立”消息满足可加性。此外，实用信息是自由能的信息理论类比：正如自由能量化系统总能量中可用于做功的部分，实用信息则量化了决策过程中实际使用的信息量。我们概述三个应用场景：具有未知赔付概率的老虎机单次博弈（即“单臂强盗问题”）；所谓“准物种”模型中生物进化速率的表征；以及金融学有效市场假说的重构。我们特别强调了各场景中信息接收方计算能力的重要性。