The three principles of reinforcement are (1) events such as incentives and reinforcers increase the activity of an organism; (2) that activity is bounded by competition from other responses; and (3) animals approach incentives and their signs, guided by their temporal and physical conditions, together called the “contingencies of reinforcement.” Mathematical models of each of these principles comprised mathematical principles of reinforcement (MPR; Killeen, 1994). Over the ensuing decades, MPR was extended to new experimental contexts. This article reviews the basic theory and its extensions to satiation, warm-up, extinction, sign tracking, pausing, and sequential control in progressive-ratio and multiple schedules. In the latter cases, a single equation balancing target and competing responses governs behavioral contrast and behavioral momentum. Momentum is intrinsic in the fundamental equations, as behavior unspools more slowly from highly aroused responses conditioned by higher rates of incitement than it does from responses from leaner contexts. Habits are responses that have accrued substantial behavioral momentum. Operant responses, being predictors of reinforcement, are approached by making them: The sight and feel of a paw on a lever is approached by placing paw on lever, as attempted for any sign of reinforcement. Behavior in concurrent schedules is governed by approach to momentarily richer patches (melioration). Applications of MPR in behavioral pharmacology and delay discounting are noted.

中文翻译：

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强化计划理论

强化的三个原则是：（1）诸如激励和强化物之类的事件会增加有机体的活性；(2) 该活动受到其他反应的竞争的限制；（3）动物在时间和身体条件的指导下接近激励及其信号，统称为“强化的意外事件”。每个原理的数学模型都包含强化的数学原理（MPR；Killeen，1994）。在接下来的几十年里，MPR 被扩展到新的实验环境。本文回顾了基本理论及其对饱足感、热身、消退、信号跟踪、暂停以及渐进比例和多个时间表的顺序控制的扩展。在后一种情况下，平衡目标和竞争反应的单个方程控制行为对比和行为动量。动量是基本方程中固有的，因为与来自较贫乏的环境的反应相比，由较高的煽动率调节的高度激发的反应的行为释放得更慢。习惯是已经积累了大量行为动力的反应。操作性反应是强化的预测因素，通过制作它们来接近：通过将爪子放在杠杆上来接近爪子在杠杆上的视觉和感觉，就像尝试任何强化迹象一样。并发计划中的行为由暂时丰富补丁（改善）的方法控制。注意到 MPR 在行为药理学和延迟贴现中的应用。