Peter Killeen

Among the many excellent presentations and posters of this conference, I was tasked with making sense of two of the most esoteric. This is my meat and potatoes. I hasten to add that they are not esoteric because they are peripheral; au contraire, they are central. They are only esoteric because you have to be an intellectual searcher to delve into them. In the face of them, they are formidable; but, relax, and contemplate them, and they are most intellectually gratifying. McDowell shows us how, through the same sort of selection processes that both animals and their habits are subject to, the basic laws of behavior arise. This is foundational—where do our laws come from?—McDowell gives us a glimpse. Cox tells us what those laws do; or don’t. He demonstrates these in the contexts that matter—very large data sets form the world of action—where our cloistered predictions may be evaluated, and improved. His Natural Language Programming Machines provide visions of what we say and do that can only be seen at this higher level. If we are to move our field to higher relevance, this is the way.

Agency is action aimed at goals selected by an agent. A deterministic world view leaves scant room for agency. To reconcile the arguments, we represent action as nested control systems, ranging from clearly deterministic to clearly volitional. Negative feedback minimizes deviations from setpoints (goals). Goals are determined by higher modules in a hierarchy of systems, ranging from gamma-efferent spindles through reflexes to operant responses; these last, and the larger system that contains them, called the Self, comprise volitional agents. When operants become habitual they descend to closed teleonomic systems-automaticity. Change in emotional states, and unpredicted changes in the context-raise them back to full volitional systems. At the highest level is the Self-the brain's model of the agent. When aroused out of open teleonomic functioning, it must reconsider means and ends. It does so by simulating action plans, using the same neural systems it uses to effect them. The simulated stimuli and responses are conscious, approximating their perceptions as experienced in real time; this verisimilitude gives them their hedonic value. Positive feedback plays a key role in these complex adaptive systems, as it focuses and holds attention on the most salient percepts and goals, permitting the self-organization of action plans. The Self is not a separate entity, but a colloquy of command modules wearing the avatar of the agent. This system is put into correspondence with Grossberg's Adaptive Resonance Theory. Free will and determinism emerge not as binary opposites, but the modulating inputs to a spectrum of systems.

Hyperbolic relations between independent and dependent variables are ubiquitous in the experimental analysis of behavior, mentioned in over 150 articles in the Journal of the Experimental Analysis of Behavior. There are two principal forms of hyperbolae: The first describes the relation between response rate and reinforcement rate on variable-interval schedules of reinforcement; it rises asymptotically toward a maximum. The second describes the relation between the current equivalent value of an incentive and its delay or (im)probability; it falls from a maximum toward an asymptote of 0. Where do these come from? What do their parameters mean? How are they related? This article answers the first two questions and addresses the last.

The rate of discounting future goods is a crucial factor in intertemporal trade‐offs, upon which depends not only individual well‐being but also that of our planet: How much privation now for a temperate future for our grandchildren? What is the best way to measure how the value of future goods decreases with its delay? The most accurate discount functions involve several covarying parameters, making interpretation equivocal. A universal and robust measure is the area under the discount curve, the AuC. The AuC of a hyperbolic discount function is a logarithmic function of the discount rate, k. The same integral also approximates the area under a hyperboloid function. A simple technique converts each datum into estimates of the discount rate, eliminating rogue data points in the process. These trimmed estimates are converted into areas and tested against data, where they succeed at predicting the AuC and its relation to log(k).

The additive utility theory of discounting is extended to probability and commodity discounting. Because the utility of a good and the disutility of its delay combine additively, increases in the utility of a good offset the disutility of its delay: Increasing the former slows the apparent discount even with the latter, time-disutility, remaining invariant, giving the magnitude effect. Conjoint measurement showed the subjective value of money to be a logarithmic function of its amount, and subjective probability-the probability weighting function-to be Prelec's (1998). This general theory of discounting (GTD) explains why large amounts are probability discounted more quickly, giving the negative magnitude effect. Whatever enhances the value of a delayed asset, such as its ability to satisfy diverse desires, offsets its delay and reduces discounting. Money's liquidity permits optimization of the portfolio of desired goods, providing added value that accounts for its shallow temporal discount gradient. GTD predicts diversification effects for delay but none for probability discounting. Operations such as episodic future thinking that increase the larder of potential expenditures-the portfolio of desirable goods-increase the value of the asset, flattening the discount gradient. States that decrease the larder, such as stress, depression, and overweening focus on a single substance like a drug, constrict the portfolio, decreasing its utility and thereby steepening the gradient. GTD provides a unified account of delay, probability, and cross-commodity discounting. It explains the effects of motivational states, dispositions, and cognitive manipulations on discount gradients. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

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.

The Trace Theory of Perception (TToP) is applied to temporal interval bisection. In this protocol, after familiarization with the referents for long or short judgments — the endpoints of the range — observers classify probe stimuli ‘short’ or ‘long’ (closer to the short or to the long referent). The midpoint of the range is predicted by TToP to be near and slightly above the geometric mean of the endpoints, and generally independent of signal modality. The observed bisection points, the time at which the probability of a long response is , deviates from those predictions. It was hypothesized that the deviations were caused by the observers’ bias to use categories equally often, which would be accomplished if the bisection point were at the median of the probes. A weighted average of the predicted midpoint and the median accounted for most of the variance in over 100 experiments, and explained the difference between linear and logarithmic spacing of probes.