Relational learning in a context of transposition: a review

In a typical transposition task, an animal is presented with a single pair of stimuli (for example, S3+ S4−, where plus and minus denote reward and nonreward and digits denote stimulus location on a sensory dimension such as size). Subsequently, an animal is presented with a testing pair that contains a previously reinforced or nonreinforced stimulus and a novel stimulus (for example, S2–S3 and S4–S5). Does the choice of a novel S2 instead of previously reinforced S3 in a testing pair S2–S3 indicate that the animal has learned a relation (i.e., “select smaller”)? This review of empirical evidence and theoretical accounts shows that an organism''s behavior in a transposition task is undoubtedly influenced by prior reinforcement history of the training stimuli (Spence, 1937). However, it is also affected by two other factors that are relational in nature—a similarity of two testing stimuli to each other and an overall similarity of the testing pair as a whole to the training pair as a whole. The influence of the two latter factors is especially evident in studies that use multiple pairs of training stimuli and a wide range of testing pairs comprising nonadjacent stimuli (Lazareva, Miner, Young, & Wasserman, 2008; Lazareva, Wasserman, & Young, 2005). In sum, the evidence suggests that both prior reinforcement history and relational information affect an animal''s behavior in a typical transposition task.     

The interaction of temporal generalization gradients predicts the context effect

In a temporal double bisection task, animals learn two discriminations. In the presence of Red and Green keys, responses to Red are reinforced after 1-s samples and responses to Green are reinforced after 4-s samples; in the presence of Blue and Yellow keys, responses to Blue are reinforced after 4-s samples and responses to Yellow are reinforced after 16-s samples. Subsequently, given a choice between Green and Blue, the probability of choosing Green increases with the sample duration-the context effect. In the present study we asked whether this effect could be predicted from the stimulus generalization gradients induced by the two basic discriminations. Six pigeons learned to peck Green following 4-s samples (S(+)) but not following 1-s samples (S(-)) and to peck Red following 4-s samples (S(+)) but not following 16-s samples (S(-)). Temporal generalization gradients for Green and Red were then obtained. Finally, the pigeons were given a choice between Green and Red following sample durations ranging from 1 to 16 s. Results showed that a) the two generalization gradients had the minimum at the S(-) duration, an intermediate value between the S(-) and the S(+) durations, and the maximum at the S(+) as well as more extreme durations; b) on choice trials, preference for Green over Red increased with sample duration, the context effect; and c) the two generalization gradients predicted the average context effect well. The Learning-to-Time model accounts for the major trends in the data.     

Hume and the nominalist tradition

Many of the central theses of Hume's philosophy – his rejection of real relations, universals, abstract objects and necessary causal relations – had precedents in the later medieval nominalist tradition. Hume and his medieval predecessors developed complex semantic theories to show both how ontologies are apt to become inflated and how, if we understand carefully the processes by which meaning is generated, we can achieve greater ontological parsimony. Tracing a trajectory from those medieval traditions to Hume reveals Hume to be more radical, particularly in his rejection of abstraction and abstract ideas. Hume's denial of general, abstract ideas is consistent with his philosophical principles but fails to appreciate the more sophisticated nominalist approaches to abstraction, the result of which is a theoretically impoverished account of our capacity for generalization.     

Empiricism,probability, and knowledge of arithmetic: A preliminary defense

The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgments of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Frege's concern about indiscernibility and circularity (Section 2.1), while other are more recent, such as Baker's concern about the unreliability of small samplings in the setting of arithmetic (Section 2.2). Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the ω-rule (Section 3.1) or to the non-computability and non-continuity of probability assignments (Section 3.2). Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments (Appendix A–Appendix C), such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated (Theorem 4 Appendix B). In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar.     

Second order inductive logic and Wilmers' principle

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship with the first order principles of Regularity and Super Regularity.     

汉语声调水平映射规则的内隐学习及其长度迁移效应

内隐学习领域关注的重要问题是被试能够习得何种结构及其相应的学习机制。远距离规则的研究为澄清这一问题提供了新的视角。现有研究已证实被试能够内隐地习得并迁移固定长度的远距离规则。按照内隐学习抽象性的观点,如果被试习得的是远距离的抽象规则本身,那么迁移也同时会发生在不同长度的材料上。因此,研究以独特的汉语声调水平映射规则为材料,通过对表面特征与底层规则之间的分离操作,探讨声调水平映射规则的内隐习得和长度迁移,结果表明被试不仅能够习得这一规则,还能够将该规则灵活迁移到不同长度的材料上,进一步为内隐学习的抽象性特点和无限性的学习机制提供强有力的新证据。     

Factors that encourage generalization from extinction to test reduce resurgence of an extinguished operant response

Two experiments investigated methods that reduce the resurgence of an extinguished behavior (R1) that occurs when reinforcement for an alternative behavior (R2) is discontinued. In Experiment 1, R1 was first trained and then extinguished while R2 was reinforced during a 5‐ or 25‐session treatment phase. For half the rats, sessions in which R2 was reinforced alternated with sessions in which R2 was extinguished. Controls received the same number of treatment sessions, but R2 was never extinguished. When reinforcement for R2 was discontinued, R1 resurged in the controls. However, the alternating groups showed reduced resurgence, and the magnitude of the resurgences observed during their R2 extinction sessions decreased systematically over Phase 2. In Experiment 2, R1 was first reinforced with one outcome (O1). The rats then had two types of double‐alternating treatment sessions. In one type, R1 was extinguished and R2 produced O2. In the other, R1 was unavailable and R2 produced O3. R1 resurgence was weakened when O2, but not O3, was delivered freely during testing. Together, the results suggest that methods that encourage generalization between R1 extinction and resurgence testing weaken the resurgence effect. They are not consistent with an account of resurgence proposed by Shahan and Craig (2017).     

Generalization of tacting actions in children with autism

This intervention compared the effects of two procedures on the generalization of a tacting repertoire (labeling) in 6 children with autism spectrum disorder. In one procedure the verbal antecedent stimulus “What is she doing?” appeared together with a person performing an action; in the other procedure, the antecedent stimulus was just the presence of the action. In initial tests, children emitted tacts only when the action was presented with the verbal antecedent. Thereafter, they learned to tact an action without the verbal antecedent and received tests to evaluate generalization to another action. Results indicated that in order to obtain generalization of tacting actions, it was necessary to learn to tact other actions without the verbal antecedent as well as learning to tact the action with the verbal antecedent. These findings have relevance for generalization of tacting actions from control by verbal antecedents to natural conditions and the production of spontaneous language.     

Fear generalization in humans: Impact of verbal instructions

Fear generalization lies at the heart of many anxiety problems, but little is known about the factors that can influence this phenomenon. The present study investigated whether verbal instructions about specific stimulus features can influence conditioned fear generalization. All participants were fear conditioned to a yellow triangle, using an electric shock. Participants had received pre-experimental instructions saying that the shapes (or colours) of the stimuli were informative for the occurrence of shock (group Shape and group Colour, respectively). Next, generalization was tested to presentations of a blue triangle (same shape) as well as a yellow square (same colour). Fear reactions were measured through skin conductance and online ratings of shock-expectancy. The results showed strongest generalization to the same shape stimulus in group Shape, versus the same colour stimulus in group Colour. Hence, the same learning experience can have opposite effects in terms of fear generalization, depending on verbally transmitted information about the relative importance of individual stimulus features.