Towards a “Sophisticated” Model of Belief Dynamics. Part II: Belief Revision.

In the companion paper (Towards a “sophisticated” model of belief dynamics. Part I), a general framework for realistic modelling of instantaneous states of belief and of the operations involving them was presented and motivated. In this paper, the framework is applied to the case of belief revision. A model of belief revision shall be obtained which, firstly, recovers the Gärdenfors postulates in a well-specified, natural yet simple class of particular circumstances; secondly, can accommodate iterated revisions, recovering several proposed revision operators for iterated revision as special cases; and finally, offers an analysis of Rott’s recent counterexample to several Gärdenfors postulates [32], elucidating in what sense it fails to be one of the special cases to which these postulates apply.     

Preference-based belief revision for rule-based agents

Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief revision for agents which reason in a simpler logic than full first-order logic, namely rule-based reasoners. We show that it is possible to define a contraction operation for rule-based reasoners, which we call McAllester contraction, which satisfies all the basic Alchourrón, Gärdenfors and Makinson (AGM) postulates for contraction (apart from the recovery postulate) and at the same time can be computed in polynomial time. We prove a representation theorem for McAllester contraction with respect to the basic AGM postulates (minus recovery), and two additional postulates. We then show that our contraction operation removes a set of beliefs which is least preferred, with respect to a natural interpretation of preference. Finally, we show how McAllester contraction can be used to define a revision operation which is also polynomial time, and prove a representation theorem for the revision operation.     

Co-induction of long-term potentiation and long-term depression at a central synapse in the leech

Most studies of long-term potentiation (LTP) have focused on potentiation induced by the activation of postsynaptic NMDA receptors (NMDARs). However, it is now apparent that NMDAR-dependent signaling processes are not the only form of LTP operating in the brain [Malenka, R. C., & Bear, M. F. (2004). LTP and LTD: An embarrassment of riches. Neuron, 44, 5–21]. Previously, we have observed that LTP in leech central synapses made by the touch mechanosensory neurons onto the S interneuron was NMDAR-independent [Burrell, B. D., & Sahley, C. L. (2004). Multiple forms of long-term potentiation and long-term depression converge on a single interneuron in the leech CNS. Journal of Neuroscience, 24, 4011–4019]. Here we examine the cellular mechanisms mediating T-to-S (T → S) LTP and find that its induction requires activation of metabotropic glutamate receptors (mGluRs), voltage-dependent Ca²⁺ channels (VDCCs) and protein kinase C (PKC). Surprisingly, whenever LTP was pharmacologically inhibited, long-term depression (LTD) was observed at the tetanized synapse, indicating that LTP and LTD were activated at the same time in the same synaptic pathway. This co-induction of LTP and LTD likely plays an important role in activity-dependent regulation of synaptic transmission.     

Generalization of conditioned fear-potentiated startle in humans: experimental validation and clinical relevance

Though generalization of conditioned fear has been implicated as a central feature of pathological anxiety, surprisingly little is known about the psychobiology of this learning phenomenon in humans. Whereas animal work has frequently applied methods to examine generalization gradients to study the gradual weakening of the conditioned-fear response as the test stimulus increasingly differs from the conditioned stimulus (CS), to our knowledge no psychobiological studies of such gradients have been conducted in humans over the last 40 years. The current effort validates an updated generalization paradigm incorporating more recent methods for the objective measurement of anxiety (fear-potentiated startle). The paradigm employs 10, quasi-randomly presented, rings of gradually increasing size with extremes serving as CS+ and CS−. The eight rings of intermediary size serve as generalization stimuli (GSs) and create a continuum-of-similarity from CS+ to CS−. Both startle data and online self-report ratings demonstrate continuous decreases in generalization as the presented stimulus becomes less similar to the CS+. The current paradigm represents an updated and efficacious tool with which to study fear generalization—a central, yet understudied conditioning-correlate of pathologic anxiety.     

Drinking without thinking: an implicit measure of alcohol motivation predicts failure to control alcohol use

Addiction is characterized by dyscontrol - substance use despite intentions to restrain. Using a sample of at-risk drinkers, the present study examined whether an implicit measure of alcohol motivation (the Implicit Association Test [IAT]; Greenwald, A.G., McGhee, D.E., & Schwartz, J.L.K. (1998). Measuring individual differences in implicit cognition: the Implicit Association Test. Journal of Personality and Social Psychology, 74, 1464-1480) would predict dyscontrol of alcohol use. Participants completed an IAT and, to elicit motivation to restrain alcohol use, were instructed that greater consumption in a taste test would impair performance on a later task for which they could win a prize. All participants viewed aversive slides and then completed a thought-listing task. Participants either exerted self-control by suppressing negative affect and thoughts regarding the slides or did not exert self-control. Post-manipulation, the groups did not differ in mood, urge to drink or motivation to restrain consumption. During the subsequent taste test, participants whose self-control resources were depleted consumed more alcohol than did those in the control group. Additionally, the IAT, but not an explicit measure of alcohol motivation, more strongly predicted alcohol use when self-control resources were depleted. The results indicate that the IAT may have utility in predicting dyscontrolled alcohol use.     

Attentional resources in visual tracking through occlusion: the high-beams effect

A considerable amount of research has uncovered heuristics that the visual system employs to keep track of objects through periods of occlusion. Relatively little work, by comparison, has investigated the online resources that support this processing. We explored how attention is distributed when featurally identical objects become occluded during multiple object tracking. During tracking, observers had to detect small probes that appeared sporadically on targets, distracters, occluders, or empty space. Probe detection rates for these categories were taken as indexes of the distribution of attention throughout the display and revealed two novel effects. First, probe detection on an occluder’s surface was better when either a target or distractor was currently occluded in that location, compared to when no object was behind that occluder. Thus even occluded (and therefore invisible) objects recruit object-based attention. Second, and more surprising, probe detection for both targets and distractors was always better when they were occluded, compared to when they were visible. This new attentional high-beams effect indicates that the ability to track through occlusion, though seemingly effortless, in fact requires the active allocation of special attentional resources.     

A Puzzle for Particulars?

In this paper we examine a puzzle recently posed by Aaron Preston for the traditional realist assay of property (quality) instances. Consider Socrates (a red round spot) and red₁—Socrates’ redness. For the traditional realist, both of these entities are concrete particulars. Further, both involve redness being `tied to’ the same bare individuator. But then it appears that red₁ is duplicated in its ‘thicker’ particular (Socrates), so that it can’t be predicated of Socrates without redundancy. According to Preston, this suggests that a concrete particular and its property instances aren’t genuinely related. We argue that Preston’s proffered solution here—to treat property instances as “mental constructs”—is fraught with difficulty. We then go on to show how, by fine-tuning the nature of bare particulars, treating them as abstract modes of things rather than concrete particulars, the traditional realist can neatly evade Preston’s puzzle.

Core information processing deficits in developmental dyscalculia and low numeracy

There are two different conceptions of the innate basis for numerical abilities. On the one hand, it is claimed that infants possess a 'number module' that enables them to construct concepts of the exact numerosities of sets upon which arithmetic develops (e.g. Butterworth, 1999; Gelman & Gallistel, 1978). On the other hand, it has been proposed that infants are equipped only with a sense of approximate numerosities (e.g. Feigenson, Dehaene & Spelke, 2004), upon which the concepts of exact numerosities are constructed with the aid of language (Carey, 2004) and which forms the basis of arithmetic (Lemer, Dehaene, Spelke & Cohen, 2003). These competing proposals were tested by assessing whether performance on approximate numerosity tasks is related to performance on exact numerosity tasks. Moreover, performance on an analogue magnitude task was tested, since it has been claimed that approximate numerosities are represented as analogue magnitudes. In 8-9-year-olds, no relationship was found between exact tasks and either approximate or analogue tasks in normally achieving children, in children with low numeracy or in children with developmental dyscalculia. Low numeracy was related not to a poor grasp of exact numerosities, but to a poor understanding of symbolic numerals.     

Benefits of multisensory learning

Studies of learning, and in particular perceptual learning, have focused on learning of stimuli consisting of a single sensory modality. However, our experience in the world involves constant multisensory stimulation. For instance, visual and auditory information are integrated in performing many tasks that involve localizing and tracking moving objects. Therefore, it is likely that the human brain has evolved to develop, learn and operate optimally in multisensory environments. We suggest that training protocols that employ unisensory stimulus regimes do not engage multisensory learning mechanisms and, therefore, might not be optimal for learning. However, multisensory-training protocols can better approximate natural settings and are more effective for learning.     

The moderating effects of stimulus valence and arousal on memory suppression

This study examined the separate and combined effects of stimulus valence and arousal on retrieval inhibition. Participants performed Anderson and Green's (2001) memory suppression task with stimuli varying across dimensions of valence and arousal. Memory was tested through free and cued recall as well as speeded recognition. Results showed that both stimulus valence and arousal influenced the extent to which participants successfully inhibited retrieval, but not in the ways anticipated. Specifically, the strongest inhibition effects were for highly arousing, pleasant words. In addition, unpleasant stimuli that were suppressed were better recalled during both cued and free-recall tasks than pleasant stimuli that were suppressed. Across all tests of memory performance, there were no significant differences between the experimental conditions for highly arousing, unpleasant words. The implications of these findings are discussed.