Probabilistic dynamic belief revision

We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing probabilistic “action models” and proposing a notion of probabilistic update product, that comes together with appropriate reduction laws.     

Attentional SNARC: there's something special about numbers (let us count the ways)

We report a study that examines whether the presentation of irrelevant, ordinal information at central fixation interacts with the allocation of attention beyond fixation. Previous research has demonstrated that number perception influences the allocation of spatial attention, such that the presentation of a spatially nonpredictive number at fixation results in attention being allocated to the left when the central number is low (e.g., 1), and attention being allocated to the right when the central number is high (e.g., 9). Here, we examine whether this attentional SNARC effect (spatial numerical association of response codes) generalizes to other ordinal sequences: letters, days, and months. Though we replicate the attentional SNARC we find that this effect is number-specific, unless participants are required to process the cue in an order-relevant fashion. This discovery of number-specificity has important implications both for the functional separation between SNARC and attention-SNARC effects, as well as lending support to recent theories regarding the specificity of a shared neural architecture between numbers and visuospatial attention.     

Using High-Probability Request Sequences to Increase Journal Writing

Written expression is a key aspect of academic success. Programs to enhance writing skills often rely on a feedback loop that consists of student production (i.e., get something on paper) and teacher feedback. Unfortunately, some students fail to produce enough written product so that the teacher can give constructive feedback. The purpose of this study was to examine two methods to increase the written word production of four students with difficulties in written expression. In the verbal prompt condition, students were given verbal prompts by their teacher to resume writing in their journals after the student stopped writing for approximately one min. In the high-p request condition, the teacher asked students to write a series of three words that typically occasioned compliance prior to asking the student to resume journal writing. Both interventions were assessed within the context of verbal praise and no verbal praise. Results suggested that both interventions increased the number of words written, particularly in the verbal praise condition. However, the high-p request sequence was more efficient and produced writing behavior that was more persistent across sessions. Results are discussed within the context of the theory of behavioral momentum.     

Systematic Withdrawal

Although AGM theory contraction (Alchourrón et al., 1985; Alchourrón and Makinson, 1985) occupies a central position in the literature on belief change, there is one aspect about it that has created a fair amount of controversy. It involves the inclusion of the postulate known as Recovery. As a result, a number of alternatives to AGM theory contraction have been proposed that do not always satisfy the Recovery postulate (Levi, 1991, 1998; Hansson and Olsson, 1995; Fermé, 1998; Fermé and Rodriguez, 1998; Rott and Pagnucco, 1999). In this paper we present a new addition, systematic withdrawal, to the family of withdrawal operations, as they have become known. We define systematic withdrawal semantically, in terms of a set of preorders, and show that it can be characterised by a set of postulates. In a comparison of withdrawal operations we show that AGM contraction, systematic withdrawal and the severe withdrawal of Rott and Pagnucco (1999) are intimately connected by virtue of their definition in terms of sets of preorders. In a future paper it will be shown that this connection can be extended to include the epistemic entrenchment orderings of Gärdenfors (1988) and Gärdenfors and Makinson (1988) and the refined entrenchment orderings of Meyer et al. (2000).     

Implementation of Belief Change Operators Using BDDs

While the theory of belief change has attracted a lot of interest from researchers, work on implementing belief change and actually putting it to use in real-world problems is still scarce. In this paper, we present an implementation of propositional belief change using Binary Decision Diagrams. Upper complexity bounds for the algorithm are presented and discussed. The approach is presented both in the general case, as well as on specific belief change operators from the literature. In an effort to gain a better understanding of the empirical efficiency of the algorithms involved, a fault diagnosis problem on combinational circuits is presented, implemented and evaluated.     

When negative evidence increases confidence: change in belief after hearing two sides of a dispute

Four experiments examined change in confidence after hearing two sides of a dispute. The results showed that a case independently judged to weakly support one side often increased confidence that the opposing side was correct. Furthermore, the stronger the first case, the more likely a subsequent weak case had a reverse impact. Traditional belief‐updating models, which tend to focus on change in belief after individual pieces of evidence rather than entire cases, cannot account for these results, and a model that can account for them is introduced. In the new model, case strength is evaluated with respect to a relatively demanding (and malleable) reference point. A weak case can fall below this demanding reference point, resulting in a reverse impact on confidence. Cases must exceed relatively high strength thresholds in order to have their intended impact because they are expected to be biased summaries of evidence. When it is clear that a weak case is unbiased, it affects confidence in the intended direction. Copyright © 2002 John Wiley & Sons, Ltd.     

Some factors that influence the acquisition of complex, stereotyped, response sequences in pigeons

Two pigeons were required to peck six to nine illuminated response keys. A response on any one of the keys darkened that key. When each key had been darkened, a reinforcer was delivered. No specific sequence of key pecking was ever required. The keys were presented in various matrices: three by two, three by three, horizontal rows, and vertical columns. The keys either presented the same stimulus, white light; or each key presented a different stimulus, a color or form. The results indicated that although there were 720 to 362,880 different sequences that would produce reinforcement, each bird developed a particular, stereotyped sequence that dominated its behavior. Variability among the birds across phases yielded less than 60 sequences, .0001 to 6 percent of the possible sequences. The data suggest that a reinforcement contingency that includes “free choice” of response sequence will produce stereotypical response sequences that function as complex “units” of behavior.     

Analytical Dispositionalism and Practical Reason

The paper examines the plausibility of analytical dispositionalism about practical reason, according to which the following claims are conceptual truths about common sense ethical discourse: i) Ethics: agents have reasons to act in some ways rather than others, and ii) Metaphysical Modesty: there is no such thing as a response independent normative reality. By elucidating two uncontroversial assumptions which are fundamental to the common sense commitment to ethics, I argue that common sense ethical discourse is most plausibly construed as committed to the denial of metaphysical modesty, and thereby as committed to the existence of a response independent normative reality.     

Effects of D-amphetamine and ethanol on variable and repetitive key-peck sequences in pigeons

This experiment assessed the effects of d-amphetamine and ethanol on reinforced variable and repetitive key-peck sequences in pigeons. Pigeons responded on two keys under a multiple schedule of Repeat and Vary components. In the Repeat component, completion of a target sequence of right, right, left, left resulted in food. In the Vary component, 4-peck sequences differing from the previous 10 produced food. d-Amphetamine (0.1-3.0 mg/kg, i.m.) was administered in two separate phases, separated by ethanol administration (1.0-2.0 g/kg, i.g.). Under control conditions, measures of variability were high in the Vary component, and lower in the Repeat component. Following administration of the highest dose of d-amphetamine, but not ethanol, response rates decreased in both components. d-Amphetamine and ethanol tended to increase overall sequence variability in the Repeat component, and had less of an effect in the Vary component. Performance in the Repeat component during Phase 2 of d-amphetamine administration was more disrupted than during Phase 1. Measures of variability and repetition based on shifts in the relative frequency distributions of the 16 possible keypeck sequences differed from those based on the overall measure of variability, highlighting the importance of considering both molar and molecular measures when assessing the effects of drugs on reinforced variability and repetition. In addition, the shifts in the relative frequency distribution of response sequences suggest that d-amphetamine produced decrements in repeat performance by decreasing discriminative control within response sequences, whereas ethanol decreased repeat performance by decreasing discriminability between components as well as discriminative control within response sequences.     

An Elementary Presentation of the Equivalence Between MV-algebras and l-groups With Strong Unit

Aim of this paper is to provide a self-contained presentation of the natural equivalence between MV-algebras and lattice-ordered abelian groups with strong unit.