Maps between some different kinds of contraction function: The finite case

In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial meet contraction over that theory. The purpose of the present paper is to study the relationship more finely, by seeking an explicit map between the component orderings involved in each of the two kinds of contraction. It is shown that at least in the finite case a suitable map exists, with the consequence that the relational, transitively relational, and antisymmetrically relational partial meet contraction functions form identifiable subclasses of the safe contraction functions, over any theory finite modulo logical equivalence. In the process of constructing the map, as the composition of four simple transformations, mediating notions of bottom and top contraction are introduced. The study of the infinite case remains open.     

Cognitive Behavioral Therapy and the Treatment of Posttraumatic Stress Disorder: Where Counseling and Neuroscience Meet

There is increasing evidence to support the biological basis of mental disorders. Subsequently, understanding the neurobiological context from which mental distress arises can help counselors appropriately apply cognitive behavioral therapy and other well‐researched cognitive interventions. The purpose of this article is to describe the neurobiological context underlying the formation and treatment of posttraumatic stress disorders, a mental disorder frequently encountered by counselors, from a cognitive therapy framework.     

Conditional Probability in the Light of Qualitative Belief Change

We explore ways in which purely qualitative belief change in the AGM tradition throws light on options in the treatment of conditional probability. First, by helping see why it can be useful to go beyond the ratio rule defining conditional from one-place probability. Second, by clarifying what is at stake in different ways of doing that. Third, by suggesting novel forms of conditional probability corresponding to familiar variants of qualitative belief change, and conversely. Likewise, we explain how recent work on the qualitative part of probabilistic inference leads to a very broad class of ‘proto-probability’ functions.     

From over-imitation to super-copying: adults imitate causally irrelevant aspects of tool use with higher fidelity than young children

Recent research has revealed a striking tendency in young children to imitate even causally irrelevant actions, a phenomenon dubbed 'over-imitation'. To investigate whether children develop beyond this, we allowed both adults and children to witness either a child or adult model performing goal-relevant and goal-irrelevant actions to extract a reward from a transparent puzzle box. Surprisingly, copying of irrelevant actions increased with age, with the adults performing the task with less efficiency than the children. Participants of all ages were more likely to perform the irrelevant actions performed by an adult model, than by a child model. These results suggest that people may become more imitative as they mature, whilst selectively copying particular models with a high level of fidelity. We suggest that this combination of faithful copying and selectivity underwrites the powerful social learning necessary for the level of cultural transmission on which our species depends.     

Logical questions behind the lottery and preface paradoxes: lossy rules for uncertain inference

We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ??lossy?? rule. A second lesson is the possibility of rational inconsistent belief; this leads us to formulate criteria for deciding when an inconsistent set of beliefs may reasonably be retained.     

Permission from an Input/Output Perspective

Input/output logics are abstract structures designed to represent conditional obligations and goals. In this paper we use them to study conditional permission. This perspective provides a clear separation of the familiar notion of negative permission from the more elusive one of positive permission. Moreover, it reveals that there are at least two kinds of positive permission. Although indistinguishable in the unconditional case, they are quite different in conditional contexts. One of them, which we call static positive permission, guides the citizen and law enforcement authorities in the assessment of specific actions under current norms, and it behaves like a weakened obligation. Another, which we call dynamic positive permission, guides the legislator. It describes the limits on the prohibitions that may be introduced into a code, and under suitable conditions behaves like a strengthened negative permission.