Most theories of learning consider inferring a function f from either observations about f or, questions about f. We consider a scenario whereby the learner observes f and asks queries to some set A. If I is a notion of learning then I[A] is the set of concept classes I-learnable by an inductive inference machine with oracle A. A and B are I-equivalent if I[A] = I[B]. The equivalence classes induced are the degrees of inferability. We prove several results about (...) when these degrees are trivial, and when the degrees are omniscient. (shrink)

Standard definitions of procrastination underscore the irrational nature of this habit, a critical criterion being that the procrastinating individual delays despite expecting to be worse off for the delay. However, an examination of more than 175 items in 18 procrastination scales reveals that they do not address such a forward-looking criterion. Consequently, scales run the risk of not separating maladaptive and irrational delays from other forms of delay. We propose that forward-looking considerations may not be the best way of operationalizing (...) the irrationality involved in procrastination and argue that scales should instead focus on past negative consequences of unnecessary delay. We suggest a new scale to measure such procrastination-related negative consequences and demonstrate that this scale, used separately or combined with established procrastination scales, performs better in predicting negative states and correlates to procrastination than established scales. The new scale seems to be helpful in separating trivial forms of unnecessary delay from maladaptive forms and hence represents a potentially valuable tool in research and clinical/applied efforts. (shrink)

This article deals with the Katta Langar manuscript, which is known as one of the earliest Qur'ān copies attributed to III. Caliph Uthman. The study consists of an introduction, a conclusion and two sections. The introduction section begins with the information that the Katta Langar Mushaf which is called by this name relative to the Katta Langar village of Uzbekistan, is in the library of the Tashkent Uzbekistan Muslims Administration. Only ninety-seven pages of the mushaf, which was lost for a (...) period, have survived. Since twelve of these leaves appear again in Katta Langar, they are meant as the Katta Langar manuscripts. Therefore, this article not only aims to examine in detail all the extant leaves of the mushaf but also the twelve leaves, which are known today as the Katta Langar manuscripts. Although the research done so far has made it clear that this mushaf is not one of the copies of Uthman, the mushaf has been the subject of many studies. The first of the studies on the Katta Langar Mushaf was published by M.E. Masson, while the most detailed work belongs to Efim Rezvan. Existing studies on the mushaf are methodologically either a publication or a catalogue study. In this study, the Katta Langar copy was compared with the sources of the mushaf literature and discussed more comprehensively. (shrink)

Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and "nearly" minimal size, i.e., within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs limits learning power. However, in scientific inference, parsimony is considered highly desirable. A lim-computablefunction is (by definition) one calculable by a total procedure allowed to change its mind finitely many times about its (...) output. Investigated is the possibility of assuaging somewhat the limitation on learning power resulting from requiring parsimonious final programs by use of criteria which require the final, correct programs to be "not-so-nearly" minimal size, e.g., to be within a lim-computable function of actual minimal size. It is shown that some parsimony in the final program is thereby retained, yet learning power strictly increases. Considered, then, are lim-computable functions as above but for which notations for constructive ordinals are used to bound the number of mind changes allowed regarding the output. This is a variant of an idea introduced by Freivalds and Smith. For this ordinal notation complexity bounded version of lim-computability, the power of the resultant learning criteria form finely graded, infinitely ramifying, infinite hierarchies intermediate between the computable and the lim-computable cases. Some of these hierarchies, for the natural notations determining them, are shown to be optimally tight. (shrink)

Limiting identification of r.e. indexes for r.e. languages (from a presentation of elements of the language) and limiting identification of programs for computable functions (from a graph of the function) have served as models for investigating the boundaries of learnability. Recently, a new approach to the study of "intrinsic" complexity of identification in the limit has been proposed. This approach, instead of dealing with the resource requirements of the learning algorithm, uses the notion of reducibility from recursion theory to compare (...) and to capture the intuitive difficulty of learning various classes of concepts. Freivalds, Kinber, and Smith have studied this approach for function identification and Jain and Sharma have studied it for language identification. The present paper explores the structure of these reducibilities in the context of language identification. It is shown that there is an infinite hierarchy of language classes that represent learning problems of increasing difficulty. It is also shown that the language classes in this hierarchy are incomparable, under the reductions introduced, to the collection of pattern languages. Richness of the structure of intrinsic complexity is demonstrated by proving that any finite, acyclic, directed graph can be embedded in the reducibility structure. However, it is also established that this structure is not dense. The question of embedding any infinite, acyclic, directed graph is open. (shrink)

Limiting identification of r.e. indexes for r.e. languages and limiting identification of programs for computable functions have served as models for investigating the boundaries of learnability. Recently, a new approach to the study of "intrinsic" complexity of identification in the limit has been proposed. This approach, instead of dealing with the resource requirements of the learning algorithm, uses the notion of reducibility from recursion theory to compare and to capture the intuitive difficulty of learning various classes of concepts. Freivalds, (...) class='Hi'>Kinber, and Smith have studied this approach for function identification and Jain and Sharma have studied it for language identification. The present paper explores the structure of these reducibilities in the context of language identification. It is shown that there is an infinite hierarchy of language classes that represent learning problems of increasing difficulty. It is also shown that the language classes in this hierarchy are incomparable, under the reductions introduced, to the collection of pattern languages. Richness of the structure of intrinsic complexity is demonstrated by proving that any finite, acyclic, directed graph can be embedded in the reducibility structure. However, it is also established that this structure is not dense. The question of embedding any infinite, acyclic, directed graph is open. (shrink)