We study the complexity of the isomorphism relation on classes of computable structures. We use the notion of FF-reducibility introduced in [9] to show completeness of the isomorphism relation on many familiar classes in the context of all ${\mathrm{\Sigma }}_{1}^{1}$ equivalence relations on hyperarithmetical subsets of ω.

The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver [20] and Harrington, Kechris and Louveau [6] show that with respect to Borel reducibility, any Borel equivalence relation strictly above equality on ω is above equality on , the power set of ω, and any Borel equivalence relation strictly above equality on the reals is above equality modulo finite on . In this article we examine the effective (...) content of these and related results by studying effectively Borel equivalence relations under effectively Borel reducibility. The resulting structure is complex, even for equivalence relations with finitely many equivalence classes. However use of Kleene’s O as a parameter is sufficient to restore the picture from the noneffective setting. A key lemma is that of the existence of two effectively Borel sets of reals, neither of which contains the range of the other under any effectively Borel function; the proof of this result applies Barwise compactness to a deep theorem of Harrington establishing for any recursive ordinal α the existence of singletons whose α-jumps are Turing incomparable. (shrink)

We study the structure of Σ11 equivalence relations on hyperarithmetical subsets of ω under reducibilities given by hyperarithmetical or computable functions, called h-reducibility and FF-reducibility, respectively. We show that the structure is rich even when one fixes the number of properly equation imagei.e., Σ11 but not equation image equivalence classes. We also show the existence of incomparable Σ11 equivalence relations that are complete as subsets of ω × ω with respect to the corresponding reducibility on sets. We study complete Σ11 (...) equivalence relations and show that existence of infinitely many properly Σ11 equivalence classes that are complete as Σ11 sets is necessary but not sufficient for a relation to be complete in the context of Σ11 equivalence relations. (shrink)

The BankXX system models the process of perusing and gathering information for argument as a heuristic best-first search for relevant cases, theories, and other domain-specific information. As BankXX searches its heterogeneous and highly interconnected network of domain knowledge, information is incrementally analyzed and amalgamated into a dozen desirable ingredients for argument (called argument pieces), such as citations to cases, applications of legal theories, and references to prototypical factual scenarios. At the conclusion of the search, BankXX outputs the set of argument (...) pieces filled with harvested material relevant to the input problem situation.This research explores the appropriateness of the search paradigm as a framework for harvesting and mining information needed to make legal arguments. In this article, we describe how legal research fits the heuristic search framework and detail how this model is used in BankXX. We describe the BankXX program with emphasis on its representation of legal knowledge and legal argument. We describe the heuristic search mechanism and evaluation functions that drive the program. We give an extended example of the processing of BankXX on the facts of an actual legal case in BankXX's application domain — the good faith question of Chapter 13 personal bankruptcy law. We discuss closely related research on legal knowledge representation and retrieval and the use of search for case retrieval or tasks related to argument creation. Finally we review what we believe are the contributions of this research to the understanding of the diverse disciplines it addresses. (shrink)

Individuals typically produce auditory sequences, such as speech or music, at a consistent spontaneous rate or tempo. We addressed whether spontaneous rates would show patterns of convergence across the domains of music and language production when the same participants spoke sentences and performed melodic phrases on a piano. Although timing plays a critical role in both domains, different communicative and motor constraints apply in each case and so it is not clear whether music and speech would display similar timing mechanisms. (...) We report the results of two experiments in which adult participants produced sequences from memory at a comfortable spontaneous (uncued) rate. In Experiment 1, monolingual pianists in Buffalo, New York engaged in three production tasks: speaking sentences from memory, performing short melodies from memory, and tapping isochronously. In Experiment 2, English-French bilingual pianists in Montréal, Canada produced melodies on a piano as in Experiment 1, and spoke short rhythmically-structured phrases repeatedly. Both experiments led to the same pattern of results. Participants exhibited consistent spontaneous rates within each task. People who produced one spoken phrase rapidly were likely to produce another spoken phrase rapidly. This consistency across stimuli was also found for performance of different musical melodies. In general, spontaneous rates across speech and music tasks were not correlated, whereas rates of tapping and music were correlated. Speech rates (for syllables) were faster than music rates (for tones) and speech showed a smaller range of spontaneous rates across individuals than did music or tapping rates. Taken together, these results suggest that spontaneous rate reflects cumulative influences of endogenous rhythms (in consistent self-generated rates within domain), peripheral motor constraints (in finger movements across tapping and music), and communicative goals based on the cultural transmission of auditory information (slower rates for to-be-synchronized music than for speech). (shrink)

In this article we evaluate the BankXX program from several perspectives. BankXX is a case-based legal argument program that retrieves cases and other legal knowledge pertinent to a legal argument through a combination of heuristic search and knowledge-based indexing. The program is described in detail in a companion article in Artificial Intelligence and Law 4: 1--71, 1996. Three perspectives are used to evaluate BankXX:(1) classical information retrieval measures of precision and recall applied against a hand-coded baseline; (2) knowledge-representation and case-based (...) reasoning, where the baseline is provided by the functionality of a well-known case-based argument program, HYPO (Ashley, 1990); and (3) search, in which the performance of BankXX run with various parameter settings, for instance, resource limits, is compared. In this article we report on an extensive series of experiments performed to evaluate the program. We also describe two additional experiments concerning(1) the program's search behavior; and (2) the use of a modified form of precision and recall based on case similarity. Finally we offer some general conclusions that might be drawn from these particular experiments. (shrink)

All of our information about the world is derived from the function of our senses, and thus they are the principal source of all our knowledge. This was recognized explicitly by early Greek philosophers, remained an important point of discussion for nineteenth‐century philosophers, and continues to be a key issue for present‐day philosophers, psychologists, and neuroscientists. It is a key issue in cognitive science because, by initiating the processes that store and evaluate information, sensory information transmission can be considered a (...) cognitive initiator. In a very real sense, who we are and how we see the world are the result of the experiences that are mediated by our sensory systems. These are some of the reasons why the study of sensory systems has occupied such a prominent place in modern cognitive neuroscience. (shrink)

This essay examines the implications for modernist studies of using the term after in After Modernism to suggest three meanings: after assuming an end-date for modernism based on linear periodizati...

SummaryUtah has the highest total fertility of any state in the United States and also the highest proportion of population affiliated with the Church of Jesus Christ of Latter-day Saints. Data were used from the 1996 Utah Health Status Survey to investigate how annual household income, education and affiliation with the LDS Church affect fertility for married women in Utah. Younger age and higher education were negatively correlated with fertility in the sample as a whole and among non-LDS respondents. Income (...) was negatively associated with fertility among non-LDS respondents. However, income was positively correlated with fertility among LDS respondents. This association persisted when instrumental variables were used to address the potential simultaneous equations bias arising from the potential endogeneity of income and fertility. The LDS religion's pronatalist stance probably encourages childbearing among those with higher income. (shrink)

The epithet χαλκοκραυνον has perturbed many, though the most recent English editors have printed it without comment. The new Liddell and Scott betrays uneasiness in its ‘epithet of the sea, perhaps false reading for χαλκαμρυγος, gleaming like copper or bronze’. Overseas scholars flatly reject it. Wilamowitz poured scorn on it in his Interpretationen and commented in his larger edition neque intelligitur et frustra temptatum est. Weir Smyth obelizes it. Bothe, Hermann, Weil, and others offered emendations. In Bursians Jahresberichte, ccxxxiv, p. (...) 104 W. Morel observed Von Erz und Blitz befreit uns Bruhns χλιαρκρουνον. This is emancipation indeed. (shrink)

The author explains Michael Oakeshott's distinctive theory of law through an explanation of its notion of authority. He explains the view that modern states are ambiguous, consisting partly of civil associations and partly of enterprise associations. Authority is not a function of people's attitudes to those in power, but exists when a government's action is itself accepted as sufficient reason for unconditional obedience. Authority in this sense cannot exist in enterprise association, commitment to which must be contingent on the fulfillment (...) of purposes common to all participants. But modern states are compulsory associations, different from each. Furthermore, authority could never be justified on a rational choice model, which must always be teleological in character. Because this means there can be no solution to the problem of political obligation, all philosophy can do is describe abstractly the Rule of Law state which does reconcile authority and liberty. (shrink)

This book introduces a new approach to the issue of radical scientific revolutions, or "paradigm-shifts," given prominence in the work of Thomas Kuhn. The book articulates a dynamical and historicized version of the conception of scientific a priori principles first developed by the philosopher Immanuel Kant. This approach defends the Enlightenment ideal of scientific objectivity and universality while simultaneously doing justice to the revolutionary changes within the sciences that have since undermined Kant's original defense of this ideal. Through a modified (...) Kantian approach to epistemology and philosophy of science, this book opposes both Quinean naturalistic holism and the post-Kuhnian conceptual relativism that has dominated recent literature in science studies. Focussing on the development of "scientific philosophy" from Kant to Rudolf Carnap, along with the parallel developments taking place in the sciences during the same period, the author articulates a new dynamical conception of relativized a priori principles. This idea applied within the physical sciences aims to show that rational intersubjective consensus is intricately preserved across radical scientific revolutions or "paradigm-shifts and how this is achieved. (shrink)

American Academy of Pediatrics (AAP) and American College of Medical Genetics (ACMG) recently provided two recommendations about predictive genetic testing of children. The Clinical Sequencing Exploratory Research Consortium's Pediatrics Working Group compared these recommendations, focusing on operational and ethical issues specific to decision making for children. Content analysis of the statements addresses two issues: (1) how these recommendations characterize and analyze locus of decision making, as well as the risks and benefits of testing, and (2) whether the guidelines conflict or (...) come to different but compatible conclusions because they consider different testing scenarios. These statements differ in ethically significant ways. AAP/ACMG analyzes risks and benefits using best interests of the child and recommends that, absent ameliorative interventions available during childhood, clinicians should generally decline to order testing. Parents authorize focused tests. ACMG analyzes risks and benefits using the interests of the child and other family members and recommends that sequencing results be examined for additional variants that can lead to ameliorative interventions, regardless of age, which laboratories should report to clinicians who should contextualize the results. Parents must accept additional analysis. The ethical arguments in these statements appear to be in tension with each other. (shrink)