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This article presents the results of a secondary analysis of the RSA-911 database from the Rehabilitation Services Administration. All successful vocational rehabilitation (VR) closures for individuals with mental retardation, cerebral palsy, and epilepsy for five data points between 1985 and 1995 were investigated. Trends in the use of competitive employment versus sheltered workshops and employment outcomes (hours and earnings) are examined. The use of supported employment in the VR system and its outcomes are also discussed. An additional analysis of the impact of the 1992 Rehabilitation Act amendments is included. Findings include increased incidence of competitive employment and supported employment services but a decrease in real earnings.

This study investigated implementation of the 1992 Rehabilitation Act Amendments and examined perceived changes in practices that expanded access to state vocational rehabilitation (VR) services as of 1996. Through the use of a national survey, data were collected from 251 VR administrators and 254 counselors. A secondary analysis of the Rehabilitation Service Administration's database (RSA-911 from fiscal years 1988,1993, and 1995) was also conducted to examine changes on key data elements. Findings related to the mandate to expand access included the reduction in eligibility timeline, use of existing information, presumption of benefit, and efforts to serve those previously underserved. Perceived changes in daily VR practices since the implementation of the law in 1992 are discussed.

Publisher Summary This chapter explains logic with denumerably long formulas and finite strings of quantifiers. In making an extension to an infinitary logic, Tarski originally suggested that infinite strings of quantifiers also be allowed. In some ways, in the denumerable case, this plan is not reasonable. The logic discussed in this paper is called L ω1 ω0 , where the second subscript indicates that the strings of quantifiers prefixing any subformula of a formula must be finite in length. L ω1 ω0 is the ordinary finitary predicate logic. Among countable systems at least, the axioms (**) do characterize the well-orderings. Non-standard models of (**) must be uncountable. The downward LOWENHEIM-SKOLEM theorem for L ω1 ω0 is that every countable set of sentences which has a model of infinite cardinality has models of all smaller infinite cardinalities. The proof is immediate when one realizes that the sub-formulas require Skolem functions for their initial quantifiers, which are each functions of only a finite number of arguments. The corresponding upward theorem is not so obvious.

Survey data from a national, random sample of 643 service providers were analyzed to examine past, current, and future utilization of integrated and segregated day and employment services. The percentage of persons in integrated employment increased to 30% in 1991, from a total of 17% documented during 1986. However, the average number of persons served in segregated, facility-based work programs has also increased since 1986, and half the respondents (N = 643) either planned to start new facility-based programs, maintain the current service capacity, or increase the number served by 1997. Implications of a dual system of integrated versus segregated services and potential incentives for stimulating conversion of facility-based services are discussed.

Logic has been long interested in whether answers to certain questions are computable in principle, since the outcome puts bounds on the possibilities of formalization. More recently, precise comparisons in the efficiency of decision methods have become available through the developments in complexity theory. These, however, are applications to logic, and a big question is whether methods of logic have significance in the other direction for the more applied parts of computability theory. Programming !anguages offer an obvious opportunity as their syntactic formalization is well advanced; however, the semantical theory can hardly be said to be complete. Though we have many examples, we have still to give wide-ranging mathematical answers to these queries: What is a machine? What is a computable process? How (or how well) does a machine simulate a process? Programs naturally enter in giving descriptions of processes. The definition of the precise meaning of a program then requires us to explain what are the objects of computation (in a way, the statics of the problem) and how they are to be transformed (the dynamics).So far the theories of automata and of nets, though most interesting for dynamics, have formalized only a portion of the field, and there has been perhaps too much concentration of the finite-state and algebraic aspects. It would seem that the understanding of higher-level program features involves us with infinite objects and forces us to pass through several levels of explanation to go from the conceptual ideas to the final simulation on a real machine. These levels can be made mathematically exact if we can find the right abstractions to represent the necessary structures.The experience of many independent workers with the method of data types as lattices (or partial orderings) under an information content ordering, and with their continuous mappings, has demonstrated the flexibility of this approach in providing definitions and proofs, which are clean and without undue dependence on implementations. Nevertheless much remains to be done in showing how abstract conceptualizations can (or cannot) be actualized before we can say we have a unified theory.

The paper (first written in 1969 and circulated privately) concerns the definition, axiomatization, and applications of the hereditarily monotone and continuous functionals generated from the integers and the Booleans (plus “undefined” elements). The system is formulated as a typed system of combinators (or as a typed λ-calculus) with a recursion operator (the least fixed-point operator), and its proof rules are contrasted to a certain extent with those of the untyped λ-calculus. For publication (1993), a new preface has been added, and many bibliographical references and comments in footnotes have been appended.

A class of Partial Equivalence Relations (PERs) is described such that the resulting full subcategory of the realizability universe has the expected properties of a good category of CPOs; that is, it is a Cartesian closed category and every endomorphism has a canonical fixed point. Moreover, the reflection functor into the subcategory of strict maps (usually called the “lifting operation”) yields a good notion of “partial map,” a necessary condition if one wishes to maintain a connection between strict maps and partial maps. It is shown that all functors that arise in practice have canonical invariant objects; hence a host of domain equations are guaranteed to have solutions.

A cross-sectional descriptive study was performed to evaluate resuscitation decisions and factors that impact these choices for young people with severe developmental disabilities residing in a skilled nursing facility. Decision-makers were provided with information to clarify resuscitation preferences. Parents/guardians of 30 of the 67 residents also completed a survey. A significant number of decision-makers changed their resuscitation preference to DNR after detailed explanations were provided. Survey results suggest that interpersonal relationships, such as those with family members, religious leader, and physician, were more influential for families who chose full resuscitation compared to those with DNR preferences. Factors such as perception of quality of life and medical condition of the individuals with developmental disabilities were not significantly different between these two groups.

The paper presents in an informal way several conflicting viewpoints concerning concepts, theories, models, and applications of λ-calculus and the combinators.

In Chapter I we encountered the rich order theoretic structure of complete lattices and of continuous lattices. Wherever it was feasible to express statements on the level of generality of dcpo s and domains we did so. Perhaps even more typical for these partially ordered sets is their wealth of topological structure. The aim of the present chapter is to introduce topology into the study – a program to be continued in Chapter III. Section II-1 begins with a discussion of the Scott topology and its connection with the convergence given in order theoretic terms by lower limits, or liminfs. This leads to a characterization theorem for domains in terms of properties of their lattices of Scott open sets (II-1.14) – a type of theorem that will become a recurrent theme (see Chapter VII). One motivation for such considerations arises from the appearances of domain theory in theoretical computer science: one typically needs the generality of domains to model the structures and constructions under consideration, while continuous lattices enter the scene as their lattices of open sets. In Section II-2 we determine that the functions continuous for the Scott topology are those preserving directed sups. We can thus express one and the same property of a function between dcpo s either in topological or in order theoretical terms. The space [ S → T ] of all Scott-continuous functions between continuous lattices is itself a continuous lattice, and the category of continuous lattices proves to be cartesian closed .

The author's discovery of domains and domain-theoretic models for the lambda -calculus in 1969 is discussed, along with the research of others working in the area at that time. >

This article describes the key ingredients and processes in transporting an empirically supported, research-developed family therapy for adolescent drug abusers, Multidimensional Family Therapy (MDFT), into an intensive day treatment program. Using the same systems change principles that guide this treatment approach, the technology transfer process has been, from its inception, a collaborative, multidimensional, systemic intervention aimed at changing organizational structures, and attitudinal and behavioral patterns with multiple staff members at several levels of the program. This article describes: (1) the conceptual and empirical basis for these technology transfer efforts; (2) the technology being adapted and transferred; and (3) the critical events and processes that have shaped the transfer of MDFT into this program. We discuss this process and the outcomes thus far through the lens of Simpson's organizational change model and specify the implications of this experience for the expansion of current conceptualization of technology transfer.

This article examines provision of postsecondary education services by the Vocational Rehabilitation (VR) system to eligible individuals with disabilities nationwide. The results of a secondary analysis of elements of the RSA-911 database from the Rehabilitation Services Administration in FY 1997 are discussed. The extent to which individuals within the VR system receive postsecondary education services is compared to the rate of individuals with and without disabilities participating in postsecondary education in the general population. An association between receipt of postsecondary services and VR outcomes is examined. Findings show that receiving postsecondary education services has little effect on the rate of successful closures in the VR system. Individuals receiving postsecondary education services from VR do show higher rates of competitive employment and improved employment outcomes including higher earnings and greater number of hours worked per week. Differences in receipt of postsecondary education services by disability type and the policy implications are discussed.

Domain theory for denotational semantics is over thirty years old. There are many variations on the idea and many interesting constructs that have been proposed by many people for realizing a wide variety of types as domains. Generally, the effort has been to create categories of domains that are cartesian closed (that is, have products and function spaces interpreting typed lambda-calculus) and permit solutions to domain equations (that is, interpret recursive domain definitions and perhaps untyped lambda-calculus).

The full category of equilogical spaces can be thought of either as ER(TOP), the category of equivalence relations on T 0 -topological spaces and equivariant continuous maps (i.e., equivalence preserving), or PER(DOM/T), the category of partial equivalence relations on Scott domains with a top (i.e., algebraic lattices) and equivariant continuous maps, or PER(POWER), the category of partial equivalence relations on power-set spaces and equivariant continuous maps. (See also the the abstract of Andrej Bauer at this meeting for a discussion of another equivalent category.) If we replace general topological spaces with countably based spaces - each given with a particular choice of a countable basis - we can then ask how the resulting categories express effective (computable) notions. The most explicit equivalent version of the category obtained is PER(P(N)), the category of partial equivalence relations over the power-set-of-N domain and equivariant continuous maps. The talk will discuss how the notion of computability appears in this category and how the category can be used as a model for a type theory enriched with a ‘computability’ modal operator. (See also the abstract of Lars Birkedal at this meeting.)

This work is a step toward the development of a logic for types and computation that includes not only the usual spaces of mathematics and constructions, but also spaces from logic and domain theory. Using realizability, we investigate a configuration of three toposes that we regard as describing a notion of relative computability. Attention is focussed on a certain local map of toposes, which we first study axiomatically, and then by deriving a modal calculus as its internal logic. The resulting framework is intended as a setting for the logical and categorical study of relative computability.

Since 1989, the author has tried to show that it is possible to put a complete semester-long course in machine-held form. Several examples have been carried out (in Mathematica), and the paper reports on the experience, on the problems encountered, and on some suggestions for future developments.

Our basic premise is that the ability to construct and modify programs will not improve without a new and comprehensive look at the entire programming process. Past theoretical research, say, in the logics of programs, has tended to focus on methods for reasoning about individual programs; little has been done, it seems to us, to develop a sound understanding of the process of programming — the process by which programs evolve in concept and in practice. At present, we lack the means to describe the techniques of program construction and improvement in ways that properly link verification, documentation and adaptability.

During the Fall Semester of 1989 I presented a junior/senior mathematics course on projective geometry at my university, with a syllabus organized along quite traditional lines. I used a Macintosh II computer and the Mathematica symbolic computation program, a product of Wolfram Research, Inc. The lectures were delivered primarily from the console, using a screen attached to the computer and projected by an overhead projector. The students were expected to do their homework on a computer, and the final examination was a project on a topic selected individually by each student, again, to be done on the computer.

In a list entitled “Epigrams on Programming” published a few years ago, the late and well known computer pioneer Alan J. Perlis said (Epigram 65): Make no mistake about it: Computers process numbers — not symbols. We measure our understanding (and control) by the extent to which we can arithmetize an activity.

Logic has been long interested in whether answers to certain questions are computable in principle, since the outcome puts bounds on the possibilities of formalization. More recently, precise comparisons in the efficiency of decision methods have become available through the developments in complexity theory. These, however, are applications to logic, and a big question is whether methods of logic have significance in the other direction for the more applied parts of computability theory. Programming languages offer an obvious opportunity as their syntactic formalization is well advanced; however, the semantical theory can hardly be said to be complete. Though we have many examples, we have still to give wide-ranging mathematical answers to these queries: What is a machine? What is a computable process? How (or how well) does a machine simulate a process? Programs naturally enter in giving descriptions of processes. The definition of the precise meaning of a program then requires us to explain what are the objects of computation (in a way, the statics of the problem) and how they are to be transformed (the dynamics). So far the theories of automata and of nets, though most interesting for dynamics, have formalized only a portion of the field, and there has been perhaps too much concentration on the finite-state and algebraic aspects. It would seem that the understanding of higher-level program features involves us with infinite objects and forces us to pass through several levels of explanation to go from the conceptual ideas to the final simulation on a real machine. These levels can be made mathematically exact if we can find the right abstractions to represent the necessary structures. The experience of many independent workers with the method of data types as lattices (or partial orderings) under an information content ordering, and with their continuous mappings, has demonstrated the flexibility of this approach in providing definitions and proofs, which are clean and without undue dependence on implementations. Nevertheless much remains to be done in showing how abstract conceptualizations can (or cannot) be actualized before we can say we have a unified theory.