Introduction

Much of this book has explored the timing and effects of various processes which are initiated as a result of reading particular sentences or types of sentence. To understand the meaning of a sentence, we make use of information from sentence structure and content, but we also make use of information which the reader already has about the situation described. However, the role of such background knowledge in theories of natural language semantics varies between approaches to the problem. In this chapter, we will argue that semantic processing is at least partially driven by the inferences which the interpreter makes, and that the knowledge state of language users is therefore of paramount importance in the process of understanding discourse.

One possible approach to modelling the semantic processes involved in sentence comprehension is exemplified by the Discourse Representation Theory (DRT) account, which is based on a set-theoretic approach to reference (Kamp and Reyle, 1993). Solving reference and scope problems is central to DRT, because inadequate reference resolution leads to incoherence in the representation of a discourse. Thus, in DRT, reference resolution is the process which occurs earliest. There is little if any emphasis on inference and the utilisation of world knowledge in comprehension within such a framework, because the spirit of the approach is to try to capture the facts of language, independent of world knowledge.

From the outset, the idea was to try to draw together parts of three vast areas of inquiry – ethics, computing, and medicine – and produce a document that would be accessible by and useful to scholars and practitioners in each domain. Daunting projects are made possible by supportive institutions and colleagues. Fortunately in this case, the support exceeded the daunt.

The idea for the book came while I was at Carnegie Mellon University's Center for Machine Translation and Center for the Advancement of Applied Ethics, and the University of Pittsburgh's Center for Medical Ethics. These three centers of excellence fostered a congenial and supportive environment in which to launch a novel project. Deep thanks are due Jaime Carbonell, Preston Covey, Peter Madsen, Alan Meisel, and Sergei Nirenburg.

In 1992 I organized a session on “Computers and Ethics in Medicine” at the annual meeting of the American Association for the Advancement of Science (AAAS) in Chicago. Four of the contributors to this volume – Terry Bynum, Randy Miller, John Snapper, and I – made presentations. A special acknowledgment is owed to Elliot R. Siegel of the National Library of Medicine and the AAAS Section on Information, Computing, and Communication for encouraging this effort, and for his wise counsel.

The original idea for a book blossomed as it became increasingly clear that there was a major gap in the burgeoning literatures in bioethics and medical informatics.

Introduction

The growth of knowledge presents some of the most interesting and demanding problems in all human inquiry.

Introduction and history

Medical computing is not merely about medicine or computing. It is about the introduction of new tools into environments with established social norms and practices.

Telling right from wrong often requires appeal to a set of values. Some values are general or global, and they range across the spectrum of human endeavor. Identifying and ranking such values, and being clear about their conflicts and exceptions, is an important philosophical undertaking. Other values are particular or local. They may be special cases of the general values. So when “freedom from pain” is offered in the essay by Professors Bynum and Fodor as a medical value, it is conceptually linked to freedom, a general value. Local values apply within and often among different human actions: law, medicine, engineering, journalism, computing, education, business, and so forth. To be consistent, a commitment to a value in any of these domains should not contradict global values. To be sure, tension between and among local and global values is the stuff of exciting debate in applied ethics. And sometimes a particular local value will point to consequences that are at odds with a general value. Debates over these tensions likewise inform the burgeoning literature in applied or professional ethics. In this chapter, Bynum and Fodor apply the seminal work of James H. Moor in an analysis of the values that apply in the health professions. What emerges is a straightforward perspective on the way to think about advancing health computing while paying homage to those values.

A conceptual intersection

The future of the health professions is computational.

This suggests nothing quite so ominous as artificial doctors and robonurses playing out “what have we wrought?” scenarios in future cyberhospitals. It does suggest that the standard of care for information acquisition, storage, processing, and retrieval is changing rapidly, and health professionals need to move swiftly or be left behind.

Mechanical judgments and intelligent machines

Modern medical practice makes use of a variety of “intelligent machines” that evaluate patient conditions, help in literature searches, interpret laboratory data, monitor patients, and much more.

Categorical structures suitable for describing partial maps, viz. domain structures, are introduced and their induced categories of partial maps are defined.

The representation of partial maps as total ones is addressed. In particular, the representability (in the categorical sense) and the classifiability (in the sense of topos theory) of partial maps are shown to be equivalent (Theorem 3.2.6).

Finally, two notions of approximation, contextual approximation and specialisation, based on testing and observing partial maps are considered and shown to coincide. It is observed that the approximation of partial maps is definable from testing for totality and the approximation of total maps; providing evidence for taking the approximation of total maps as primitive.

Categories of Partial Maps

To motivate the definition of a partial map, observe that a partial function u : A ⇀ B is determined by its domain of definition dom(u) ⊆ A and the total function dom(u) → B induced by the mapping a ↦ u(a). Thus, every partial function A ⇀ B can be described by a pair consisting of an injection D ↣ A and a total function D → B with the same source.

In this chapter we study the categorical constructions for interpreting data types. We start by observing that the notion of pairing in a category of partial maps (with a minimum of structure) cannot be the categorical product. The appropriate interpretation for product types (partial products) is the categorical product in the category of total maps endowed with a pairing operation on partial maps extending the pairing of total maps. Once the notion of product is established, partial exponentials are defined as usual, and some properties of Poset-partial-exponentials are presented. Next colimits are studied. The situation is completely different from that of limits. For example, an object is initial in the category of total maps if and only if it is so in the category of partial maps. A characterisation of certain colimits (including coproducts) in a category of partial maps, due to Gordon Plotkin, is given. We further relate colimits in the category of total maps and colimits in the category of partial maps by means of the lifting functor. Finally, we provide conditions on a Cpo-category of partial maps under which ω-chains of embeddings have colimits. This is done in the presence of the lifting functor, and for arbitrary categories of partial maps.

Partial Binary Products

The data type for pairing in pΚ cannot be the categorical product because, under reasonable assumptions, this would lead to inconsistency.

We have initiated an abstract approach to domain theory as needed for the denotational semantics of deterministic programming languages. To provide an explicit semantic treatment of non-termination, we decided to make partiality the core of our theory. Thus, we focussed on categories of partial maps. We have studied the representability of partial maps and shown its equivalence with classifiability. We have observed that, once partiality is taken as primitive, a notion of approximation may be derived. In fact, two notions of approximations based on testing and observing partial maps have been considered and shown to coincide. Further we have characterised when the approximation relation between partial maps is domain-theoretic in the (technical) sense that the category of partial maps Cpo-enriches with respect to it.

Concerning the semantics of type constructors in categories of partial maps we have: presented a characterisation of colimits of diagrams of total maps due to Gordon Plotkin; studied order-enriched partial cartesian closure; and provided conditions to guarantee the existence of the limits needed to solve recursive type equations. Concerning the semantics of recursive types we have: made Peter Freyd's notion of algebraic compactness the central concept; motivated the compactness axiom; established the fundamental property of parameterised algebraically compact categories (slightly extending a previous result of Peter Freyd); and shown that in algebraically compact categories recursive types reduce to inductive types. Special attention has been paid to Cpo-algebraic compactness, leading to the identification of a 2-category of kinds with very strong closure properties.

We thoroughly study the semantics of inductive and recursive types. Our point of view is that types constitute the objects of a category and that type constructors are bifunctors on the category of types. By a bifunctor on a category we mean a functor on two variables from the category to itself, contravariant in the first, covariant in the second.

First, following Peter Freyd, the stress is on the study of algebraically complete categories, i.e. those categories admitting all inductive types (in the sense that every endofunctor on them has an initial algebra—this is understood in a setting in which the phrase “every endofunctor” refers to a class of enriched endofunctors—see Definition 6.1.4). After observing that algebraic completeness guarantees the existence of parameterised initial algebras, we identify, under the name of parameterised algebraically complete categories, all those categories which are algebraically complete and such that every parameterised inductive type constructor gives rise to a parameterised inductive type (see Definition 6.1.7). Type constructors on several variables are dealt with by Bekič's Lemma, from which follow both the Product Theorem for Parameterised Algebraically Complete Categories (Theorem 6.1.14) and also the dinaturality of Fix (the functor delivering initial algebras).

Second, again following Peter Freyd, algebraic completeness is refined to algebraic compactness by imposing the axiom that, for every endofunctor, the inverse of an initial algebra is a final coalgebra. The compactness axiom is motivated with a simple argument showing that every bifunctor on an algebraically compact category admits a fixed-point.