Ashcroft and Wadge [4] have criticized effort spent on describing existing programming languages and have suggested a more active, prescriptive role for denotational semantics in designing languages of the future. Accepting some truth in this, this chapter contains a semantics for Prolog. While there are existing Prologs, plural, logic programming is still a research area and a denotational semantics is one way to investigate variations in it.

Prolog [9] is a programming language based on first-order predicate logic. A Prolog program can be thought of in two ways. It can be taken to be a set of logical assertions or facts about a world or some part of a world. This is the declarative semantics of the program. It can also be taken as a set of procedure definitions which gives its procedural semantics.

The declarative semantics are very elegant in that the program stands for some basic facts and certain other facts that logically follow from them. No side-effects or considerations of the order of evaluation are involved. Unfortunately, to make Prolog run and to make it run efficiently, some programs require side-effects such as input–output and the order of evaluation to be taken into account. This can only be understood procedurally.

Here a denotational semantics of a subset of Prolog is given. This defines the backtracking search and unification processes of Prolog. Later the definition is translated into Algol-68 to form an interpreter. Prolog is still a research language and giving a denotational semantics enables it to be compared with other languages in a uniform framework.

There is great variety amongst programming languages in the area of data structures and type checking. It is only possible to deal with some of the more straightforward issues in this chapter.

Some languages, such as BCPL [52], are typeless, or have only one type. All BCPL variables have the type ‘word’. This enables BCPL to rival assembly code in application while being much more readable and concise. There are dangers, however; the compiler cannot detect type errors because there are none.

Languages that do provide types are characterized by the kind of data structures, the time at which types are checked and how much the programmer can define. Simple types, such as integer, stand for basic domains like Int. Structured types – arrays and records – stand for derived domains. There are hard problems, however, in deciding what a programmer-defined type, particularly one defined by possibly recursive equations, stands for – see recent conference proceedings [1, 2, 31]. This is obviously connected with recursive domains (§4.3).

APL [27] is a dynamically typed language. Each constant has a particular type – integer, character or vector or array of one of these. The value currently assigned to a variable therefore has some type, but both the value and the type may change as the program runs. Each APL operator is only applicable to certain types, so it is possible to add 1 to an integer or to a vector of integers but not to a character.

Objectivity and the human sciences

Philosophy of science and schema theory have provided us with two approaches to a theory of knowledge as construction. In this theory, a knowing subject bases a dialogue with external reality on schemas or theoretical languages embodying a “construction of reality.” Schema theory builds on elementary processes of assimilation and accommodation whereby the individual's sensorimotor schemas come to provide anticipations of the effects of action in the world. We have seen similar processes, operating at the level of groups rather than individuals, in the network view of philosophy of science. Both schema theory and the network view of science have led to a theory of language in which metaphor is normative, with literal meaning as the limiting case.

The resulting epistemology combines coherence and correspondence criteria of truth and dissolves the barriers between “objective” science and nonscience. In this chapter, we look at the alternatives to “objectification” proposed as modes of knowledge in hermeneutic and critical philosophy and suggest that our viewpoint reveals unities in these diversities. Just as we see a continuum between literal and metaphorical meanings, so we do not posit a sharp dichotomy between the natural sciences on the one hand and the social or literary hermeneutic sciences on the other. Special pragmatic or “objective” aims are predominant in the natural sciences, though also to some extent applicable elsewhere; on the other hand, hermeneutic considerations apply in the natural sciences, particularly in connection with theoretical interpretations and “world models.”

Our task now is to develop a theory of human knowledge that makes contact with the AI concepts and the notion of the embodied subject of the previous chapter. We call this approach schema theory, and have already outlined its features in Section 1.3. We provide our view of the current shape of schema theory as a scientific discipline within cognitive science and also point to ways the theory must develop if we are to use it in addressing such issues as freedom, the person in society, and the possibilities of religious knowledge. We stress that schema theory is not a closed subject, nor is there any consensus as to what constitutes its current status. Even the notion of a “schema” as “intermediate functional entity” in cognitive processes is not fully delimited but will evolve with developments in cognitive science.

Our approach to schema theory denies language the primary role in cognition. True, with language “in place,” we seek to understand its substrates, both within the human brain and in the social nexus. But when we take an evolutionary or developmental view, language is no longer primary. Even though as adults we are immersed in language, we seek to burst the bounds of language to construct a richer epistemology. Schema theory seeks to mediate between the billionsfold complexity of neurons and the thousands-fold complexity of words.

We have presented schemas as embodying a constructed reality that is always open to further adaptation, explaining why there must be a plurality of view-points, yet also offering mechanisms for reflective critique and self-correction that protect us from an uncritical relativism. In the previous chapter, we considered the “Great Schema,” a reading of the Bible that views the God reality of which it is the schema as immutable, whereas the hermeneutic process adapts our understanding of this fixed reality to changing human conditions.

This concluding chapter presents the case for a different view: seeing secular schemas as a reading of the human condition as lying wholly within the spatiotemporal realm, with no appeal to God or to a “voluntarist” free will. Such schemas could be in flux yet maintain their ability to embody a multilevel reality encompassing persons and society as well as things. We show how ethics and human values might evolve without being grounded in a fixed God reality but rather in the critical development of a pluralist world view. First, we stress the extent to which our schema-based epistemology provides a schema that can be adapted by religious and secularist alike and that provides a measure of agreement despite dramatic disagreements about the ultimate constitution of Reality.

A measure of agreement

The last page of the New Testament offers the following stern warning of the sacredness of its text:

Religion as primitive science

Our discussion of hermeneutics and critical theory has led to this question: What are the constraints and criteria for the success of social schemas? A schema theory of many-leveled interactions between the individual and the social may provide the mechanism of schema correction and development, but it cannot by itself specify the social functions that the feedback systems serve, nor the consciously adopted goals that human beings intentionally feed into these systems. Guided missiles have externally specified targets, and homeostatic biological systems have a goal of survival, ensured by natural selection mechanisms. What are the goals of social systems?

There are three possible types of answer to this question, which we call scientistic, hermeneutic, and critical. Scientism is the view that the criteria for the success of social schemas can be read off the facts without intervention of any but scientific criteria. This view recognizes that facts in themselves do not entail human judgments of good and bad, but it claims that these judgments cen be elicited from deep natural structures of human biology, psychology, and social interaction. These structures can be described and explained, for instance, in the science of evolution and by natural scientific methods applied to the social sciences. The model for such a scientistic interpretation of social norms, therefore, tends to be biological science, in which the goals of feedback schemas are patent: functional coherence, stability, and survival.