Preface
This book presents a rigorous, comprehensive, modern, and detailed account
of the mathematical methods and tools required for the semantic analysis of
logic programs. It is, in part, the outcome of a fruitful research collaboration between the authors over the last decade or so and contains many of
the results we obtained during that period. In addition, it discusses the work
of many other authors and places it within the overall context of the subject matter. A major feature of the book is that it significantly extends the
tools and methods from the order theory traditionally used in the subject
to include non-traditional methods from mathematical analysis depending on
topology, generalized distance functions, and their associated fixed-point theory. The need for such methods arises for several reasons. One reason is the
non-monotonicity of some important semantic operators, associated with logic
programs, when negation is included in the syntax of the underlying language,
and another arises in the context of neural-symbolic integration, as discussed
briefly in the next paragraph and in more detail in the Introduction. Furthermore, it is our belief that certain of our results, although here focused on
logic programming, have much wider applicability and should prove useful in
other parts of theoretical computer science not immediately related to logic
programming. However, we do not discuss this issue in the book in detail and
instead we give references to the literature at appropriate places in the text
in order to aid readers interested in investigating this point more thoroughly.
All the well-known, important semantics in logic programming are developed in the book from a unified point of view using both order theory and the
non-traditional methods just alluded to, and this provides an illustration of
the main objectives of the book. In addition, the interrelationships between
the various semantics are closely examined. Moreover, a significant amount of
space is devoted to examining the integration of logic programming and connectionist systems (or neural networks) from the point of view of semantics.
Indeed, in the wide sense of integrating discrete models of computation with
continuous models, one can expect to employ a mix of mathematical tools of
both a discrete and continuous nature, as illustrated by the particular choice
of models we make here. Therefore, there is a need in the study of the semantics of logic programming (and in the study of general models of computation)
for a self-contained and detailed exposition of the development of both conventional and non-conventional methods and techniques, as just explained,
and their interaction. This book sets out to provide such an exposition, at
xv
This book presents a rigorous, comprehensive, modern, and detailed account
of the mathematical methods and tools required for the semantic analysis of
logic programs. It is, in part, the outcome of a fruitful research collaboration between the authors over the last decade or so and contains many of
the results we obtained during that period. In addition, it discusses the work
of many other authors and places it within the overall context of the subject matter. A major feature of the book is that it significantly extends the
tools and methods from the order theory traditionally used in the subject
to include non-traditional methods from mathematical analysis depending on
topology, generalized distance functions, and their associated fixed-point theory. The need for such methods arises for several reasons. One reason is the
non-monotonicity of some important semantic operators, associated with logic
programs, when negation is included in the syntax of the underlying language,
and another arises in the context of neural-symbolic integration, as discussed
briefly in the next paragraph and in more detail in the Introduction. Furthermore, it is our belief that certain of our results, although here focused on
logic programming, have much wider applicability and should prove useful in
other parts of theoretical computer science not immediately related to logic
programming. However, we do not discuss this issue in the book in detail and
instead we give references to the literature at appropriate places in the text
in order to aid readers interested in investigating this point more thoroughly.
All the well-known, important semantics in logic programming are developed in the book from a unified point of view using both order theory and the
non-traditional methods just alluded to, and this provides an illustration of
the main objectives of the book. In addition, the interrelationships between
the various semantics are closely examined. Moreover, a significant amount of
space is devoted to examining the integration of logic programming and connectionist systems (or neural networks) from the point of view of semantics.
Indeed, in the wide sense of integrating discrete models of computation with
continuous models, one can expect to employ a mix of mathematical tools of
both a discrete and continuous nature, as illustrated by the particular choice
of models we make here. Therefore, there is a need in the study of the semantics of logic programming (and in the study of general models of computation)
for a self-contained and detailed exposition of the development of both conventional and non-conventional methods and techniques, as just explained,
and their interaction. This book sets out to provide such an exposition, at
xv