Preface

At present, this in-progress text represents only a speck of the material in play in Bringsjord's courses at Rensselaer. The bulk of this material exists in Bringsjord's brain, and makes its way onto overhaed projectors and into notebooks and onto whiteboards as pedagogical needs prompt him. The speck that is this text draws heavily on the texts Bringsjord has essentially memorized in the decade or so he has taught mathematical and philosophical logic, e.g., the excellent Mathematical Logic, by Ebbinghaus, Flum and Thomas. Not that long ago it him that perhaps it was time to work toward his own text. Realizing that he couldn't pull this off on his own, he turned to Kosta Arkoudas, who had himself been wanting to write a textbook.

The present working text will gradually evolve into a new, singular, state-of-the-art book. The following will be distinctive aspects of this book.

• The text will be supported by a sophisticated, interactive, multi-dimensional web site that will offer materials of help to instructors and students alike. For example, proof checkers will be made available, as well simulation packages for Turing machines, register machines, and neural networks.
• This book will make the material in question hands-on with help from a number of systems, e.g., OTTER. These systems will be included on CD, DVD, and will also be obtainable from the web site.
• This book is utterly comprehensive. To give a sense of its comprehensiveness, the text
  • covers the full range of proof theories for all standard extensional logics;
  • includes full coverage of uncomputability (both from the standpoint of discrete machines and from the standpoint of neural networks);
  • covers computability from the standpoint of Turing machines, register machines, abaci, and programming languages of an imperative, functional, and declarative sort.