As the 21st century begins, the power of our magical new tool and partner, the computer, is increasing at an astonishing rate. Computers that perform billions of operations per second are now commonplace. Multiprocessors with thousands of little computers - relatively little! -can now carry out parallel computations and solve problems in seconds that only a few years ago took days or months. Chess-playing programs are on an even footing with the world's best players. IBM's Deep Blue defeated world champion Garry Kasparov in a match several years ago. Increasingly computers are expected to be more intelligent, to reason, to be able to draw conclusions from given facts, or abstractly, to prove theorems-the subject of this book. Specifically, this book is about two theorem-proving programs, THEO and HERBY. The first four chapters contain introductory material about automated theorem proving and the two programs. This includes material on the language used to express theorems, predicate calculus, and the rules of inference. This also includes a description of a third program included with this package, called COMPILE. As described in Chapter 3, COMPILE transforms predicate calculus expressions into clause form as required by HERBY and THEO. Chapter 5 presents the theoretical foundations of seman­ tic tree theorem proving as performed by HERBY. Chapter 6 presents the theoretical foundations of resolution-refutation theorem proving as per­ formed by THEO. Chapters 7 and 8 describe HERBY and how to use it.

This new book carefully describes how automated reasoning is performed. It introduces all necessary analytical and mathematical tools to discuss basic inference rules of binary resolution and binary factoring. Two computer programs and source code are provided to use as examples. Advanced students, professionals and researchers in computer science, computer engineering, artificial intelligence and logic programming will find the book a useful text/reference.

A brief introduction to COMPILE, HERBY and THEO.- Predicate calculus, well-formed formulas and theorems.- COMPILE: transforming well-formed formulas to clauses.- Inference procedures.- Proving theorems by constructing closed semantic trees.- Resolution-refutation proofs.- HERBY: A semantic tree theorem prover.- Using HERBY.- THEO: A resolution-refutation theorem prover.- Using THEO.- A look at HERBY's source code.- A look at THEO's source code.- Other theorem provers.- References.