## Foundations of Logic ProgrammingThis is the second edition of the first book to give an account of the mathematical foundations of Logic Programming. Its purpose is to collect, in a unified and comprehensive manner, the basic theoretical results of Logic Programming, which have previously only been available in widely scattered research papers. In addition to presenting the technical results, the book also contains many illustrative examples. Many of the examples and problems are part of the folklore of Logic Programming and are not easily obtainable elsewhere. The second edition contains about 70 % more material than the first edition. There are two new chapters, one on a more general class of programs in which the body of a program statement can be an arbitrary first order formula, and one on Deductive Database Systems. Further material on negation has been added to the third chapter. In addition, the problem sections of each chapter have been expanded so that there are now over 100 problems. The book is intended to be self-contained, the only prerequisites being some familarity with PROLOG and knowledge of some basic undergraduate mathematics. The book is aimed at researchers and graduate students in Logic Programming, Artificial Intelligence and Database Systems. The material is suitable either as a reference book for researchers or as a text book for a graduate course on the theoretical aspects of Logic Programming and Deductive Database Systems. |

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### Contents

PRELIMINARIES 1 Introduction | 1 |

2 First Order Theories | 4 |

3 Interpretations and Models | 10 |

Copyright | |

21 other sections not shown

### Common terms and phrases

AeBp answer for comp(P axioms chapter complete Herbrand complete lattice computation rule computed answer conjunctive normal form consequence of comp(P correct answer deductive database defined definite goal definite program Definition Let equality theory exists failure rule finitely failed SLDNF-tree fixpoint follows free variables function symbols G a definite G a normal gfp(Tp Herbrand base Herbrand interpretation Herbrand universe incorrect statement instance induction hypothesis infinite input clause integrity constraint intended interpretation lemma logic programming logical consequence mgu's missing(v model for comp(D neco negation as failure node normal form normal goal normal program occur check occurs positively order language order theory ordinal pre-interpretation predicate symbol program and G program clause program statement PROLOG systems Proof proposition Prove Pu{G query complexity refutation resp SLD-refutation SLD-resolution SLD-tree SLDNF-refutation subgoal subset successor ordinal Suppose theorem tree true wrt type theory typed first order uncovered atom unifiable unification algorithm unsatisfiable wrong(v