Foundations of Logic ProgrammingIn the two and a half years since the frrst edition of this book was published, the field of logic programming has grown rapidly. Consequently, it seemed advisable to try to expand the subject matter covered in the first edition. The new material in the second edition has a strong database flavour, which reflects my own research interests over the last three years. However, despite the fact that the second edition has about 70% more material than the first edition, many worthwhile topic!! are still missing. I can only plead that the field is now too big to expect one author to cover everything. In the second edition, I discuss a larger class of programs than that discussed in the first edition. Related to this, I have also taken the opportunity to try to improve some of the earlier terminology. Firstly, I introduce "program statements", which are formulas of the form A+-W, where the head A is an atom and the body W is an arbitrary formula. A "program" is a finite set of program statements. There are various restrictions of this class. "Normal" programs are ones where the body of each program statement is a conjunction of literals. (The terminology "general", used in the first edition, is obviously now inappropriate). |
Contents
1 | |
2 First Order Theories | 4 |
3 Interpretations and Models | 10 |
4 Unification | 20 |
5 Fixpoints | 26 |
Problems for Chapter 1 | 33 |
DEFINITE PROGRAMS 6 Declarative Semantics 35 | 34 |
7 Soundness of SLDResolution | 40 |
NORMAL PROGRAMS 12 Negative Information | 71 |
13 Finite Failure | 74 |
14 Programming with the Completion | 77 |
15 Soundness of SLDNFResolution | 84 |
16 Completeness of SLDNFResolution | 95 |
Problems for Chapter 3 | 102 |
35 | 106 |
PROGRAMS | 107 |
8 Completeness of SLDResolution | 47 |
9 Independence of the Computation Rule | 49 |
10 SLDRefutation Procedures | 55 |
11 Cuts | 63 |
Problems for Chapter 2 | 66 |
DEDUCTIVE DATABASES | 141 |
PERPETUAL PROCESSES 173 | 172 |
REFERENCES | 195 |
NOTATION | 205 |
Other editions - View all
Common terms and phrases
AeBp answer for comp(P answer for PU axioms 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 induction hypothesis infinite input clause integrity constraint intended interpretation lemma logic programming logical consequence metric space mgu's missing(v model for comp(D negation as failure node normal form normal goal normal program occur check occurs positively order theory ordinal P U G pre-interpretation predicate symbol program and G program clause program statement PROLOG systems Proof proposition Prove PU G query refutation SLD-refutation SLD-resolution SLD-tree SLDNF-refutation SLDNF-tree for PU subset successor ordinal theorem true wrt type theory uncovered atom unifiable unification algorithm unsatisfiable wrong(v