Abstract
The research on systems of logic programming with modules has followed two mainstreams, programming-in-the-large, where compositional operators are provided for combining separate and independent modules, and programming-in-the-small, which aims at enhancing logic programming with new logical connectives.
In this paper, we present a general model theoretic approach to modular logic programming which combines programming in-the-large and in-the-small in a satisfactory way. Rather than inventing completely new constructs, however, we resort to a well-known concept in formal logic: generalized quantifiers. We show how generalized quantifiers can be incorporated into logic programs, both for Horn logic programs as well as in the presence of negation. Our basic observation is then that a logic program can be seen as a generalized quantifier, and we obtain a semantics for modular logic programs this way.
Generalized quantifiers in logic programs gives rise to interesting classes of logic programs. We present a taxonomy of natural such classes, and investigate their properties. In particular, their expressive power over finite structures is analyzed.
Extended Abstract, with most proofs omitted. An extended technical report including all proofs is available from the authors.
Preview
Unable to display preview. Download preview PDF.
References
K. Apt, H. Blair, and A. Walker. Towards a Theory of Declarative Knowledge. In Minker [27], pp. 89–148.
A. Badia, M. Gyssens, and D. V. Gucht. Query languages with generalized quantifiers. In R.Ramakrishnan, editor, Applications of Logic Databases, pp. 235–258. Kluwer Academic Publishers, 1995.
J. Barwise and R. Cooper. Generalized Quantifiers and Natural Language. Linguistic and Philosophy, 4:159–219, 1981.
M. Bugliesi, E. Lamma, and P. Mello. Modularity in Logic Programming. J. Logic Programming, 19/20:443–502, 1994.
A. Dawar. Generalized Quantifiers and Logical Reducibilities. J. Logic and Computation, 5(2):213–226, 1995.
A. Dawar, G. Gottlob, and L. Hella. Capturing Relativized Complexity Classes without Order. Mathematical Logic Quarterly, to appear. Technical Report CD-TR 96/105, CD Lab for Expert Systems, TU Vienna, 1996.
J. Dix. A Classification Theory of Semantics of Normal Logic Programs: Strong Properties. Fundamenta Informaticae, 22:227–255, 1995.
J. Dix. A Classification Theory of Semantics of Normal Logic Programs: Weak Properties. Fundamenta Informaticae, 22:257–288, 1995.
J. Dix. Semantics of Logic Programs: Their Intuitions and Formal Properties. An Overview. In Logic, Action and Information. Proc. Konstanz Colloquium in Logic and Information (LogIn'92), pp. 241–329. DeGmyter, 1995.
T. Eiter, G. Gottlob, and N. Leone. Abduction From Logic Programs: Semantics and Complexity. Theoretical Computer Science, to appear.
T. Eiter, G. Gottlob, and H. Mannila. Adding Disjunction to Datalog. In Proc. PODS '94, pp. 267–278, 1994.
T. Eiter and G. Gottlob. Expressiveness of Stable Model Semantics for Disjunctive Logic Programs with Functions. J. Logic Programming, to appear. CD-TR 96/103, CD Lab for Expert Systems, TU Vienna.
T. Eiter, G. Gottlob, and H. Veith. Logic Programming: Modularity and Revision. In Abstract presented at the Workshop Logic Databases: The Meaning of Change, Dagstuhl, September 1996.
H. Gaifman and E. Shapiro. Fully Abstract Compositional Semantics for Logic Programs. In Proc. 16th ACM Symp. POPL, pp. 134–142. 1989
M. Garey and D. S. Johnson. Computers and Intractability — A Guide to the Theory of NP-Gompleteness. W. H. Freeman, New York, 1979.
M. Gelfond and V. Lifschitz. The Stable Model Semantics for Logic Programming. In Proc. Fifth Intl CSLP, pp. 1070–1080, 1988.
L. Giordano and A. Martelli. Structuring Logic Programs: A Modal Approach. J.Logic Programming, 21:59–94, 1994.
G. Gottlob. Relativized Logspace and Generalized Quantifiers over Finite Structures. In Proc. IEEE LICS '95, pages 65–78, 1995. Extended version Journal of Symbolic Logic, to appear.
L. Henkin. Some Remarks on Infinitely Long Formulas. In Infinitistic Methods, Proc. Symp. on Foundations of Mathematics, pp. 167–183. Warsaw, Panstwowe Wydawnictwo Naukowe and Pergamon Press, 1961.
P. Hsu and D. Parker. Improving SQL with Generalized Quantifiers. In Proc. 11th Intl Conference on Data Engineering, 1995.
P. Lindström. First Order Predicate Logic with Generalized Quantifiers. Theoria, 32:186–195, 1966.
J. Lloyd. Foundations of Logic Programming. Springer, Berlin, 1984.
P. Mancarella and D. Pedreschi. An Algebra of Logic Programs. In Proc. ICLP'88, pp. 1006–1023. MIT-Press, 1988.
W. Marek and M. Truszczyński. Revision specifications by means of revision programs. In Logics in AI. Proc. JELIA '94, LNAI, 1994.
W. Marek and M. Truszczyński. Revision Programming, database updates and integrity constraints. In Proc. ICDT '95, LNCS 893, pp. 368–382, 1995.
D. Miller. A Theory of Modules in Logic Programming. In Proc. ILPS '86, pp.106–114. 1986.
J. Minker, editor. Foundations of Deductive Databases and Logic Programming. Morgan Kaufman, 1988.
A. Mostowski. On a Generalization of Quantifiers. Fundamenta Mathematicae, 44:12–36, 1957.
R. O'Keefe. Towards an Algebra for Constructing Logic Programs. In Proc. IEEE Symposium on Logic Programming, pp. 152–160. IEEE CS Press, 1985.
C. H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.
T. Przymusinski. On the Declarative and Procedural Semantics of Stratified Deductive Databases. In Minker [27], pp. 193–216.
T. Przymusiński and H. Turner. Update by Means of Inference Rules. In Proc. LPNMR '95, LNCS 928, pp. 156–174, 1995.
D. Saccá. Deterministic and Nondeterministic Stable Model Semantics for Unbound DATALOG Queries. In Proc. ICDT-95, LNCS 893, pp. 353–367, 1995.
J. Schlipf. The Expressive Powers of Logic Programming Semantics. J. Computer and System Sciences, 51(1):64–86, 1995. Abstract in Proc. PODS 90, pp. 196–204.
I. Stewart. Logical Characterizations of Bounded Query Classes I: Logspace oracle machines. Fundamenta Informaticae, 18:65–92, 1993.
I. Stewart. Logical Characterizations of Bounded Query Classes II: Logspace oracle machines. Fundamenta Informaticae, 18:93–105, 1993.
K. Wagner. Bounded Query Classes. SIAM J. Comp., 19(5):833–846, 1990.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Eiter, T., Gottlob, G., Veith, H. (1997). Modular logic programming and generalized quantifiers. In: Dix, J., Furbach, U., Nerode, A. (eds) Logic Programming And Nonmonotonic Reasoning. LPNMR 1997. Lecture Notes in Computer Science, vol 1265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63255-7_22
Download citation
DOI: https://doi.org/10.1007/3-540-63255-7_22
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63255-9
Online ISBN: 978-3-540-69249-2
eBook Packages: Springer Book Archive