Mathematical programming embeddings of logic

Journal of Automated Reasoning

Volumn 29, Issue 1, 2002, Pages 91-106

  Borkar, Vivek S ^a   Chandru, Vijay ^b   Mitter, Sanjoy K ^c  

^a TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

^b INDIAN INSTITUTE OF SCIENCE   (India)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

CLP(R); Mathematical programming; Predicate logic

Indexed keywords

ALGORITHMS; COMPUTABILITY AND DECIDABILITY; COMPUTATIONAL COMPLEXITY; INTEGER PROGRAMMING; LINEAR PROGRAMMING; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBABILISTIC LOGICS; SEMANTICS; THEOREM PROVING; TOPOLOGY; VARIATIONAL TECHNIQUES;

COMPACTNESS THEOREM; CONSTRAINT LOGIC PROGRAMMING; HORN LOGIC; PREDICATE LOGIC; PROPOSITIONAL LOGIC;

LOGIC PROGRAMMING;

EID: 0036624833     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020521718123     Document Type: Article

References (24)

1. Andersen, K. A. and Hooker, J. N.: A linear programming framework for logics of uncertainty, Manuscript, Mathematical Institute, Århus University, 8000 Århus C, Denmark, 1992.
2. Araque, G. J. R. and Chandru, V.: Some facets of satisfiability, Technical Report CC-91-13, Institute for Interdisciplinary Engineering Studies, Purdue University, West Lafayette, IN 47907, USA, 1991
3. Blair, C., Jeroslow, R. G. and Lowe, J. K.: Some results and experiments in programming techniques for propositional logic, Comput. Oper. Res. 13 (1988), 633-645.
4. Borkar, V. S., Chandru, V. and Mitter, S. K.: A linear programming model of first order logic, Technical Report IISc-CSA-95-5, Indian Institute of Science, 1995.
5. Chandru, V. and Hooker, J. N.: Extended horn sets in propositional logic, J. ACM 38(1) (1991), 205-221.
6. Chandru, V. and Hooker, J. N.: Optimization Methods for Logical Inference, Wiley-Interscience, 1999.
7. Conforti, M. and Cornuéjols, G.: A class of logical inference problems soluble by linear programming, J. ACM 33 (1994), 670-675.
8. Gallo, G. and Rago, G.: A hypergraph approach to logical inference for datalog formulae, working paper, Dip. di Informatica, University of Pisa, Italy, September 1990.
9. Hooker, J. N.: A mathematical programming model for probabilistic logic, working paper 05-88-89, Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA 15213, July 1988.
10. Hooker, J. N.: Input proofs and rank one cutting planes, ORSA J. Comput. 1 (1989), 137-145.
11. Hooker, J. N.: New methods for computing inferences in first order logic, Ann. Oper. Res. (1993), 479-492.
12. Jaffar, J. and Lassez, J.-L.: Constraint logic programming, Technical Report 86/73, Department of Computer Science, Monash University, 1986.
13. Jaffar, J. and Lassez, J.-L.: Constraint logic programming, in Proc. 14th Symposium on Principles of Programming Languages, Munich, Jan. 1987, pp. 111-119.
14. Jaffar, J. and Maher, M. J.: Constraint logic programming: A survey, J. Logic Programming 19/20 (1994), 503-581.
15. Jeroslow, R. G.: Computation-oriented reductions of predicate to propositional logic, Decision Support Systems 4 (1988), 183-197.
16. Jeroslow, R. G.: Logic-Based Decision Support: Mixed Integer Model Formulation, Ann. Discrete Math. 40, North-Holland, Amsterdam, 1989.
17. Kagan, V., Nerode, A. and Subrahmanian, V. S.: Computing definite logic programs by partial instantiation and linear programming, Technical Report 93-15, Mathematical Sciences Institute, Cornell University, 1993.
18. Kavvadias, D. and Papadimitriou, C. H.: A linear programming approach to reasoning about probabilities, Ann. Math. Artificial Intelligence 1 (1990), 189-206.
19. Munkres, J. R.: Topology: A First Course, Prentice-Hall, 1975.
20. Nilsson, N. J.: Probabilistic logic, Artificial Intelligence 28 (1986), 71-87.
21. Rockafeller, R. T.: Convex Analysis, Princeton University Press, 1970.
22. Schrijver, A.: Theory of Linear and Integer Programming, Wiley, New York, 1986.
23. Schöning, U.: Logic for Computer Scientists, Birkhäuser, 1989.
24. Wang, J.-C. and Vande Vate, J.: Question-asking strategies for Horn clause systems, Ann. Math. Artificial Intelligence 1 (1990).