by Cesare Tinelli, Mehdi Harandi
Frontiers of Combining Systems, volume 3 of Applied Logic Series
ftp://ftp.cs.uiowa.edu/pub/tinelli/papers/TinHar-FROCOS-96.pdf
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Abstract:
The Nelson-Oppen combination procedure, which combines satisfiability procedures for a class of first-order theories by propagation of equalities between variables, is one of the most general combination methods in the field of theory combination. We describe a new non-deterministic version of the procedure that has been used to extend the Constraint Logic Programming Scheme to unions of constraint theories. The correctness proof of the procedure that we give in this paper not only constitutes a novel and easier proof of Nelson and Oppen's original results, but also shows that equality sharing between the satisfiability procedures of the component theories, the main idea of the method, can be confined to a restricted set of variables. While working on the new correctness proof, we also found a new characterization of the consistency of the union of first-order theories. We discuss and give a proof of such characterization as well.
Citations
|
755
|
Constraint logic programming
– Jaffar, Lassez
- 1987
|
|
655
|
Constraint Logic Programming: A Survey
– Jaffar, Maher
- 1994
|
|
270
|
Simplification by cooperating decision procedures
– Nelson, Oppen
- 1979
|
|
179
|
Mathematical Logic
– Shoenfield
- 1967
|
|
133
|
Deciding combinations of theories
– Shostak
- 1984
|
|
104
|
Unification in the union of disjoint equational theories: Combining decision procedures
– Baader, Schulz
- 1996
|
|
66
|
A practical decision procedure for arithmetic with function symbols
– Shostak
- 1979
|
|
28
|
On the combination of symbolic constraints, solution domains, and constraint solvers
– Baader, Schulz
- 1995
|
|
28
|
Combination techniques for non-disjoint equational theories
– Domenjoud, Klay, et al.
- 1994
|
|
27
|
Complexity, convexity and combinations of theories
– Oppen
- 1980
|
|
23
|
Combining unification algorithms
– Boudet
- 1993
|
|
21
|
Combination Techniques and Decision Problems for Disunification
– Baader, Schulz
- 1995
|
|
18
|
Combination of constraint solving techniques: An algebraic point of view
– Baader, Schulz
- 1995
|
|
17
|
Unification in a combination of equational theories: An efficient algorithm
– Boudet
- 1990
|
|
17
|
Combination of unification algorithms
– Schmidt-Schau��
- 1989
|
|
15
|
Combination of unification algorithms
– Herold
- 1986
|
|
15
|
Unification in a combination of equational theories with shared constants and its application to primal algebras
– Ringeissen
- 1992
|
|
14
|
Combining satisfiability procedures by equality-sharing
– Nelson
- 1984
|
|
11
|
Unification in Combinations of Collapse-free Theories with Disjoint Sets of Function Symbols
– Tid'en
- 1986
|
|
6
|
Model Theory, volume 73 of Studies in Logic and the foundations of mathematics
– Chang, Keisler
- 1990
|
|
5
|
Constraint solving by narrowing in combined algebraic domains
– Kirchner, Ringeissen
- 1994
|
|
5
|
Extending the CLP scheme to unions of constraint theories
– Tinelli
- 1995
|
|
2
|
Unification in combinations of collapse-free regular theories
– Yelik
- 1987
|
|
1
|
Unification in a combination of equatlonal theories: An e/clent algorithm
– Boudet
- 1990
|
|
1
|
Constraint Logic Programming
– JaiYar, Lasses
- 1987
|
|
1
|
A constraint solver in finite algebras A New Correctness Proof of the Nelson-Oppen Combination Procedure 17 and its combination with unification algorithms
– Kirchner, Pdngelssen
- 1992
|
|
1
|
Combining satlsfiabillty procedures by equa]Jty-sharlng
– Nelson
- 1984
|
|
1
|
Unification in a combination of equatlonal theories with shared constants and its app]]catlon to primal algebras
– Pdngelssen
- 1992
|
|
1
|
Unification in a combination of disjoint equatlonal theories
– Schmldt-SchauB
|
|
1
|
Combination of unification algorithms
– Schmldt-SchauB
- 1989
|
|
1
|
Unification in combinations of collapse-free theories with disjoint sets of function symbols
– TidSn
- 1986
|
|
1
|
Combining unification algorithms for confined equatlonal theories
– unknown authors
- 1987
|
|
1
|
Unification in combinations of collapse-free regular theories
– unknown authors
- 1987
|
|
1
|
Unification in a combination of disjoint equational theories
– Schmidt-Schau
|
|
1
|
Combining unification algorithms for confined equational theories
– Yelik
- 1987
|
