Nelson–Oppen combination method
E904163
algorithm in automated reasoning
decision procedure framework
method in mathematical logic
method in satisfiability modulo theories
satisfiability decision procedure
theory combination method
The Nelson–Oppen combination method is a decision procedure framework that combines satisfiability solvers for different first-order theories to determine the satisfiability of formulas in their union.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Nelson–Oppen combination method canonical | 3 |
| Nelson–Oppen combination | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11090200 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Nelson–Oppen combination method Context triple: [Satisfiability Modulo Theories, relatedTo, Nelson–Oppen combination method]
-
A.
Satisfiability Modulo Theories (SMT)
Satisfiability Modulo Theories (SMT) is a framework in computer science and mathematical logic for deciding the satisfiability of logical formulas with respect to background theories such as arithmetic, bit-vectors, arrays, and data types, widely used in verification, synthesis, and automated reasoning.
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B.
Z3: An Efficient SMT Solver
Z3: An Efficient SMT Solver is a high-performance satisfiability modulo theories (SMT) solver widely used in program verification, formal methods, and automated reasoning.
-
C.
“A Decision Method for Elementary Algebra and Geometry”
“A Decision Method for Elementary Algebra and Geometry” is Alfred Tarski’s influential work that presents a procedure for deciding the truth of statements in elementary algebra and geometry, laying foundations for decision theory in mathematical logic.
-
D.
Davis–Putnam algorithm
The Davis–Putnam algorithm is a pioneering procedure in automated theorem proving and propositional logic satisfiability that laid foundational groundwork for modern SAT solvers.
-
E.
First-Order Logic and Automated Theorem Proving
"First-Order Logic and Automated Theorem Proving" is a foundational textbook that systematically introduces first-order logic while presenting key methods and algorithms used in automated theorem proving.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Nelson–Oppen combination method Target entity description: The Nelson–Oppen combination method is a decision procedure framework that combines satisfiability solvers for different first-order theories to determine the satisfiability of formulas in their union.
-
A.
Satisfiability Modulo Theories (SMT)
Satisfiability Modulo Theories (SMT) is a framework in computer science and mathematical logic for deciding the satisfiability of logical formulas with respect to background theories such as arithmetic, bit-vectors, arrays, and data types, widely used in verification, synthesis, and automated reasoning.
-
B.
Z3: An Efficient SMT Solver
Z3: An Efficient SMT Solver is a high-performance satisfiability modulo theories (SMT) solver widely used in program verification, formal methods, and automated reasoning.
-
C.
“A Decision Method for Elementary Algebra and Geometry”
“A Decision Method for Elementary Algebra and Geometry” is Alfred Tarski’s influential work that presents a procedure for deciding the truth of statements in elementary algebra and geometry, laying foundations for decision theory in mathematical logic.
-
D.
Davis–Putnam algorithm
The Davis–Putnam algorithm is a pioneering procedure in automated theorem proving and propositional logic satisfiability that laid foundational groundwork for modern SAT solvers.
-
E.
First-Order Logic and Automated Theorem Proving
"First-Order Logic and Automated Theorem Proving" is a foundational textbook that systematically introduces first-order logic while presenting key methods and algorithms used in automated theorem proving.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
algorithm in automated reasoning
ⓘ
decision procedure framework ⓘ method in mathematical logic ⓘ method in satisfiability modulo theories ⓘ satisfiability decision procedure ⓘ theory combination method ⓘ |
| appliedIn |
SMT solvers
ⓘ
constraint solving ⓘ formal hardware verification ⓘ formal software verification ⓘ model checking ⓘ program verification ⓘ |
| assumes |
decidability of each component theory
ⓘ
pairwise disjoint signatures of component theories ⓘ stably infinite theories ⓘ |
| author |
Derek C. Oppen
ⓘ
Greg Nelson ⓘ |
| basedOn | combination of decision procedures ⓘ |
| category |
algorithms in computer-aided verification
ⓘ
decision procedures in logic ⓘ |
| field |
automated reasoning
ⓘ
first-order logic ⓘ formal methods ⓘ satisfiability modulo theories ⓘ
linked to:
Satisfiability Modulo Theories (SMT)
theory of computation ⓘ |
| goal | decide satisfiability of formulas in the union of first-order theories ⓘ |
| influenced |
design of modern SMT solvers
ⓘ
research on theory combination ⓘ |
| input | quantifier-free formulas over a combination of theories ⓘ |
| namedAfter |
Derek C. Oppen
ⓘ
Greg Nelson ⓘ |
| originalPublicationTitle | Simplification by cooperating decision procedures ⓘ |
| originalPublicationVenue | ACM Transactions on Programming Languages and Systems ⓘ |
| output | satisfiable or unsatisfiable ⓘ |
| property |
complete for stably infinite, disjoint theories
ⓘ
modular with respect to component theories ⓘ |
| publicationYear | 1979 ⓘ |
| relatedTo |
DPLL(T) framework
ⓘ
linked to:
DPLL(T)
Shostak combination method ⓘ satisfiability modulo theories ⓘ |
| typicalComponentTheory |
theory of arrays
ⓘ
theory of linear arithmetic ⓘ theory of lists ⓘ theory of uninterpreted functions ⓘ |
| uses |
arrangements of equalities and disequalities over shared variables
ⓘ
cooperating decision procedures ⓘ equality propagation between theories ⓘ variable (or term) purification ⓘ |
How these facts were elicited
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Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Nelson–Oppen combination method Description of subject: The Nelson–Oppen combination method is a decision procedure framework that combines satisfiability solvers for different first-order theories to determine the satisfiability of formulas in their union.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.