Robinson unification algorithm
E911972
The Robinson unification algorithm is the foundational procedure in automated theorem proving that computes the most general unifier of logical expressions, forming the basis of first-order logic resolution methods.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Robinson unification algorithm canonical | 1 |
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
algorithm in logic
ⓘ
procedure in automated theorem proving ⓘ unification algorithm ⓘ |
| assumes | first-order terms built from variables, function symbols, and constants ⓘ |
| basedOn |
substitution in first-order logic
ⓘ
term rewriting ⓘ |
| complexity | runs in time roughly linear in term size with appropriate data structures ⓘ |
| coreConcept |
most general unifier
ⓘ
occurs check ⓘ substitution set ⓘ term matching ⓘ |
| failsWhen |
function symbols at same position differ
ⓘ
occurs check detects cyclic substitution ⓘ |
| field |
artificial intelligence
ⓘ
automated theorem proving ⓘ first-order logic ⓘ mathematical logic ⓘ |
| formalizes | unification problem for first-order terms ⓘ |
| influenced |
automated deduction systems
ⓘ
design of logic programming languages ⓘ |
| input |
pair of first-order terms
ⓘ
set of equations between terms ⓘ |
| introducedBy | John Alan Robinson NERFINISHED ⓘ |
| introducedIn | 1960s ⓘ |
| introducedInContextOf | resolution principle ⓘ |
| namedAfter | John Alan Robinson NERFINISHED ⓘ |
| output |
failure if terms are not unifiable
ⓘ
most general unifier ⓘ |
| property |
complete for unification of first-order terms
ⓘ
computes most general unifier if it exists ⓘ sound ⓘ |
| purpose |
compute most general unifier
ⓘ
support resolution-based theorem proving ⓘ unify logical expressions ⓘ |
| relatedTo |
Herbrand universe
NERFINISHED
ⓘ
SLD-resolution NERFINISHED ⓘ resolution refutation ⓘ |
| step |
apply substitution to remaining equations
ⓘ
orient equation to substitute variable by term ⓘ repeat until no equations remain or conflict arises ⓘ select unsolved equation between terms ⓘ |
| usedIn |
Prolog implementations
ⓘ
constraint logic programming ⓘ logic programming ⓘ resolution theorem proving ⓘ term rewriting systems NERFINISHED ⓘ type inference systems ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.