specialCaseOf
P7025
predicate
Indicates that one entity represents a more specific, exceptional, or restricted instance of the general situation, rule, or relationship expressed by another entity.
All labels observed (17)
| Label | Occurrences |
|---|---|
| specialCase | 154 |
| hasSpecialCase | 131 |
| specialCaseOf canonical | 95 |
| specialCaseAt | 10 |
| includesAsSpecialCase | 9 |
| specialCaseOn | 5 |
| specialCaseAtTheta | 3 |
| specialCaseCondition | 3 |
| exceptionToAntlers | 2 |
| specialForm | 2 |
| areSpecialCaseOf | 1 |
| degree1SpecialCase | 1 |
| isCaseOf | 1 |
| solvableInSpecialCase | 1 |
| specialCaseExample | 1 |
| specialCaseFor | 1 |
| specialCaseWhen | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: specialCaseOf
Generated description
Indicates that one entity represents a more specific, exceptional, or restricted instance of the general situation, rule, or relationship expressed by another entity.
Sample triples (421)
| Subject | Object |
|---|---|
|
Riemannian manifold
linked to:
Riemannian manifolds
|
smooth manifold with additional structure ⓘ |
| binomial theorem | (a + b)^2 = a^2 + 2ab + b^2 via predicate surface "hasSpecialCase" ⓘ |
| binomial theorem | (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 via predicate surface "hasSpecialCase" ⓘ |
| binomial theorem | (a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4 via predicate surface "hasSpecialCase" ⓘ |
| Cervidae | Rangifer tarandus females also grow antlers via predicate surface "exceptionToAntlers" ⓘ |
| Cervidae | Hydropotes inermis lacks antlers via predicate surface "exceptionToAntlers" ⓘ |
| Kullback–Leibler divergence | Csiszár f-divergence ⓘ |
| Rényi entropy | collision entropy at α = 2 via predicate surface "hasSpecialCase" ⓘ |
| Rényi entropy | min-entropy as α → ∞ via predicate surface "hasSpecialCase" ⓘ |
| Rényi entropy | max-entropy as α → 0 via predicate surface "hasSpecialCase" ⓘ |
| Euclidean space | Hilbert space ⓘ |
| Levi-Civita connection | metric connection ⓘ |
| Levi-Civita connection | torsion-free connection ⓘ |
| multinomial theorem | reduces to binomial theorem when m = 2 via predicate surface "specialCase" ⓘ |
| generalized binomial theorem | reduces to classical binomial theorem when α is a nonnegative integer via predicate surface "specialCase" ⓘ |
| Gaussian distribution | standard normal distribution via predicate surface "hasSpecialCase" ⓘ |
| Noether's problem |
Noether's problem for abelian groups
via predicate surface "hasSpecialCase"
ⓘ
linked to:
Noether's problem
|
| Noether's problem |
Noether's problem for cyclic groups
via predicate surface "hasSpecialCase"
ⓘ
linked to:
Noether's problem
|
| Noether's problem |
Noether's problem over the rational numbers
via predicate surface "hasSpecialCase"
ⓘ
linked to:
Noether's problem
|
| Noether's problem | Noether's problem over algebraically closed fields via predicate surface "hasSpecialCase" ⓘ |
| Noether's problem |
Noether's problem for p-groups
via predicate surface "hasSpecialCase"
ⓘ
linked to:
Noether's problem
|
| Noether's problem |
Noether's problem for symmetric groups
via predicate surface "hasSpecialCase"
ⓘ
linked to:
Noether's problem
|
| Noether's problem |
Noether's problem for dihedral groups
via predicate surface "hasSpecialCase"
ⓘ
linked to:
Noether's problem
|
| Rényi divergence | α = 1 via predicate surface "specialCaseAt" ⓘ |
| Rényi divergence | α = 0 via predicate surface "specialCaseAt" ⓘ |
| Rényi divergence | α = ∞ via predicate surface "specialCaseAt" ⓘ |
| Ornstein–Uhlenbeck process |
Langevin equation
ⓘ
linked to:
Langevin dynamics
|
| Ornstein–Uhlenbeck process |
Gaussian Markov process
ⓘ
linked to:
Markov processes
|
| Ricci flow | geometric heat flow ⓘ |
| Smoluchowski coagulation equation | constant kernel coagulation model via predicate surface "hasSpecialCase" ⓘ |
| Smoluchowski coagulation equation | additive kernel coagulation model via predicate surface "hasSpecialCase" ⓘ |
| Smoluchowski coagulation equation | multiplicative kernel coagulation model via predicate surface "hasSpecialCase" ⓘ |
|
Itô process
linked to:
Itô processes
|
Brownian motion via predicate surface "specialCase" ⓘ |
|
Itô process
linked to:
Itô processes
|
martingale with zero drift via predicate surface "specialCase" ⓘ |
| Steinmetz solid | intersection of two equal cylinders of radius r with perpendicular axes via predicate surface "specialCase" ⓘ |
| Euler’s formula for complex exponentials | Euler’s identity e^{i\pi} + 1 = 0 via predicate surface "hasSpecialCase" ⓘ |
| Tucker’s lemma | discrete ham sandwich–type results via predicate surface "hasSpecialCase" ⓘ |
| Lebesgue spaces | Hilbert space when p = 2 via predicate surface "specialCase" ⓘ |
| Crank–Nicolson scheme | theta-method with θ = 1/2 ⓘ |
| Heisenberg model | one-dimensional spin-1/2 chain via predicate surface "solvableInSpecialCase" ⓘ |
| Kronecker delta | discrete orthogonality relation ⓘ |
| telegrapher's equations | lossless line equations when R = 0 and G = 0 via predicate surface "specialCase" ⓘ |
| telegrapher's equations | distortionless line condition when R/L = G/C via predicate surface "specialCase" ⓘ |
| Pradosha vrata | Maha Pradosha vrata via predicate surface "specialForm" ⓘ |
| Sperner's lemma |
polytopal Sperner lemma
ⓘ
linked to:
Sperner's lemma
|
| Euclidean metric | Lp metric ⓘ |
| Fermat's Last Theorem | Pythagorean triples when n = 2 via predicate surface "specialCaseFor" ⓘ |
| Fermat point | coincides with the obtuse vertex when the triangle has an angle of at least 120 degrees via predicate surface "specialCase" ⓘ |
| Fermat curve | unit circle for n = 2 via predicate surface "specialCase" ⓘ |
| Fermat curve | superelliptic curve y^m = f(x) ⓘ |