logicalForm
P4940
predicate
Indicates a relationship where an expression is associated with its structured, formal logical representation.
All labels observed (8)
| Label | Occurrences |
|---|---|
| logicalForm canonical | 59 |
| formalExpression | 6 |
| hasLogicalForm | 5 |
| formalStatementInvolves | 2 |
| formalizableAs | 2 |
| logicalInterpretation | 2 |
| logicalFunction | 1 |
| quantifierForm | 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: logicalForm
Generated description
Indicates a relationship where an expression is associated with its structured, formal logical representation.
Sample triples (78)
| Subject | Object |
|---|---|
|
Axiom of Extensionality in set theory
surface form:
Axiom of Extensionality
|
first-order sentence with equality and membership ⓘ |
| Dirichlet principle | existence statement for minimizers of an energy functional ⓘ |
| Yao’s next-bit test | if a generator passes the next-bit test then it is pseudorandom ⓘ |
| Yao’s next-bit test | if a generator is pseudorandom then it passes the next-bit test ⓘ |
| Knaster–Kuratowski–Mazurkiewicz lemma | existence statement ⓘ |
| Playfair's axiom | uniqueness axiom for parallels ⓘ |
|
Karp reductions
surface form:
Karp reduction
|
single call transformation from one instance to another ⓘ |
| Beal conjecture | implication from existence of solution to existence of common prime factor ⓘ |
| Cartan magic formula | L_X = i_X d + d i_X as operators on differential forms ⓘ |
| Kleene’s normal form theorem | existential statement about primitive recursive functions T and U ⓘ |
| Gale’s theorem on linear inequalities | either-or alternative theorem NERFINISHED ⓘ |
| Euler criterion | if and only if statement ⓘ |
| orthogonality thesis | independence claim between two variables: intelligence and final goals ⓘ |
| Infinitude | unbounded quantity via predicate surface "hasLogicalForm" ⓘ |
| Infinitude | endless extension via predicate surface "hasLogicalForm" ⓘ |
| Third Law of Robotics | self-preservation constrained by higher-priority duties to humans via predicate surface "hasLogicalForm" ⓘ |
| Cauchy’s integral test | if and only if statement between series and integral convergence under hypotheses ⓘ |
| Cauchy’s mean value theorem | existence theorem ⓘ |
| Bessel inequality | for all x and all orthonormal sequences (e_n), sum |⟨x,e_n⟩|^2 ≤ ||x||^2 ⓘ |
| Münchhausen trilemma | trilemma with three exhaustive and problematic alternatives ⓘ |
| Ontological argument for the existence of God | reductio ad absurdum ⓘ |
| Ontological argument for the existence of God | modal logic argument ⓘ |
| Borel–Cantelli lemmas | implication between series of probabilities and limsup event probability ⓘ |
|
Kolmogorov space (T0 space)
surface form:
Kolmogorov space
|
for all distinct x,y there exists an open set containing x and not y or containing y and not x ⓘ |
| Liouville's inequality in Diophantine approximation | inequality involving absolute values and powers of denominators ⓘ |
| Steinberg relations | for all a in F^× with 1-a in F^×, {a,1-a}=0 ⓘ |
| Steinberg relations | for all a_1,a_2 in F^× with a_1+a_2=1, {a_1,a_2}=0 ⓘ |
|
calculus of constructions
surface form:
Calculus of Constructions
|
intuitionistic higher-order logic via predicate surface "logicalInterpretation" ⓘ |