statusInLogic
P16106
predicate
Indicates the logical status or role an entity holds within a formal reasoning or inference context.
All labels observed (4)
| Label | Occurrences |
|---|---|
| logicalStatus | 14 |
| consistencyStatus | 1 |
| statusInLogic canonical | 1 |
| statusInModernLogic | 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: statusInLogic
Generated description
Indicates the logical status or role an entity holds within a formal reasoning or inference context.
Sample triples (17)
| Subject | Object |
|---|---|
| liar paradox | central test case for theories of truth and meaning ⓘ |
| Zermelo–Fraenkel set theory | not known to be provably consistent within itself via predicate surface "consistencyStatus" ⓘ |
| von Neumann paradox in set theory | consistent with Zermelo–Fraenkel set theory plus the axiom of choice (ZFC) via predicate surface "logicalStatus" ⓘ |
| Yablo's paradox | generates contradiction under classical assumptions about truth via predicate surface "logicalStatus" ⓘ |
| identity of indiscernibles | second-order principle via predicate surface "logicalStatus" ⓘ |
| Basic Law V | known to be inconsistent with second-order logic plus full comprehension via predicate surface "statusInModernLogic" ⓘ |
| Moore's paradox | logically consistent via predicate surface "logicalStatus" ⓘ |
| Conway’s soldiers | mathematically solved in the standard formulation via predicate surface "logicalStatus" ⓘ |
| Bernstein set | existence provable in ZFC via predicate surface "logicalStatus" ⓘ |
| Playfair's axiom | equivalent to Euclid's parallel postulate in Euclidean geometry via predicate surface "logicalStatus" ⓘ |
|
Liouville number
linked to:
Liouville numbers
|
proper subset of transcendental numbers via predicate surface "logicalStatus" ⓘ |
| Slutsky substitution matrix is negative semidefinite | necessary condition for rationalizable Hicksian demand via predicate surface "logicalStatus" ⓘ |
| Slutsky substitution matrix is negative semidefinite | not sufficient alone for full integrability via predicate surface "logicalStatus" ⓘ |
| Polish notation | syntactic convention via predicate surface "logicalStatus" ⓘ |
| Skolem arithmetic | recursively axiomatizable via predicate surface "logicalStatus" ⓘ |
| Skolem arithmetic | decidable by effective procedure via predicate surface "logicalStatus" ⓘ |
| GRH | independent of current axioms is unknown via predicate surface "logicalStatus" ⓘ |