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 |
|---|---|
| Russell’s paradox | self-referential contradiction ⓘ |
| implicit function theorem | local existence and uniqueness theorem ⓘ |
| Silver Rule | prohibition ⓘ |
| Silver Rule | negative duty ⓘ |
| Barber paradox | set of all people in the village who do not shave themselves via predicate surface "formalizableAs" ⓘ |
| Barber paradox | question whether the barber is a member of that set via predicate surface "formalizableAs" ⓘ |
| liar paradox | sentence that asserts its own falsity ⓘ |
| Burali-Forti paradox | reductio ad absurdum argument ⓘ |
| Noether's isomorphism theorems | equivalence of quotient by intersection and quotient of quotient ⓘ |
| Noether's isomorphism theorems | equivalence of quotient by normal subgroup and quotient of group ⓘ |
| Noetherian induction | second-order principle expressible in first-order theories with well-founded relations ⓘ |
|
Born rule
linked to:
Born rule in quantum mechanics
|
P(i) = |c_i|^2 for a state |ψ⟩ = Σ_i c_i |i⟩ via predicate surface "formalExpression" ⓘ |
|
Born rule
linked to:
Born rule in quantum mechanics
|
P(a) = ⟨ψ|Π_a|ψ⟩ where Π_a is the projector onto the eigenspace of outcome a via predicate surface "formalExpression" ⓘ |
| Cantor’s theorem | ∀S ¬∃f : S → P(S) such that f is surjective via predicate surface "formalExpression" ⓘ |
| Cantor’s theorem | ∀S (|S| < |P(S)|) via predicate surface "formalExpression" ⓘ |
| axiom of choice | for every family F of nonempty sets there exists a function f with domain F such that f(X) is in X for all X in F via predicate surface "quantifierForm" ⓘ |
| Doctrine of Being | derivation of categories from pure being via predicate surface "logicalFunction" ⓘ |
| axiom schema of separation | infinite family of axioms, one for each formula φ ⓘ |
| Kronecker’s lemma | if-then statement about limits of sequences ⓘ |
| Kronecker delta | truth value of equality between indices via predicate surface "logicalInterpretation" ⓘ |
| Basic Law V | abstraction principle ⓘ |
| Fermat polygonal number theorem | universal-existential statement about representations of integers ⓘ |
| Banach fixed-point theorem | if a mapping is a contraction on a complete metric space then it has a unique fixed point ⓘ |
| law of large numbers | limits of sample means via predicate surface "formalStatementInvolves" ⓘ |
| law of large numbers | probability measures via predicate surface "formalStatementInvolves" ⓘ |
| Moorean shift | denies skeptic’s conclusion instead of skeptic’s premises ⓘ |
| Moorean shift | treats skeptic’s argument as modus tollens and replies with modus ponens ⓘ |
| d’Alembert’s principle | ∑ᵢ (Fᵢ − mᵢ aᵢ) · δrᵢ = 0 via predicate surface "formalExpression" ⓘ |
| The Right of Equal Freedom | conditional limitation on liberty ⓘ |
| Amdahl's law | S = 1 / ((1 − P) + P / N) via predicate surface "formalExpression" ⓘ |
| Cauchy sequence | ∀ε>0 ∃N ∀m,n≥N : d(x_m,x_n)<ε via predicate surface "hasLogicalForm" ⓘ |
| Cauchy convergence criterion | biconditional between convergence and Cauchy property in complete spaces ⓘ |
| Cauchy condensation test | biconditional between convergence of two series ⓘ |
| Kelvin–Planck statement of the second law of thermodynamics | impossibility statement ⓘ |
| Paradoxes of motion | argument from infinite tasks ⓘ |
| Paradoxes of motion | argument from divisibility ⓘ |
| Paradoxes of plurality | reductio ad absurdum ⓘ |
| dominated convergence theorem | (f_n→f a.e. and |f_n|≤g integrable) ⇒ lim_n ∫ f_n dμ = ∫ f dμ ⓘ |
| Jordan curve theorem | existence and uniqueness of two complementary regions ⓘ |
| Hadamard three-circle theorem | convexity inequality for a function of log radius ⓘ |
| On Non-Existence | trilemma about being, knowing, and saying ⓘ |
| Hooded man paradox | argument about knowledge of persons under different descriptions via predicate surface "hasLogicalForm" ⓘ |
| Masked man paradox | substitution of identicals in epistemic contexts ⓘ |
| Ramsey sentence | there exists some entities such that the theory’s axioms hold of them ⓘ |
| counterpart theory | uses counterpart quantification across worlds ⓘ |
| Closed Graph Theorem | if graph(T) is closed in X×Y then T is bounded ⓘ |
| Closed Graph Theorem | T is bounded implies graph(T) is closed in X×Y ⓘ |
| First Welfare Theorem | if an allocation is a competitive equilibrium, then it is Pareto efficient ⓘ |
| fundamental theorem of arithmetic | existence and uniqueness theorem ⓘ |
| Goldbach conjecture | for all even n > 2, there exist primes p and q such that n = p + q ⓘ |