De Morgan's laws
E428884
De Morgan's laws are fundamental rules in Boolean algebra and set theory that relate conjunctions and disjunctions through negation, forming a cornerstone of classical logic.
All labels observed (1)
| Label | Occurrences |
|---|---|
| De Morgan's laws canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T4290508 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: De Morgan's laws Context triple: [Augustus De Morgan, knownFor, De Morgan's laws]
-
A.
Herbrand disjunction
Herbrand disjunction is a logical formula formed as a finite disjunction of ground instances of a first-order formula, central to Herbrand’s theorem in proof theory and automated reasoning.
-
B.
An Investigation of the Laws of Thought
An Investigation of the Laws of Thought is George Boole’s foundational 1854 treatise that established Boolean algebra and helped lay the groundwork for modern mathematical logic and computer science.
-
C.
Leibnizian logic
Leibnizian logic is the rationalist, formal approach to logic and calculation developed by Gottfried Wilhelm Leibniz, emphasizing symbolic representation, logical calculus, and the reduction of mathematical and philosophical reasoning to precise logical principles.
-
D.
Kirchhoff's circuit laws
Kirchhoff's circuit laws are fundamental rules in electrical engineering that describe how electric charge and energy are conserved in electrical circuits through relationships among currents and voltages.
-
E.
Kluge's law
Kluge's law is a proposed sound law in Proto-Germanic historical linguistics that explains the development of certain geminate consonants from earlier consonant clusters.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: De Morgan's laws Target entity description: De Morgan's laws are fundamental rules in Boolean algebra and set theory that relate conjunctions and disjunctions through negation, forming a cornerstone of classical logic.
-
A.
Herbrand disjunction
Herbrand disjunction is a logical formula formed as a finite disjunction of ground instances of a first-order formula, central to Herbrand’s theorem in proof theory and automated reasoning.
-
B.
An Investigation of the Laws of Thought
An Investigation of the Laws of Thought is George Boole’s foundational 1854 treatise that established Boolean algebra and helped lay the groundwork for modern mathematical logic and computer science.
-
C.
Leibnizian logic
Leibnizian logic is the rationalist, formal approach to logic and calculation developed by Gottfried Wilhelm Leibniz, emphasizing symbolic representation, logical calculus, and the reduction of mathematical and philosophical reasoning to precise logical principles.
-
D.
Kirchhoff's circuit laws
Kirchhoff's circuit laws are fundamental rules in electrical engineering that describe how electric charge and energy are conserved in electrical circuits through relationships among currents and voltages.
-
E.
Kluge's law
Kluge's law is a proposed sound law in Proto-Germanic historical linguistics that explains the development of certain geminate consonants from earlier consonant clusters.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
Boolean algebra law
ⓘ
logical law ⓘ rule of inference ⓘ set theory law ⓘ |
| appliesTo |
logical connectives
ⓘ
set operations ⓘ |
| category |
identity in Boolean algebra
ⓘ
theorem in logic ⓘ theorem in set theory ⓘ |
| componentOf |
axioms of Boolean algebra
ⓘ
equational theory of Boolean algebras ⓘ |
| expresses |
equivalence between negated conjunction and disjunction of negations
ⓘ
equivalence between negated disjunction and conjunction of negations ⓘ |
| field |
Boolean algebra
NERFINISHED
ⓘ
classical logic ⓘ digital logic ⓘ propositional logic ⓘ set theory ⓘ |
| generalizationOf |
De Morgan's laws for propositions
NERFINISHED
ⓘ
De Morgan's laws for sets NERFINISHED ⓘ |
| hasConsequence | negation distributes over conjunction and disjunction in classical logic ⓘ |
| hasForm |
¬(P ∧ Q) ≡ (¬P) ∨ (¬Q)
ⓘ
¬(P ∨ Q) ≡ (¬P) ∧ (¬Q) ⓘ |
| hasSetForm |
(A ∩ B)^c = A^c ∪ B^c
ⓘ
(A ∪ B)^c = A^c ∩ B^c ⓘ |
| historicalPeriod | 19th century ⓘ |
| holdsIn |
Boolean algebras
NERFINISHED
ⓘ
classical propositional logic ⓘ set algebras ⓘ |
| namedAfter | Augustus De Morgan NERFINISHED ⓘ |
| relatedTo |
complementation laws in Boolean algebra
ⓘ
distributive laws ⓘ law of double negation ⓘ |
| relatesConcept |
complement
ⓘ
conjunction ⓘ disjunction ⓘ intersection ⓘ negation ⓘ union ⓘ |
| usedIn |
complementation of logical conditions in programming
ⓘ
conversion between CNF and DNF ⓘ derivation of normal forms ⓘ design of digital circuits ⓘ proof transformations ⓘ simplification of Boolean expressions ⓘ simplification of logical expressions ⓘ |
| validIn |
finite Boolean algebras
ⓘ
infinite Boolean algebras ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: De Morgan's laws Description of subject: De Morgan's laws are fundamental rules in Boolean algebra and set theory that relate conjunctions and disjunctions through negation, forming a cornerstone of classical logic.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.