Continuous Lattices
E755396
Continuous Lattices is a foundational work in domain theory and lattice theory that introduced a mathematical framework for modeling computation and denotational semantics.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Continuous Lattices canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8751937 — 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: Continuous Lattices Context triple: [Dana Scott, notableWork, Continuous Lattices]
-
A.
Lattice Theory
Lattice Theory is a foundational mathematical text that systematically develops the theory of lattices and ordered structures, profoundly influencing modern algebra and order theory.
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B.
Tarski’s fixed point theorem
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
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C.
Birkhoff’s representation theorem for finite distributive lattices
Birkhoff’s representation theorem for finite distributive lattices is a fundamental result in lattice theory that characterizes every finite distributive lattice as isomorphic to the lattice of lower (order) ideals of a finite poset.
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D.
Recursive Functions and Intuitionistic Mathematics
Recursive Functions and Intuitionistic Mathematics is a seminal work by Stephen Kleene that develops the theory of recursive (computable) functions within the framework of intuitionistic logic and mathematics.
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E.
Hilbert-style deductive systems
Hilbert-style deductive systems are axiomatic proof systems in mathematical logic that use a small set of axiom schemas and a few inference rules (typically including modus ponens) to derive theorems in formal theories such as Zermelo–Fraenkel set theory.
- 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: Continuous Lattices Target entity description: Continuous Lattices is a foundational work in domain theory and lattice theory that introduced a mathematical framework for modeling computation and denotational semantics.
-
A.
Lattice Theory
Lattice Theory is a foundational mathematical text that systematically develops the theory of lattices and ordered structures, profoundly influencing modern algebra and order theory.
-
B.
Tarski’s fixed point theorem
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
-
C.
Birkhoff’s representation theorem for finite distributive lattices
Birkhoff’s representation theorem for finite distributive lattices is a fundamental result in lattice theory that characterizes every finite distributive lattice as isomorphic to the lattice of lower (order) ideals of a finite poset.
-
D.
Recursive Functions and Intuitionistic Mathematics
Recursive Functions and Intuitionistic Mathematics is a seminal work by Stephen Kleene that develops the theory of recursive (computable) functions within the framework of intuitionistic logic and mathematics.
-
E.
Hilbert-style deductive systems
Hilbert-style deductive systems are axiomatic proof systems in mathematical logic that use a small set of axiom schemas and a few inference rules (typically including modus ponens) to derive theorems in formal theories such as Zermelo–Fraenkel set theory.
- F. None of above. chosen
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
monograph ⓘ |
| author |
D. S. Scott
ⓘ
G. Gierz ⓘ J. D. Lawson ⓘ K. H. Hofmann ⓘ K. Keimel ⓘ M. Mislove ⓘ |
| centralConcept |
algebraic lattices
ⓘ
complete partial orders ⓘ continuity of posets ⓘ topological methods in order theory ⓘ |
| contributedTo | denotational semantics ⓘ |
| field |
domain theory
ⓘ
lattice theory ⓘ mathematics ⓘ order theory ⓘ theoretical computer science ⓘ |
| hasImpactOn |
category-theoretic models of computation
ⓘ
fixed-point logics ⓘ logic in computer science ⓘ type theory ⓘ |
| influenced |
denotational semantics of programming languages
ⓘ
semantics of lambda calculus ⓘ semantics of recursive definitions ⓘ |
| providesFrameworkFor |
domain-theoretic semantics
ⓘ
modeling computation ⓘ |
| topic |
Scott topology
ⓘ
Scott-continuous function ⓘ approximation in posets ⓘ complete lattice ⓘ continuous lattice ⓘ directed complete partial order ⓘ domains in computation ⓘ way-below relation ⓘ |
| usedIn |
fixed-point theory in computation
ⓘ
models of higher-order functions ⓘ models of non-deterministic computation ⓘ programming language semantics ⓘ |
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: Continuous Lattices Description of subject: Continuous Lattices is a foundational work in domain theory and lattice theory that introduced a mathematical framework for modeling computation and denotational semantics.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.