Isabelle/FOL
E822902
Isabelle/FOL is the classical first-order logic object logic of the Isabelle proof assistant, providing a framework for formalizing and verifying mathematical theorems and logical systems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Isabelle/FOL canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9810054 — 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: Isabelle/FOL Context triple: [Isabelle, hasComponent, Isabelle/FOL]
-
A.
Isabelle proof assistant
Isabelle proof assistant is a widely used interactive theorem prover and generic proof assistant designed for formal verification and mathematical logic, particularly known for its support of higher-order logic.
-
B.
Isabelle/HOL: A Proof Assistant for Higher-Order Logic
"Isabelle/HOL: A Proof Assistant for Higher-Order Logic" is a foundational book and system documentation that presents the Isabelle/HOL interactive theorem prover, widely used for formal verification and higher-order logic reasoning in computer science and mathematics.
-
C.
LCF theorem prover
The LCF theorem prover is an early interactive proof system that pioneered the use of higher-order logic and the LCF-style architecture, forming the conceptual basis for later provers like HOL and Isabelle.
-
D.
HOL theorem prover
The HOL theorem prover is an interactive proof assistant for higher-order logic, widely used in formal verification of hardware, software, and mathematical theories.
-
E.
HOL4
HOL4 is an interactive theorem prover for higher-order logic, widely used in formal verification and based on the LCF approach to ensuring soundness.
- 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: Isabelle/FOL Target entity description: Isabelle/FOL is the classical first-order logic object logic of the Isabelle proof assistant, providing a framework for formalizing and verifying mathematical theorems and logical systems.
-
A.
Isabelle proof assistant
Isabelle proof assistant is a widely used interactive theorem prover and generic proof assistant designed for formal verification and mathematical logic, particularly known for its support of higher-order logic.
-
B.
Isabelle/HOL: A Proof Assistant for Higher-Order Logic
"Isabelle/HOL: A Proof Assistant for Higher-Order Logic" is a foundational book and system documentation that presents the Isabelle/HOL interactive theorem prover, widely used for formal verification and higher-order logic reasoning in computer science and mathematics.
-
C.
LCF theorem prover
The LCF theorem prover is an early interactive proof system that pioneered the use of higher-order logic and the LCF-style architecture, forming the conceptual basis for later provers like HOL and Isabelle.
-
D.
HOL theorem prover
The HOL theorem prover is an interactive proof assistant for higher-order logic, widely used in formal verification of hardware, software, and mathematical theories.
-
E.
HOL4
HOL4 is an interactive theorem prover for higher-order logic, widely used in formal verification and based on the LCF approach to ensuring soundness.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
first-order logic formalization
ⓘ
object logic ⓘ |
| basedOn | classical predicate logic ⓘ |
| compatibleWith |
Isar proof language
NERFINISHED
ⓘ
ML-level tactics in Isabelle ⓘ |
| developedAt | Technische Universität München (via Isabelle project) NERFINISHED ⓘ |
| developedBy | Lawrence C. Paulson (as part of Isabelle) NERFINISHED ⓘ |
| distributedWith |
Isabelle/HOL
NERFINISHED
ⓘ
Isabelle/ZF NERFINISHED ⓘ |
| documentedIn |
Isabelle Reference Manual
NERFINISHED
ⓘ
Isabelle/Isar Reference Manual NERFINISHED ⓘ |
| hasComponent |
axioms for classical logic
ⓘ
rules for equality reasoning ⓘ rules for quantifier introduction and elimination ⓘ |
| hasFeature |
Hilbert-style axiomatization (in early versions)
ⓘ
built-in resolution prover ⓘ classical tableau-style reasoning (via tactics) ⓘ natural deduction rules ⓘ sequent-style rules ⓘ |
| hasFileName | FOL.thy ⓘ |
| hasSemantics | Tarskian first-order semantics (informally underlying) ⓘ |
| hasSyntax |
existential quantifier ∃
ⓘ
logical connectives (∧, ∨, ¬, →, ↔) ⓘ term language with variables, function symbols, and predicate symbols ⓘ universal quantifier ∀ ⓘ |
| historicalRole | early default object logic of Isabelle ⓘ |
| implementedIn | Isabelle theory files ⓘ |
| loadedVia | theory import in Isabelle ⓘ |
| logicType | classical first-order logic ⓘ |
| partOf |
Isabelle
NERFINISHED
ⓘ
Isabelle proof assistant NERFINISHED ⓘ |
| provides |
basic logical infrastructure for other Isabelle object logics
ⓘ
classical reasoning tactics ⓘ inference rules for first-order logic ⓘ tactics for first-order reasoning ⓘ |
| stillUsedFor |
examples in logic and theorem proving tutorials
ⓘ
experiments with pure first-order reasoning ⓘ |
| supersededInPracticeBy | Isabelle/HOL NERFINISHED ⓘ |
| supports |
classical reasoning
ⓘ
equality ⓘ first-order reasoning ⓘ quantifiers ⓘ |
| usedFor |
formalizing mathematical theorems
ⓘ
teaching logic and theorem proving ⓘ verifying logical systems ⓘ |
| usedIn |
formal methods research
ⓘ
interactive theorem proving ⓘ |
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: Isabelle/FOL Description of subject: Isabelle/FOL is the classical first-order logic object logic of the Isabelle proof assistant, providing a framework for formalizing and verifying mathematical theorems and logical systems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Isabelle