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Research draft

proposition

vr.tr.proposition · INF.MED

Let an agent handle propositions by logical form, truth value, proof status and related notions such as conjectures and theorems.

Thing Registry Information and virtual systems

Research draft, second pass

A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.

written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify

Researched by: Claude

Purpose and description

Let an agent handle propositions by logical form, truth value, proof status and related notions such as conjectures and theorems.

A statement that is either true or false, in logic and mathematics; in mathematics, also a proved statement of lesser importance than a theorem, while unproved statements are conjectures and open problems.

What it is for: Reasoning, proof and knowledge representation.

It can be determine logical form; check proof status of mathematical statements; distinguish propositions, theorems and conjectures; represent statements formally.

Distinguishing features

Bears a truth value

Can be simple or compound

Proof status matters in mathematics

Basis of logic

What it looks like

Sentences or formulas stating something.

How it is recognised

Declarative statements with truth values

Proposition, lemma, theorem, conjecture

Business propositions are a different sense

Related models

is a kind of - category

mathematical object and idea

is related to - status

theorem and conjecture

is studied by - field

logic

is connected by - relations

logical relation

In practice

Families and kinds

atomic and compound propositions

mathematical propositions and lemmas

conjectures

open problems such as Hilbert problems

Standards and regulation

ISO 80000-2 logical notation

Failure modes and hazards

Treating conjectures as proved

Ambiguous natural language statements

Also called

conjecturePollock's conjectureCuboid conjecturesLandau's problemsKurepa ConjectureHilbert's problemsMersenne conjecturesAtiyah conjecturecomputational hardness assumptionhomological conjectures in commutative algebraHopf conjectureKaplansky's conjecturesLocal Langlands conjecturesMorita conjecturesRavenel conjecturesSerre's multiplicity conjecturesStandard Conjectures on Algebraic CyclesStark conjecturesTait conjecturestorsion conjectureDecisional Diffie–Hellman assumptionspurious languageRadbruch formulaÇomarmathematical factsynthetic statementanalytic statementtheoretical assumptionsuccinct non-interactive argumentcorollarystatement by relative personconversepostulateobjectivecategorical propositionfalse statementfalse confessionconsequentup topremise

+26

Where this came from

wikidata · CC0 1.0

Source repository Registry entry point

Also registered as vr.tr.proposition-act

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Logic Form and truth.

Form determines analysis.

Form

Structure.

Form

Logical form.

  1. What is the logical form of the statement? definition
  2. Is it atomic or compound? definition

Truth

Truth value.

Truth

Truth value.

  1. Is the statement true, false or undetermined? boundary
  2. On what basis? provenance
Mathematics Proof status.

Status must be accurate.

Status

Proved or open.

Status

Proof status.

  1. Is it proved, disproved or open? provenance
  2. Which source confirms the status? provenance

Naming

Lemma, theorem.

Naming

Naming.

  1. Is it called a proposition, lemma, theorem or conjecture here? definition
  2. Why? definition
Formal Formalisation.

Formal systems check proofs.

Formalised

Proof assistants.

Formalised

Formalisation.

  1. Has the statement been formalised in a proof assistant? provenance
  2. In which library? provenance

Language

Natural language.

Language

Natural language.

  1. Is the natural language statement ambiguous? boundary
  2. How can it be made precise? action
Senses Disambiguation.

Proposition has other senses.

Business

Value proposition.

Business

Business sense.

  1. Is a business or value proposition meant? boundary
  2. Which entry fits? action

Ballot

Ballot measure.

Ballot

Ballot sense.

  1. Is a ballot proposition meant? boundary
  2. Which entry fits? action

What the second pass must settle

  • Should conjectures be a separate entry?
  • How should proof status be tracked?
  • How should formal libraries be linked?
Draft as JSON