Causal and Normative Content

This module formalizes:

• se100.note.CausalNormative — Causal and Normative Content as Primitive Classifications

Causal and normative propositions are treated as primitive, accountability-context-relative content classifications.

The classifications are not reduced to surface vocabulary or to a formal decision procedure. No decidability, exhaustiveness, mutual exclusion, or computational classification method is assumed.

A proposition may therefore be:

• causal;
• normative;
• both causal and normative; or
• neither causal nor normative

in a given accountability context.

structure SE.NeutralSubstrate.Classification.CausalNormativeClassification (L : Logic.Language.PropositionalLanguage) : Type (max u (v + 1))

An abstract, context-relative classification of object-language propositions as causal or normative.

Concrete realizations may determine these classifications through domain analysis, governance rules, expert judgment, or another declared method. This theory assumes only that the classifications have been fixed for the relevant accountability context.

• Context : Type v

  The carrier of accountability contexts in which content classifications are fixed.

• causal : self.Context → L.Proposition → Prop

  Whether a proposition is classified as causal in an accountability context.

• normative : self.Context → L.Proposition → Prop

  Whether a proposition is classified as normative in an accountability context.

def SE.NeutralSubstrate.Classification.CausalProposition {L : Logic.Language.PropositionalLanguage} (K : CausalNormativeClassification L) (c : K.Context) (p : L.Proposition) : Prop

A proposition is causal in an accountability context when the selected classification system classifies it as causal.

Equations

• SE.NeutralSubstrate.Classification.CausalProposition K c p = K.causal c p

def SE.NeutralSubstrate.Classification.NormativeProposition {L : Logic.Language.PropositionalLanguage} (K : CausalNormativeClassification L) (c : K.Context) (p : L.Proposition) : Prop

A proposition is normative in an accountability context when the selected classification system classifies it as normative.

Equations

• SE.NeutralSubstrate.Classification.NormativeProposition K c p = K.normative c p

def SE.NeutralSubstrate.Classification.CausalOrNormativeProposition {L : Logic.Language.PropositionalLanguage} (K : CausalNormativeClassification L) (c : K.Context) (p : L.Proposition) : Prop

A proposition is causal or normative in an accountability context when it has at least one of the two primitive classifications.

Equations

• One or more equations did not get rendered due to their size.