update

Author: denisecase

glossary/core_ontology_concepts.tex

@@ -184,11 +184,16 @@ \subsection*{Core Ontology Concepts}
         without embedding it as a foundational fact.
         See also \emph{Embedding}, \emph{Reification}.
 
-  \item[Substrate]
-        The foundational layer of an ontology,
-        consisting of entities, identity conditions, and persistence criteria.
-        A neutral substrate excludes causal and normative primitives,
-        serving as a stable base for divergent interpretive layers.
-        Also called \emph{substrate layer} or \emph{foundational layer}.
+\item[Substrate]
+      The foundational layer of an ontology that functions as a shared
+      representational base across interpretive frameworks.
+      Formally, the \emph{substrate ontology} is the ontology whose
+      foundational layer provides entities together with identity
+      and persistence conditions.
+      For brevity, this paper refers to that ontology simply as the
+      \emph{substrate}.
+      A neutral substrate excludes causal and normative primitives,
+      serving as a stable base for divergent interpretive layers.
+      Also called \emph{substrate layer} or \emph{foundational layer}.
 
 \end{description}

glossary/neutrality_interpretation.tex

@@ -24,15 +24,15 @@ \subsection*{Neutrality and Interpretation}
         and framework-level conclusions, which may vary.
 
   \item[Compatibility]
-        The property of an ontology and an interpretive framework
+        The property of a substrate ontology and an interpretive framework
         such that their combination does not entail contradiction.
         Formally: $\mathcal{S} \cup \mathcal{F} \not\vdash \bot$.
 
   \item[Consistency ($\not\vdash \bot$)]
         The property of a set of statements such that no contradiction
         can be derived from its assertions.
         The notation $\mathcal{S} \not\vdash \bot$ indicates
-        that an ontology $\mathcal{S}$ is consistent;
+        that a substrate ontology $\mathcal{S}$ is consistent;
         $\mathcal{S} \vdash \bot$ indicates that $\mathcal{S}$ is inconsistent
         (i.e., both $p$ and $\neg p$ can be derived for some proposition $p$).
 

se100_the_ontological_neutrality_theorem.pdf

@@ -168,7 +168,7 @@
 
 \bigskip
 \noindent\textbf{Preview of Main Result.}
-\emph{Let $\mathcal{S}$ be an ontology intended to function
+\emph{Let $\mathcal{S}$ be a substrate ontology intended to function
   as a neutral substrate across diverse interpretive frameworks.
   Then $\mathcal{S}$ satisfies the requirements of neutrality
   if and only if its foundational Level of Abstraction
@@ -204,7 +204,9 @@
   accountability;
   neutrality constraints;
   extension stability;
-  causal and normative commitment
+  interpretive non-commitment;
+  pre-causal;
+  pre-normative
 }
 
 \input{sections/01_intro}

se100_the_ontological_neutrality_theorem.tex

@@ -92,10 +92,17 @@ \subsection*{Design Problems in Shared Representation}
 Under this conception of neutrality, the substrate must remain
 usable across divergent legal, political, and analytic frameworks
 without requiring revision of the substrate itself.
+
+In this paper, a \emph{substrate ontology} is an ontology that serves
+as the shared representational base across interpretive frameworks.
+Its foundational layer provides the entities and relations over which
+interpretive frameworks reason and derive conclusions.
+For brevity, this ontology may be referred to as the \emph{substrate}.
+
 This requires a careful selection of the
 Level of Abstraction (LoA)~\citep{floridi2008levels}
 at which the substrate operates.
-Following Floridi, we argue that an LoA is
+Following Floridi, an LoA is
 defined by the set of observables it makes available;
 for a substrate to remain neutral,
 it must operate at an LoA that excludes
@@ -115,6 +122,7 @@ \subsection*{Design Problems in Shared Representation}
 \emph{conclusions}: causal attributions, responsibility
 assignments, or normative evaluations that are not
 asserted by the substrate itself.
+
 A \emph{neutral substrate} constrains which propositions may
 be asserted as commitments so that multiple frameworks may
 derive incompatible conclusions from the same substrate
@@ -137,7 +145,7 @@ \subsection*{Design Problems in Shared Representation}
 Under persistent disagreement, extensions to the substrate may
 introduce incompatible causal accounts or normative attributions,
 and those extensions are not required to converge.
-We treat substrate revision as an impermissible
+Substrate revision is treated as an impermissible
 mechanism for resolving interpretive conflict: the substrate
 must remain stable across extensions whose conclusions are
 mutually inconsistent.

sections/01_intro.tex

@@ -118,7 +118,7 @@ \subsection{Legal Ontologies: LKIF and Related Approaches}
 When legal interpretations diverge,
 as they routinely do across jurisdictions, over time,
 or under political contestation,
-the substrate itself must be revised
+the substrate ontology itself must be revised
 to accommodate disagreement.
 
 The result established here
@@ -171,11 +171,11 @@ \subsection{Philosophy of Information: Levels of Abstraction}
 While Floridi uses these concepts
 to analyze the nature of data and knowledge, this paper applies
 them specifically to the problem of ontological neutrality.
-We argue that neutrality is a function of
+Under this view, neutrality is a function of
 operating at a foundational LoO
 with a deliberately restricted LoA.
 This paper extends Floridi's work by proving
-that certain classes of observables, causal and normative,
+that certain classes of observables, namely causal and normative,
 necessarily introduce interpretive entropy that
 renders an LoA unstable with respect to extensions.
 

sections/02_related.tex

@@ -77,7 +77,7 @@ \subsection{Interpretive Non-Commitment}
 The first requirement,
 under this definition of neutrality,
 is interpretive non-commitment.
-An ontology satisfies this requirement
+A substrate ontology satisfies this requirement
 if it does not assert any proposition
 whose truth value can vary across admissible interpretive frameworks.
 
@@ -118,7 +118,7 @@ \subsection{Interpretive Non-Commitment}
 
 \begin{definition}[Interpretive Non-Commitment]
   \label{def:interpretive-non-commitment}
-  An ontology $\mathcal{S}$ satisfies \emph{interpretive non-commitment}
+  A substrate ontology $\mathcal{S}$ satisfies \emph{interpretive non-commitment}
   if it does not assert any framework-variant proposition:
   there is no proposition $p$ such that $\mathcal{S} \vdash p$
   and $p$ is framework-variant with respect to $\mathbb{F}$.
@@ -138,7 +138,7 @@ \subsection{Interpretive Non-Commitment}
 under this definition,
 must therefore refrain from
 settling such questions at the ontological level.
-If an ontology asserts that a particular action was
+If a substrate ontology asserts that a particular action was
 obligatory, forbidden, or permitted,
 it necessarily privileges one normative framework over others.
 Similarly, if it asserts that one event caused another,
@@ -147,9 +147,9 @@ \subsection{Interpretive Non-Commitment}
 Rather, causal conclusions depend on explanatory frameworks
 (e.g., statistical, mechanistic, or legal standards of causation)
 that may legitimately differ across admissible frameworks.
-In both cases, the ontology ceases to be neutral with respect to interpretation.
+In both cases, the substrate ontology ceases to be neutral with respect to interpretation.
 
-Interpretive non-commitment does not require the ontology
+Interpretive non-commitment does not require the substrate ontology
 to ignore normative or causal discourse altogether.
 Rather, it requires that the substrate operate
 at a Level of Abstraction (LoA)~\citep{floridi2008levels,floridi2011philosophy}
@@ -178,12 +178,12 @@ \subsection{Extension Stability}
 The second requirement,
 given the neutrality role defined above,
 is extension stability.
-An ontology satisfies this requirement if it remains consistent
+A substrate ontology satisfies this requirement if it remains consistent
 when extended by incompatible interpretive frameworks.
 
 \begin{definition}[Extension Stability]
   \label{def:extension-stability}
-  An ontology $\mathcal{S}$ satisfies \emph{extension stability}
+  A substrate ontology $\mathcal{S}$ satisfies \emph{extension stability}
   if for all admissible frameworks $\mathcal{F} \in \mathbb{F}$,
   $\mathcal{S} \cup \mathcal{F} \not\vdash \bot$.
 \end{definition}
@@ -221,7 +221,7 @@ \subsection{Extension Stability}
 the introduction of a new interpretive framework
 requires retracting or revising ontological assertions.
 
-Consider a substrate $\mathcal{S}$ used by two interpretive frameworks,
+Consider a substrate ontology $\mathcal{S}$ used by two interpretive frameworks,
 $\mathcal{F}_1$ and $\mathcal{F}_2$, that contradict each other
 ($\mathcal{F}_1 \cup \mathcal{F}_2 \vdash \bot$).
 For $\mathcal{S}$ to remain stable, it must be separately consistent
@@ -256,7 +256,7 @@ \subsection{Scope of Neutrality}
 
 It is important to emphasize that neutrality,
 as defined here, is not global.
-A neutral ontology is not neutral with respect to
+A neutral substrate is not neutral with respect to
 existence, identity, or classification.
 It must take substantive positions on what kinds of entities exist,
 how they are distinguished, and what criteria govern their persistence.
@@ -325,10 +325,10 @@ \subsection{Scope of Neutrality}
 These requirements establish that neutrality is
 not a lack of content, but a categorical constraint:
 to remain stable under pluralistic interpretation,
-a foundational ontology satisfies both requirements if and only if it is
+a substrate ontology satisfies both requirements if and only if it is
 strictly pre-causal and pre-normative.
 
-The next section establishes the central result:
-a substrate satisfies both neutrality requirements
-if and only if its foundational layer excludes
-causal and normative commitments.
+The next section establishes the central result,
+identifying the structural constraints a substrate ontology
+must satisfy to function as a neutral substrate
+across divergent interpretive frameworks.

sections/03_requirements.tex

@@ -3,26 +3,25 @@
 \section{Formal Development of the Ontological Neutrality Theorem}
 \label{sec:formal-dev}
 
-Because interpretive frameworks derive conclusions
-while ontologies assert commitments,
-embedding framework-contestable propositions as substrate commitments
-produces incompatibility with some admissible framework.
-The following argument formalizes this constraint.
-
-This section establishes a necessary and sufficient condition
-on substrate design: the neutrality requirements
-defined in Section~\ref{sec:requirements}
-are satisfied if and only if causal and normative commitments
-are excluded from the substrate layer.
+Section~\ref{sec:requirements} defined the two neutrality
+requirements governing a substrate ontology:
+interpretive non-commitment and extension stability.
+This section establishes the relationship between those requirements
+and the structure of the substrate layer.
+
+Specifically, it proves that a substrate satisfies the neutrality
+requirements if and only if causal and normative commitments are excluded
+from the substrate.
 The argument is structural and logical rather than empirical:
-it follows from the interaction
-between interpretive disagreement and substrate-level ontological assertion.
+it follows from the interaction between interpretive disagreement
+and substrate-level commitments.
 All necessity and sufficiency claims in this section
-are relative to those requirements.
+are relative to the definitions introduced in
+Section~\ref{sec:requirements}.
 
 \subsection{Neutrality as Compatibility Across Admissible Frameworks}
 
-By definition, a neutral ontological substrate must remain compatible
+By definition, a neutral substrate must remain compatible
 with multiple admissible interpretive frameworks,
 even when those frameworks disagree.
 Compatibility here is understood in a strong sense:
@@ -56,7 +55,8 @@ \subsection{Neutrality as Compatibility Across Admissible Frameworks}
 across all admissible interpretive frameworks.
 If the substrate asserts a proposition whose truth
 depends on a particular causal or normative interpretation,
-then there exist admissible frameworks that derive the negation of that proposition.
+then there exist admissible frameworks that derive
+both that proposition and its negation.
 Because neutrality requires the substrate to remain logically
 consistent when extended by every admissible framework,
 asserting such a proposition at the substrate layer
@@ -69,9 +69,9 @@ \subsection{Neutrality as Compatibility Across Admissible Frameworks}
 A neutral substrate may contain vocabulary for representing
 causal or normative claims, provided those claims are represented as
 interpretive assertions rather than asserted as substrate-layer facts.
-What neutrality excludes is the elevation of a particular
-causal or normative conclusion to a foundational commitment of the ontology,
-since such conclusions may be rejected by other admissible frameworks.
+What neutrality excludes is asserting a causal or normative
+proposition as a substrate-level commitment,
+since such propositions may be rejected by some admissible framework.
 
 \subsection{Framework-Contestability and Substrate Incompatibility}
 \label{subsec:general-lemma}
@@ -81,7 +81,7 @@ \subsection{Framework-Contestability and Substrate Incompatibility}
 
 \begin{lemma}[Framework-Contestability Lemma]
 \label{lem:contestability}
-Let $\mathcal{S}$ be an ontology satisfying the neutrality requirements,
+Let $\mathcal{S}$ be a substrate ontology satisfying the neutrality requirements,
 and let $p$ be a proposition whose truth conditions depend on
 the conclusions of an interpretive framework rather than on
 framework-invariant referential structure.
@@ -117,15 +117,15 @@ \subsection{Normative Commitments}
 It is therefore a routine and expected feature of accountability systems
 that admissible frameworks disagree about normative conclusions.
 
-By Lemma~\ref{lem:contestability}, asserting any such conclusion
+By Lemma~\ref{lem:contestability}, asserting any such proposition
 as a substrate-layer commitment privileges one normative framework over others.
 Any framework that denies the asserted commitment becomes
 incompatible with the substrate,
 as it cannot be layered atop it without contradiction or revision.
 This incompatibility is not a matter of missing context or insufficient detail;
 it arises from the ontological act of asserting a contested normative
-commitment as a foundational fact.
-As a result, no ontology that asserts normative commitments
+commitment as a foundational fact of the substrate.
+As a result, no substrate that asserts normative commitments
 at the foundational layer can satisfy interpretive non-commitment,
 and when alternative normative interpretations arise,
 as they inevitably do,
@@ -138,24 +138,25 @@ \subsection{Causal Commitments}
 
 Causal attributions are framework-dependent
 in the sense of Lemma~\ref{lem:contestability}.
-Claims such as \textit{event A caused event B}
+Claims such as \textit{ $e_1$ caused $e_2$}
 depend on background assumptions about causal mechanisms,
 variable selection, counterfactual reasoning, and model scope.
 Distinct causal frameworks may be equally admissible
 while disagreeing about specific causal relationships.
 
 By Lemma~\ref{lem:contestability}, asserting any causal relation
-as a substrate-layer commitment necessarily commits the ontology
+as a substrate-layer commitment necessarily commits the substrate
 to one causal model among many.
 Frameworks that reject that model cannot be layered onto
 the substrate without conflict.
 Importantly, this argument does not rely on the presence
 of an active dispute over a specific event.
-Causal attribution cannot be asserted as a substrate-layer commitment
+Causal attribution cannot be asserted
+as a substrate-layer commitment
 without committing to a particular counterfactual or mechanistic logic:
-as soon as an ontology asserts $A \to B$ as a causal commitment,
-it excludes any framework that treats $A$ and $B$ as merely correlated
-or as having a common cause $Z$.
+as soon as a substrate asserts $\mathsf{Caused}(e_1,e_2)$,
+it excludes any framework that treats $e_1$ and $e_2$ as merely correlated
+or as effects of a common cause $z$.
 
 To be clear, \textit{pre-causal does not mean acausal}.
 The substrate does not deny that causation exists
@@ -272,7 +273,7 @@ \subsection{Reification and Contextual Modeling}
 This is precisely the externalization the theorem requires.
 
 Reification preserves interpretive non-commitment
-only if the ontology refrains from simultaneously
+only if the substrate refrains from simultaneously
 asserting the reified content as a substrate-layer truth.
 If causal or normative relations are both asserted
 as substrate-layer facts and reified as claims,
@@ -304,7 +305,7 @@ \subsection{The Ontological Neutrality Theorem}
 
 \begin{theorem}[Ontological Neutrality Theorem]
   \label{thm:neutrality}
-  Let $\mathcal{S}$ be an ontology intended to function
+  Let $\mathcal{S}$ be a substrate ontology intended to function
   as a neutral substrate across diverse interpretive frameworks,
   and let $\mathbb{F}$ be the set of admissible interpretive frameworks.
   Then $\mathcal{S}$ satisfies the requirements of neutrality

sections/04_formal_dev.tex

@@ -4,7 +4,10 @@ \section*{Appendix A. Glossary of Terms}
 \addcontentsline{toc}{section}{Appendix A. Glossary of Terms}
 
 This appendix defines key terms used throughout the paper,
-organized into three groups.
+organized into three conceptual groups:
+core ontology concepts,
+neutrality and interpretation,
+and causal and normative concepts.
 
 \input{glossary/core_ontology_concepts}
 \input{glossary/neutrality_interpretation}