Sense Boundaries

Where one domain of meaning ends and another begins

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A6Written accountThe formal treatment of context boundaries and translation between them.

This interlude introduces the sense boundary (A6): a context-indexed equivalence that partitions uses of a term into sense classes. The pomegranate — fruit, color, motif — is the canonical worked example. A6 is a proto-operator: it names what must be represented but defers the transport machinery to A10, A16, and A28. Volume I, Chapter 5 (The Empire of Tables), follows different inquiries into a depicted pomegranate; here the question is how a declared sense can support another operation.

The Word That Splits

Consider the word pomegranate.

In one sentence, it names a fruit—spherical, leathery-skinned, filled with ruby-red arils. In another sentence, it names a color—deep red, between crimson and burgundy. In a third, it names a decorative motif—a stylized image of the fruit.

Whatever their historical path (metaphor, metonymy, convention), these senses now behave as distinct referents that share a spelling. A pomegranate print dress does not contain fruit. A pomegranate accent wall is not edible. The word has split, and the splits have become stable enough that each can anchor an entire design vocabulary.

Now consider what a system must do when it encounters pomegranate in a product description:

"This silk scarf features a pomegranate motif in deep burgundy."

The sentence distinguishes its motif from its color. A query for red objects can use one part; a query for fruit imagery needs the other. Retrieving the word does not decide which inquiry the description supports.

A string-matching system will retrieve documents containing the word pomegranate. Some will be about fruit. Some will be about color. Some will be about decorative patterns. The token match is correct. Unless another operation interprets the passage, it supplies no classification of the active sense.

A schema-governed system might have separate predicates: fruit:pomegranate, color:pomegranate, motif:pomegranate. If the predicate exists, the query is typed. But this presupposes that the predicate inventory exists and is maintained—that someone has already done the governance work of recognizing "pomegranate motif" as a category worth certifying. An extensible catalog can admit a new definition and supporting evidence. Until that work is adequate for the receiving contract, the stored description alone does not certify its interpretation.

This is not a failure of intelligence. It is a failure of structure. The system lacks the object that would let it say: in this context, "pomegranate" denotes a motif, not a fruit. That object is a sense boundary.

Disambiguation Is Boundary-Drawing

Word sense disambiguation is sometimes treated as a classification problem: given a word in context, assign it to one of several pre-defined senses. The classifier learns from examples; at inference time, it outputs a label.

This framing is incomplete. A label tells you which sense was chosen; it does not tell you how that choice should behave when reused. If you classify "pomegranate" as motif in one context, and later encounter a new context where the same evidence applies, does the classification transfer? What if the new context adds constraints that make motif inconsistent?

The richer concept is boundary-drawing. To disambiguate is not merely to label; it is to draw a boundary that separates uses into equivalence classes. Within the boundary, all instances are "the same sense." Across the boundary, they are not.

A source can use one word in several senses without inconsistency. What needs stability is the interpretation claimed for the particular use or declared class of uses. A textile catalog may describe a fruit motif and a color on the same page. If its records enter another catalog, preserving those distinctions lets the recipient compare colors, find images of fruit, or investigate an unresolved description without demanding that the source choose one meaning for the word everywhere.

Transport is where the machinery becomes non-trivial. A maintained labeling system can already track revisions and context. The additional question here is what an earlier assignment warrants when another operation uses it.

A catalog’s sense inventory also records choices about its intended inquiries. A distinction maintained for finding fruit imagery may be too coarse for studying a decorative tradition. Keeping the earlier label does not prevent a later inquiry from distinguishing more; it does require the later user to say what the new distinction adds.

A6: Sense Boundary (Proto-Operator)

We introduce a minimal formal object to capture the intuition.

Sense Boundary (Proto-Operator) — A6

Let $U$ be a context (a view with signature, constraints, and provenance regime).

Define a context-indexed equivalence $\sim_U$ on uses $(w, c)$ , where $w$ is a wordform and $c$ is the local constraint context:

(w, c) \sim_U (w', c') \quad \text{iff} \quad (w, c) \text{ and } (w', c') \text{ denote the same sense in context } U

Once the sense criterion is supplied and is an equivalence relation, it partitions uses into sense classes within $U$ . The definition does not discover the criterion. A use may be intentionally ambiguous or allusive; preserving that fact can be more accurate than forcing a unique sense assignment.

At this stage, we specify that sense boundaries exist, must persist, and are scoped to contexts. Transport obligations—how boundaries persist across context changes—are formalized in A10/A16/A28.

Remark(Why 'Proto-Operator'?)

A6 is not yet a fully operational definition. It says what a sense boundary is (a partition of uses) but not how to compute one or how to transport one when contexts merge. The formal machinery for transport requires the equivalence witnesses of Part II and the gluing structure of Part III. Here we only demand that the system represent the distinction and its scope; the criterion for when multiple scoped distinctions can be composed is deferred.

Remark(Connection to A5)

A6 is the smallest place where A5's coherence contract bites. The first disagreement is not a contradiction of facts, but a collision of senses. Two views that draw different boundaries for "pomegranate" are not logically inconsistent—they are locally valid but globally unreconciled. This is exactly the situation A5 clause 4 (conflict handling) is designed to address: the system must produce a witnessed reconciliation artifact, not silently collapse.

Toy Model: Three Sentences

Example(Sense Flip)

Consider three sentences:

"The pomegranate tree bore fruit in October."
"The fabric featured a pomegranate motif in gold thread."
"She chose pomegranate for the accent wall."

Sentence 1 uses pomegranate to identify the fruit-bearing tree. The biological use differs from the decorative and color uses below.

In sentence 2, pomegranate denotes a decorative motif.

In sentence 3, pomegranate denotes a color.

Each sentence provides constraints that determine which sense is active:

tree, bore, fruit → biological entity
fabric, motif, thread → decorative pattern
accent wall + color-selection context → color

A system with sense boundaries would recognize these as three distinct equivalence classes. A query for "pomegranate fruit" would not retrieve the fabric or the wall. A query for "pomegranate motif" would retrieve the fabric but not the tree or the wall.

The critical observation: the majority sense alone does not settle these uses. A rule that assigns the fruit sense to every occurrence would misclassify the stated motif and color examples. No claim about their relative frequency is needed to establish that failure.

What a Boundary Artifact Might Look Like

To make the "witnessed object" discipline concrete, consider the shape of a boundary assertion. In the easy case, scopes are disjoint:

Boundary Assertion
  term:       "pomegranate"
  sense:      motif
  scope:      this identified use in TextileCatalogB, interpreted as imagery
  evidence:   quoted use and contextual assessment; co-occurrence is supporting evidence
  regime:     OWA (other senses may exist in other scopes)
  
Competing Boundary
  term:       "pomegranate"
  sense:      fruit
  scope:      this identified use in GroceryCatalogA, interpreted as produce
  
Reconciliation
  status:     scoped coexistence (no collapse required)
  witness:    the identified uses have separate declared interpretations; no substitution requested

This is not yet formalized—the witness structure, the scope algebra, the reconciliation logic are all deferred. But the shape is visible: a boundary is not a label floating in isolation; it is a claim with scope, evidence, and a declared relationship to competing claims.

The Fashion Catalog

Return to the running example.

A product description reads:

"Silk midi dress with pomegranate print. Burgundy on cream ground."

The catalog has a print_type field with values like floral, geometric, abstract, animal. Where does pomegranate belong?

If pomegranate print means a representation of the fruit, it might be floral (botanicals) or representational.
If pomegranate print means the stylized motif (in this hypothetical catalog), it might be geometric or traditional.
If the cataloger is unfamiliar with the pomegranate motif tradition, they might default to floral because the fruit is plant-based.

The decision is a sense boundary. Once drawn, it determines:

Which queries retrieve this dress
Which recommendations it appears alongside
Which analytics categories it contributes to

If the boundary is drawn incorrectly—or inconsistently across the catalog—downstream systems inherit the error. A shopper searching for "traditional motifs" will not find the dress. A merchandiser analyzing "geometric prints" will see distorted counts.

This is T6 (Predicate Invention) in miniature: the system needs a predicate pomegranate_motif that the schema does not yet contain. It is also T2 (Reference) in miniature: the same word refers to different things, and the system must track which thing is meant. And it is T7 (Contextual Equivalence) in miniature: whether "pomegranate" equals "pomegranate" depends on the context of comparison.

What Sense Boundaries Require

A6 is a statement of existence: sense boundaries exist and are scoped to contexts. But existence is cheap. The hard requirement is stability under transport.

Consider what happens when two catalogs merge:

Catalog A has drawn a boundary: pomegranate = fruit.
Catalog B has drawn a boundary: pomegranate = motif.

When the catalogs merge, the repeated word need not identify overlapping referents or conflicting claims. The receiving query must decide which uses to relate. The options are:

Collapse: Treat all pomegranates as the same sense (loses information).
Fork: Retain separate predicates, pomegranate_A and pomegranate_B, with mappings where a further inquiry supports them.
Reconcile: Recognize that the boundaries are contextually scoped and can coexist if the scope is made explicit and the reconciliation is witnessed.

Separate predicates and explicit mappings can also preserve information. A6 does not supply those mappings or decide which distinctions a receiving inquiry can safely combine. The later account provides:

Witnessed equivalence (A10, Part II): an explicit record that two terms are "the same" in a given context, with justification.
Transport maps (A16, Part III): rules for how equivalences change when contexts change.
Reconciliation artifacts (A5, clause 4): first-class objects that record when overlap agreement fails and how the disagreement is resolved.

A6 names the object. The machinery that makes it operational is constructed in Parts II and III.

What the Next Use Asks

A shopper looking for a fruit motif need not ask the catalog to reconcile its color names. A color comparison need not settle the motif’s history. The same description can support both inquiries while leaving other questions open. Preserving it under separate, mapped predicates is a resource for those uses, not a refusal to integrate.

A6 states the boundary a receiving operation must represent; it does not discover that boundary or certify a translation. The later reference, invention and contextual-equivalence examples return to these obligations. Their difficulty begins where a useful earlier distinction is asked to support a different operation.

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