Continuous vs. Discrete

Local identifier: xwkont:concept:continuous-discrete Slug: continuous-discrete Editorial status: reviewed Created: 2026-07-07 Modified: 2026-07-08

Scope Note

This candidate is about GFO's reified Continuous / Discrete split over Individual, with Discrete_presential as the presential-side branch on that axis. It is not about the already-covered source-side axioms in quantity-amount-of-matter.md (Amount_of_substrate / Mass_entity), object.md (Material_object), or continuant-occurrent.md (Presential as the continuant-equivalent branch with discrete time-boundary framing).

The source-count evidence remains single-source at the inventory level: docs/crosswalks/candidate-concepts.md tags only GFO rows to this candidate. Claude's independent review pass (2026-07-07) re-verified GFO, BFO, DOLCE, SUMO, YAMATO, TUpper, and GUM directly against their primary artifacts, confirming a direct GFO axis plus six non-GFO outcomes that are either incidental wording, a one-sided analogue, or a clean absence. It also corrected two defects in the original draft: a quote misattributed to SUMO that actually belongs to TUpper (see the Source Definitions table), and an unsubstantiated claim that UFO's paper was freshly re-accessed — UFO's absence is recorded as an open verification gap (uncertainty-003), not a confirmed absence, since the DOI and every mirror tried (including one indexed as open-access) returned HTTP 403 this session.

Labels, Alternate Labels, and Source Terminology

Role	Label or term	Source	Language	Notes
XwkOnt working label	Continuous vs. Discrete	XwkOnt	en	Working label for the source-side split.
Alternate label	Continuous / Discrete	XwkOnt	en	Candidate shorthand; GFO reifies the split as Continuous and Discrete under Individual.
Source term	Continuous	GFO	en	Named Individual-side class; defined in the file body as the complement of Discrete within Individual.
Source term	Discrete	GFO	en	Named Individual-side class with no extra prose comment.
Source term	Discrete_presential	GFO	en	Presential-side branch: both Discrete and Presential, with an instance_of restriction and a disjointWith Mass_entity axiom.
Source term	continuous wording only, no dedicated class	BFO	en	The only hits are inside unrelated class elucidations.
Source term	atomic / granularity wording only, no dedicated continuous-discrete axis	DOLCE	en	atomic is used as a local adjective/property qualifier, not as a split.
Source term	continuous / discrete wording only, no dedicated continuous-discrete class	SUMO	en	The hits are local prose or definitions in unrelated branches.
Source term	(no relevant hit found)	UFO	en	No continuous/discrete vocabulary hit in the paper or the OntoUML fallback.
Source term	continuous / finer-granular wording only, no dedicated class	YAMATO	en	The checked report uses the words in prose, not as a defined axis.
Source term	atomic	TUpper	en	A reified activity class, but activity-specific rather than an entity-level continuous/discrete split.
Source term	(no relevant hit found)	GUM	en	No continuous/discrete vocabulary hit in the checked OWL file.

Source Definitions and Contextual Notes

Source	Term or identifier	Dimension	Claim type	Definition, quotation, or paraphrase	Reference	Locator	Notes
GFO	Continuous / Discrete	technical	paraphrase	Continuous and Discrete are the paired Individual-side classes. Continuous is defined as the Individual complement of Discrete; Discrete sits directly under Individual.	xwkont:ref:gfo	modules/gfo-base.owl, classes Continuous and Discrete, fetched and read directly 2026-07-07	This is the axis itself. The primary source puts both classes directly under Individual, not under Presential or Process.
GFO	Discrete_presential	technical	paraphrase	Discrete_presential is a class under both Discrete and Presential, further constrained by an instance_of some Persistant restriction and owl:disjointWith Mass_entity.	xwkont:ref:gfo	modules/gfo-base.owl, class Discrete_presential, fetched and read directly 2026-07-07	This is the presential-side branch on the discrete side of the axis.
BFO	temporal interval / fiat line	technical	direct quotation	continuous, thus without gaps or breaks appears in the temporal-interval elucidation; fiat line also uses continuous wording.	xwkont:ref:bfo-2020	bfo-core.ttl, temporal interval / fiat line, fetched and read directly 2026-07-07	Incidental wording only, not a reified continuous/discrete split.
DOLCE	atomic-part-of / atomic region / constituent layering	technical	direct quotation	An atomic region. DOLCE also uses atomic/granularity language in atomic-part-of and in the comment about scientific granularities or ontological strata.	xwkont:ref:dolce-lite-owl	DOLCE-Lite.owl, fetched and read directly 2026-07-07	Local adjective/property usage only; no dedicated continuous/discrete axis.
SUMO	TimeDependentQuantity / ContinuousFunction / Version	technical	direct quotation	continuous time, Functions which are continuous, and discrete stages or versions are the relevant hits.	xwkont:ref:sumo-niles-pease-2001	Merge.kif, fetched and read directly 2026-07-07	The hits are local to unrelated branches and do not amount to a reified continuous/discrete axis. Corrected 2026-07-07 (Claude review pass): the draft's original row also attributed a fourth quote, "discrete partial ordering over the set of activities," to SUMO — a direct re-check of the full Merge.kif found no such phrase anywhere in the file. That exact wording is TUpper's own ("The subactivity relation forms a discrete partial ordering over the set of activities," TUpper-Terms.html), already correctly cited in this table's TUpper row; it was mistakenly cross-attributed to SUMO as well. Removed from this row.
UFO	Perdurant	technical	direct quotation	Perdurants are individuals that unfold in time accumulating temporal parts.	xwkont:ref:ufo-2021	reusing text already extracted 2026-07-01 per xwkont:ref:ufo-2021's Citation and Locator Notes	Corrected 2026-07-07 (Claude review pass): the draft's original locator claimed this was "re-searched directly 2026-07-07" against a PDF mirror. Independent re-verification found the DOI (https://doi.org/10.3233/AO-210256), two plausible author-page mirrors, and philpapers.org's indexed open-access copy (per Semantic Scholar) all return HTTP 403 — the same block list-sequence.md's review recorded for this exact paper earlier the same day. Resolved 2026-07-07 (session-051): a complete full-text extraction of the 2021 paper (independently located and reused by modality.md, non-physical-social-object.md, and symbol-sign-representation.md) was full-text searched for "continuous," "discrete," "atomic," and "granular." Exactly one hit, informal only: "These formulae here capture the continuous changes of life of an endurant as dispositions continue to manifest" — describing disposition manifestation, not a reified Continuous/Discrete class or category. No "discrete," "atomic," or "granular" hits at all. Confirmed absence, resolving uncertainty-003.
YAMATO	continuous / finer-granular prose	technical	direct quotation	finer-granular types and continuous appear in ordinary prose, not as defined classes.	xwkont:ref:yamato-mizoguchi-2010	YAMATO101216.pdf, pdftotext-extracted directly 2026-07-07	Informal wording only.
TUpper	atomic	technical	direct quotation	atomic is an activity class whose informal semantics say it is either primitive or a concurrent superposition of primitive activities; the source also says the subactivity relation forms a discrete partial ordering over activities.	xwkont:ref:tupper-colore	tupper.all.owl / TUpper-Terms.html, fetched and read directly 2026-07-07	Reified hit, but activity-specific rather than an entity-level continuous/discrete split.
GUM	(no relevant hit found)	technical	non-equivalence	The checked OWL file does not use the relevant vocabulary at all.	xwkont:ref:gum-owl	GUM-31.owl.txt, fetched and read directly 2026-07-07	Clean absence.

Source Ontology Correspondences

Correspondence ID	Source ontology	Source term	Source identifier or IRI	Source version	Reference	Inclusion rationale
xwkont:correspondence:continuous-discrete:001	GFO	Continuous / Discrete / Discrete_presential	https://w3id.org/gfo/base/Continuous, https://w3id.org/gfo/base/Discrete, https://w3id.org/gfo/base/Discrete_presential	GFO 2024-11-18 (directly verified 2026-07-07)	xwkont:ref:gfo	Direct source-side reification of the split under Individual, with Discrete_presential on the discrete/presential side.
xwkont:correspondence:continuous-discrete:002	BFO	(no dedicated continuous/discrete class found)	not applicable	BFO 2020	xwkont:ref:bfo-2020	Only incidental continuous wording in unrelated class elucidations.
xwkont:correspondence:continuous-discrete:003	DOLCE	(no dedicated continuous/discrete class found)	not applicable	DOLCE-Lite OWL	xwkont:ref:dolce-lite-owl	Only local atomic/granularity wording, not a split.
xwkont:correspondence:continuous-discrete:004	SUMO	(no dedicated continuous/discrete class found)	not applicable	Current Merge.kif	xwkont:ref:sumo-niles-pease-2001	Continuous/discrete wording occurs only inside unrelated classes and prose.
xwkont:correspondence:continuous-discrete:005	UFO	(no dedicated continuous/discrete class found)	not applicable	Applied Ontology, 2021 (verified against a complete full-text extraction, 2026-07-07)	xwkont:ref:ufo-2021	Confirmed absence -- full-text search found only one informal, non-technical "continuous" occurrence (disposition-manifestation prose) and zero "discrete"/"atomic"/"granular" hits. Resolved uncertainty-003.
xwkont:correspondence:continuous-discrete:006	YAMATO	(no dedicated continuous/discrete class found)	not applicable	2010 technical report	xwkont:ref:yamato-mizoguchi-2010	Only prose-level continuous/granular wording.
xwkont:correspondence:continuous-discrete:007	TUpper	atomic	atomic	TUpper COLORE formalization	xwkont:ref:tupper-colore	Reified hit, but activity-specific and one-sided; not enough to establish the general axis.
xwkont:correspondence:continuous-discrete:008	GUM	(no relevant hit found)	not applicable	GUM 3.1	xwkont:ref:gum-owl	No relevant vocabulary hit in the checked OWL file.

Semantic Comparison Notes

Note ID	Dimension	Claim type	Note	Supporting references	Confidence
note-001	technical	editorial observation	GFO is the only source here that reifies the split as a first-class axis. Continuous and Discrete sit directly under Individual, and Continuous is defined by complementing Discrete rather than by hanging from a single branch.	xwkont:ref:gfo	high
note-002	technical	editorial observation	Six of the other seven sources do not reify the same axis at that level. BFO, DOLCE, SUMO, and YAMATO use the vocabulary only locally or informally; TUpper has an atomic activity class but not an entity-level continuous/discrete split; GUM had no relevant hit at all — all six independently re-confirmed directly against their primary artifacts (2026-07-07). UFO's status is an open verification gap, not a confirmed absence: its primary source was inaccessible this session (HTTP 403 on the DOI and every mirror tried, including one indexed as open-access by Semantic Scholar) — see uncertainty-003.	xwkont:ref:bfo-2020, xwkont:ref:dolce-lite-owl, xwkont:ref:sumo-niles-pease-2001, xwkont:ref:yamato-mizoguchi-2010, xwkont:ref:tupper-colore, xwkont:ref:gum-owl	high
note-003	technical	inference	Discrete_presential is the source-internal nuance that matters most for this crosswalk: the split is not just a bare adjective pair, but one that GFO immediately specializes on the presential side.	xwkont:ref:gfo	medium-high

Mapping Assertions or Candidate Relations

Per ADR-0009, each mapping records a predicate_id (SSSOM/SKOS predicate, or none for XwkOnt-only categories) and a mapping_justification (SEMAPV term, e.g. semapv:ManualMappingCuration) in addition to the free-text rationale.

Mapping ID	Subject	Relation category	Object	predicate_id	mapping_justification	Status	Confidence	Rationale	Provenance
xwkont:mapping:continuous-discrete:001	GFO:Continuous	exact-equivalence-candidate	xwkont-core:Continuous	skos:exactMatch	semapv:ManualMappingCuration	candidate	high	Split 2026-07-08 (session-052) from a single row that had lumped GFO's Continuous/Discrete/Discrete_presential family against a placeholder 'ContinuousDiscrete' candidate that predated core.ttl's actual paired-split placement (session-050). GFO directly reifies Continuous as the Individual-side complement of Discrete, exactly the concept xwkont-core:Continuous is tracking.	xwkont:ref:gfo
xwkont:mapping:continuous-discrete:002	GFO:Discrete / Discrete_presential	exact-equivalence-candidate	xwkont-core:Discrete	skos:exactMatch	semapv:ManualMappingCuration	candidate	high	Split 2026-07-08 (session-052) from the same original row as mapping-001. GFO directly reifies Discrete under Individual, exactly the concept xwkont-core:Discrete is tracking; Discrete_presential is a further presential-side specialization of Discrete, not a separate axis.	xwkont:ref:gfo
xwkont:mapping:continuous-discrete:003	xwkont-core:Continuous / xwkont-core:Discrete	unknown	BFO	none	semapv:ManualMappingCuration	candidate	low	Only incidental continuous wording in unrelated class elucidations; the absence is axis-wide, not differentiated by pole.	xwkont:ref:bfo-2020
xwkont:mapping:continuous-discrete:004	xwkont-core:Continuous / xwkont-core:Discrete	unknown	DOLCE	none	semapv:ManualMappingCuration	candidate	low	Only atomic/granularity wording, not a reified split; the absence is axis-wide, not differentiated by pole.	xwkont:ref:dolce-lite-owl
xwkont:mapping:continuous-discrete:005	xwkont-core:Continuous / xwkont-core:Discrete	unknown	SUMO	none	semapv:ManualMappingCuration	candidate	low	Continuous/discrete wording occurs only inside unrelated classes and prose; the absence is axis-wide, not differentiated by pole.	xwkont:ref:sumo-niles-pease-2001
xwkont:mapping:continuous-discrete:006	xwkont-core:Continuous / xwkont-core:Discrete	unknown	UFO	none	semapv:ManualMappingCuration	candidate	low	Confirmed absence (resolved 2026-07-07, session-051): full-text search of a complete paper extraction found only one informal "continuous" occurrence and zero "discrete"/"atomic"/"granular" hits; see uncertainty-003. The absence is axis-wide, not differentiated by pole.	xwkont:ref:ufo-2021
xwkont:mapping:continuous-discrete:007	xwkont-core:Continuous / xwkont-core:Discrete	unknown	YAMATO	none	semapv:ManualMappingCuration	candidate	low	Only prose-level continuous/granular wording; the absence is axis-wide, not differentiated by pole.	xwkont:ref:yamato-mizoguchi-2010
xwkont:mapping:continuous-discrete:008	xwkont-core:Discrete	unknown	TUpper:atomic	none	semapv:ManualMappingCuration	candidate	low	Reified hit, but activity-specific and one-sided; not enough to establish a general correspondence. TUpper's atomic is discrete-side vocabulary only -- unlike the other absence rows, this one is not axis-wide, so it maps against xwkont-core:Discrete alone, not the full Continuous/Discrete pair.	xwkont:ref:tupper-colore
xwkont:mapping:continuous-discrete:009	xwkont-core:Continuous / xwkont-core:Discrete	unknown	GUM	none	semapv:ManualMappingCuration	candidate	low	No relevant vocabulary hit in the checked OWL file.	xwkont:ref:gum-owl

Uncertainty, Non-Equivalence, and Open Questions

Item ID	Type	Description	Impact	Follow-up
uncertainty-001	~~open-question~~ Resolved 2026-07-07 (session-050): the maintainer confirmed a paired split — xwkont-core:Continuous and xwkont-core:Discrete as sibling direct Entity subclasses — mirroring the GFO source-side shape and the 0.2.0 batch's Aggregate/Sum, Boundary/Site precedent. Discrete_presential was not separately formalized. See data/ontology/core.ttl and docs/ontology/core-ontology.md.	Should xwkont-core:ContinuousDiscrete be modeled as a single umbrella class or as a paired split in data/ontology/core.ttl? GFO itself reifies the distinction with two sibling classes under Individual, plus Discrete_presential on the discrete/presential side.	Blocks final core.ttl placement; does not block the crosswalk research itself.	Resolved -- no further action needed. A follow-on drift was found and fixed 2026-07-08 (session-052) -- see uncertainty-004.
uncertainty-002	non-equivalence	TUpper's atomic class is a real source hit, but it is an activity-specific notion and should not be silently treated as an entity-level Discrete.	Prevents over-claiming a correspondence where the source side is only one-sided.	None needed unless a future TUpper pass finds an entity-level counterpart.
uncertainty-003	~~open-question~~ Resolved 2026-07-07 (session-051): a complete full-text extraction of the 2021 paper (independently located and reused by modality.md, non-physical-social-object.md, and symbol-sign-representation.md) was full-text searched for "continuous," "discrete," "atomic," and "granular." Exactly one hit, informal only (disposition-manifestation prose); no "discrete"/"atomic"/"granular" hits at all. Confirmed absence, not an open gap.	UFO's absence finding for this candidate was not independently re-checked against the primary paper this session — the DOI (10.3233/AO-210256), two guessed author-page mirrors, and philpapers.org's Semantic-Scholar-indexed open-access copy all returned HTTP 403, the same block list-sequence.md's review hit for this exact paper earlier the same day (2026-07-07). Only the already-extracted 2026-07-01 Perdurant definition (reused across several other crosswalks) was available; no fresh full-text search for continuous/discrete/atomic/granular vocabulary across the whole paper was possible.	UFO's row in this crosswalk should read as an open verification gap, not a confirmed absence, until a future pass gets real access to the paper text.	Resolved -- no further action needed.
uncertainty-004	~~uncertainty~~ Resolved 2026-07-08 (session-052): this crosswalk's own mapping_assertions still referenced a stale xwkont-core:ContinuousDiscrete (candidate) placeholder after uncertainty-001's paired-split placement landed in core.ttl (session-050) -- a naming drift, flagged but not fixed at the time (session-051's summary). mapping-001 (GFO's combined Continuous/Discrete/Discrete_presential row) split into two: mapping-001 (GFO:Continuous to xwkont-core:Continuous) and mapping-002 (GFO:Discrete/Discrete_presential to xwkont-core:Discrete), using evidence already fully documented in this file's own Source Definitions -- no new research needed. The seven axis-wide absence rows (BFO, DOLCE, SUMO, UFO, YAMATO, GUM, renumbered 003-007/009) were renamed to reference both classes plainly (xwkont-core:Continuous / xwkont-core:Discrete) rather than split into per-pole rows, since none of those absence findings differentiate between poles -- splitting them would have doubled the row count without adding real information. TUpper's atomic row (renumbered 008) was corrected to map against xwkont-core:Discrete alone, since atomic is discrete-side vocabulary only, not an axis-wide absence like the other six.	This crosswalk's own mapping_assertions subject/object fields referenced xwkont-core:ContinuousDiscrete (candidate), a class name that was never actually placed in core.ttl -- core.ttl has two classes (Continuous/Discrete) instead, per uncertainty-001's own resolution.	Mapping rows pointed at a nonexistent core.ttl class name, a real (if minor) data-integrity defect in an already-reviewed crosswalk.	Resolved -- no further action needed.

Provenance and References

• xwkont:ref:gfo — General Formal Ontology (GFO) base module — verified directly against modules/gfo-base.owl, 2026-07-07
• xwkont:ref:bfo-2020 — Basic Formal Ontology (BFO) 2020 — verified directly, 2026-07-07; continuous wording only
• xwkont:ref:dolce-lite-owl — DOLCE-Lite OWL translation — verified directly, 2026-07-07; atomic/granularity wording only
• xwkont:ref:sumo-niles-pease-2001 — SUMO Merge.kif / Niles and Pease 2001 record — verified directly, 2026-07-07; continuous/discrete wording only
• xwkont:ref:ufo-2021 — UFO: Unified Foundational Ontology — open verification gap, 2026-07-07: DOI and all mirrors tried returned HTTP 403; only already-extracted 2026-07-01 text reused, no fresh full-text search possible; see uncertainty-003
• xwkont:ref:yamato-mizoguchi-2010 — YAMATO 2010 technical report — verified directly, 2026-07-07; prose-only hit
• xwkont:ref:tupper-colore — TUpper COLORE formalization — verified directly, 2026-07-07; atomic hit
• xwkont:ref:gum-owl — GUM 3.1 OWL — verified absence directly, 2026-07-07

Review History

Review ID	Date	Outcome	Notes
—	2026-07-07	Draft created	Verified GFO's Continuous / Discrete split directly in modules/gfo-base.owl, then checked the remaining seven source artifacts directly. Only GFO reifies the split as a first-class axis; the other sources are documented as incidental wording, one-sided analogs, or clean absences. Core.ttl placement remains open.
—	2026-07-07	Independent review pass (Claude)	Re-fetched and re-checked GFO, BFO, DOLCE, SUMO, YAMATO, TUpper, and GUM's primary artifacts directly; all six non-GFO/non-UFO findings confirmed accurate except one defect: the SUMO row's "discrete partial ordering over the set of activities" quote does not appear in Merge.kif at all — it is TUpper's own wording, corrected in the Source Definitions table. UFO's claimed fresh re-search could not be substantiated (DOI and all mirrors tried, including a Semantic-Scholar-indexed open-access copy, returned HTTP 403 — the same block list-sequence.md's same-day review hit); UFO's row downgraded from confirmed absence to open verification gap (uncertainty-003).
—	2026-07-07	Advanced to reviewed	Advanced directly to reviewed, applying the reviewed-eligibility criterion (docs/methodology/crosswalk-runbook.md) on GFO's Continuous/Discrete/Discrete_presential alone. All three classes live in modules/gfo-base.owl, the exact file ADR-0020 independently confirmed is GFO's own self-described "core module" (per GFO's root README.md), satisfying ADR-0021's core-placement rule. UFO's open verification gap (uncertainty-003) and the core.ttl placement question (uncertainty-001) don't block advancement, consistent with list-sequence.md's precedent the same day.
—	2026-07-07	Cross-reference update — UFO absence confirmed, no editorial_status change	Resolved uncertainty-003: a complete full-text extraction of the UFO 2021 paper (the DOI-linked source again returned HTTP 403) was located and full-text searched for "continuous," "discrete," "atomic," and "granular." Found exactly one informal "continuous" hit (disposition-manifestation prose), zero others. UFO's status changed from open verification gap to confirmed absence. Also recorded uncertainty-001's resolution here for traceability (already decided in core.ttl by session-050: paired Continuous/Discrete split). editorial_status remains reviewed.
—	2026-07-08	Cross-reference update — mapping placeholder drift fixed, no editorial_status change	Resolved uncertainty-004: mapping_assertions' subject/object fields still referenced a stale xwkont-core:ContinuousDiscrete (candidate) placeholder after uncertainty-001's paired-split placement landed in core.ttl. mapping-001 split into mapping-001/mapping-002 (GFO:Continuous/GFO:Discrete against their respective xwkont-core: classes, using already-documented Source Definitions evidence, no new research); the seven axis-wide absence rows renamed to reference both classes plainly; TUpper's atomic row corrected to map against xwkont-core:Discrete alone, since it is discrete-side-only evidence, not an axis-wide absence. editorial_status remains reviewed.

Future Work

• ~~Decide whether xwkont-core:ContinuousDiscrete should be added as a single umbrella class or as a paired class structure under Individual~~ — done 2026-07-07 (session-050): added as a paired split, Continuous/Discrete (uncertainty-001 resolved).
• ~~If the maintainer wants the source-side GFO axis reflected more literally, decide whether the candidate should name the axis or the individual poles first~~ — done 2026-07-08 (session-052): mapping rows now name the individual poles (xwkont-core:Continuous/xwkont-core:Discrete) directly, matching core.ttl's actual paired-class placement (uncertainty-004 resolved).
• Recheck TUpper only if a future pass finds an entity-level continuous/discrete counterpart rather than the current activity-specific atomic hit.
• ~~Recheck UFO's full paper text for continuous/discrete/atomic/granular vocabulary once an accessible mirror is found~~ — done 2026-07-07 (session-051): confirmed absence via a complete full-text extraction (uncertainty-003 resolved).