sorts if they are properly to be categorized as instantiating the different universals or types (we use these terms interchangeably in what follows) recognized by BFO. To specify these conditions we will utilize a semi-formalized English that has approximately the expressivity of first-order logic (FOL) with identity. We use ‘category’ to refer to those universals at the most general and domain-neutral level. BFO treats only of categories in this sense. A category is a formal (= domain-neutral) universal, as contrasted with the material (domain-specific) universals represented in one or other domain ontology. BFO:fiat object part is a category in this sense; not however organism or weapon, or mortgage contract. Spatial, temporal and spatiotemporal region terms are counted as representing formal universals in this sense, since they apply in all domains. In the formulations we will use: ‘b’, ‘c’, ‘d’, etc., for instances (spatio-temporal particulars); ‘t,’ ‘t’, etc., for temporal regions (instants or intervals) ‘r,’ ‘r’, ‘s,’ ‘s’, etc., for spatial and spatiotemporal regions, We use ‘A’, ‘B’, ‘C’, ‘P’, etc. for universals. Note that ‘A’, ‘B’, ‘C’, ‘P’, etc. are common (names for universals), rather than predicates. We use ‘instance_of’, ‘has_participant’ and similar bold-face expressions to express relations involving instances, and ‘part_of’ and similar italicized expressions to express relations exclusively involving universals. We also use italics to mark out BFO terms. Figure 1: The BFO 2.0 is_a Hierarchy How to read this document Use of boldface indicates a label for an instance-level relation. Use of italics indicates a BFO term (or a term from a BFO-conformant ontology). All such terms are singular common nouns or noun phrases. All BFO terms represent some formal (= domain-neutral) universal. This document is intended both as a specification and a user’s guide to BFO 2.0. Those parts of the document which belong to the specification are indicated by the special formatting, as follows: trial,
Instance-type relations John’s heart instantiates human heart. In this document we discuss relations in all three groups. Note that relations of none of sorts are first-class entities (to see why not, see the discussion of the Bradley regress in [20]). However, there are first-class entities, such as relational qualities and relational processes (see below), which are relational in the sense that they link multiple relata. First-class entities are entities which have counterparts both at the level of instances (John’s act of kissing Mary yesterday) and at the level of universals (kiss, act, person). Primitive and defined terms We use terms (such as ‘BFO:object’ or ‘Patrick Hayes’) to refer to entities, and relational expressions (such as ‘has_participant’) to assert that relations obtain between such entities. note(ontology)[For both terms and relational expressions in BFO, we distinguish between primitive and defined. ‘Entity’ is an example of one such primitive term. Primitive terms in a highest-level ontology such as BFO are terms that are so basic to our understanding of reality that there is no way of defining them in a non-circular fashion. For these, therefore, we can provide only elucidations, supplemented by examples and by axioms. ] a(entity)[Elucidation: An entity is anything that exists or has existed or will [001-001]] as(entity)[Examples: Julius Caesar\, the Second World War\, your body mass index\, Verdi’s Requiem ] Definitions We distinguish between terms and relational expressions. Definitions of terms are required to be always of the form: A = Def. B which Ds
a(continuant_part_of)[Domain: continuant] a(continuant_part_of)[Range: continuant The range for ‘t’ (as in all cases throughout this document unless otherwise specified) is: temporal region.] as(continuant_part_of)[Examples: Mary’s arm continuant_part_of Mary in the time of her life prior to her operation\; the Northern hemisphere of the planet Earth is a part of the planet Earth at all times at which the planet Earth exists. ] continuant_part_of is antisymmetric. [120-001] ] continuant_part_of is transitive. [110-001] ] continuant_part_of satisfies weak supplementation. [121-001] (What this means is that: If x continuant_part_of y at t & not x = y, then there is some z such that (z continuant_part_of y at t & there is no w(w continuant_part_of z & w continuant_part_of x at t)), Here z is, as it were, some remainder that results when x is imagined to have been removed from y.)] a(continuant-part-of)[Axiom: continuant_part_of satisfies unique product. [122-001] ] a(continuant_part_of)[Theorem: continuant_part_of is reflexive (every continuant entity is a continuant_part_of itself). [111-002] ] The occurrent_part_of relation a(occurrent_part_of)[Elucidation: b occurrent_part_of c =Def. b is a part of c & b and c are occurrents. [003-002]] a(occurrent_part_of)[Domain: occurrent] a(occurrent_part_of)[Range: occurrent]
Axiom: If b is an occurrent and c is a continuant and b s-depends_on c at t, then c exists at some time during the temporal region spanned by b. [129-001] Axiom: If b is an occurrent and c is an occurrent and b s-depends_on c at t, then c exists at t. [130-001]] An s-dependent continuant entity cannot migrate from one independent continuant bearer to another. The entities that s-depends_on something include specifically and generically dependent continuants, which s-depends_on in every case on one or more independent continuants which are their bearers, and which may in addition stand in relations among themselves; occurrents, which s-depends_on in every case on one or more independent continuants which participate in them. Occurrents may in addition stand in one-sided and reciprocal s-depends_on relations to other entities, including qualities, dispositions and occurrents (see [46, chapter 8; 20, 22] and the discussion of process profiles, below). Types of s-dependence Examples of one-sided s-dependence of a dependent continuant on an independent continuant: example(s-depends on)[one-sided s-dependence of a dependent continuant on an independent continuant: an instance of headache s-depends_on some head] example(s-depends on)[one-sided s-dependence of a dependent continuant on an independent continuant: an instance of temperature s-depends_on some organism] Example of s-dependence of a process on something:
a(member_part_of)[Definition: b member_part_of c at t =Def. b is an object & there is at t a mutually and pairwise disjoint partition of c into objects x1, …, xn (for some n > 1) with b = xi for some 1 ≤ i ≤ n. [026-004] a(member_part_of)[Domain: object] a(member_part_of)[Range: object aggregate] a(member_part_of)[Theorem: if b member_part_of c at t then b continuant_part_of c at t. [104-001] ] as(member_part_of)[Examples: each tree in a forest is a member_part of the forest\; each in a chess set is a member part of the chess set; each Beatle in the collection called The Beatles is a member part of The Beatles. ] a(object aggregate)[Elucidation: b is an object aggregate means: b is a material entity consisting exactly of a plurality of objects as member_parts at all times at which b exists. [025-004]] Thus aggregate)[if b is an object aggregate, then if b exists at t, there are objects o1, …,on at t such that: for all x (x continuant_part_of b at t iff x overlaps some oi at t) ] Here ‘overlaps’ is used in the standard way to mean: ‘shares a common part with’. definition(object-aggregate)[An entity b is an object aggregate at t if and only if there is a mutually exhaustive and pairwise disjoint partition of b into objects at t [63]. ] as(object aggregate)[Examples: a symphony orchestra\, the aggregate of bearings in a constant velocity axle joint\, the nitrogen atoms in the atmosphere\, a collection of cells in a blood biobank. ] The member parts of an object aggregate are the proximal parts of the aggregate – those parts that determine the aggregate as an aggregate (sometimes referred to as ‘grains’ or ‘granular parts’ [74]).
as(independent For any independent continuant b and any time t there is some spatial region r such that b is located_in r at t. [134-001] Axiom: For any independent continuant b and any time t, if b is located_in r at t then there is some region r that is continuant_part_of r and such that b is occupies_spatial_region r at t. [135-001]] For all independent continuants a and b, parthood implies location. at(continuant_part_of)[Axiom: if b continuant_part_of c at t and b is an independent continuant, then b is located_in c at t. [047-002] ] and boundaries, too, may stand in the located_in relation, as for example when we say that 5th Avenue is located in New York, or that a portion of the Franco-German boundary is located in the Rhein valley. Problem cases for the located_in relation As pointed out in [52] there are problem cases for this account, in that, for example an insect located near the stem of a wine glass would be counted as located_in the wine glass; similarly crumbs placed in the hole of a donut would be counted as located_in the donut. Briefly, users of located_in should use an intuitive test to the effect that: if b is not in the interior of c but is rather in some hole or cavity attached to c’s outer boundary, then b located_in c will obtain only if this hole is a fillable hole in the sense defined by Casati and Varzi [52]. The cup-shaped hole in the wine glass is fillable in this sense; not however the concave spaces around the stem. Chaining rules a(located_in)[Axiom: for all independent continuants b, c, and d: if b continuant_part_of c at t & c located_in d at t, then b located_in d at t. [048-001]] for all independent continuants b, c, and d: if b located_in c at t & c continuant_part_of d at t, then b located_in d at t. [049-001]]
Since temporal regions are temporal parts (though not temporal proper parts) of themselves, this means, in particular, that zero-dimensional temporal regions (temporal instants) are also occurrents. Subtypes of occurrent are: process process profile (experimental) history process boundary temporal region zero-dimensional temporal region one-dimensional temporal region spatiotemporal region Projection relations a(projects_onto)[Elucidation: To say that each spatiotemporal region s temporally_projects_onto some temporal region t is to say that t is the temporal extension of s. [080-003]] a(projects_onto)[Elucidation: To say that spatiotemporal region s spatially_projects_onto spatial region r at t is to say that r is the spatial extent of s at t. [081-003]] Every spatiotemporal region projects onto some temporal region, and at every time instant within its extent onto some spatial region (all of this relative to some frame).
The occupies and occurs_in relations a(occupies_spatiotemporal_region)[Elucidation: p occupies_spatiotemporal_region s. This is a primitive relation between an occurrent p and the spatiotemporal region s which is its spatiotemporal extent. [082-003] Domain: occurrent Range: spatiotemporal region] a(occupies_temporal_region)[Elucidation: p occupies_temporal_region t. This is a primitive relation between an occurrent p and the temporal region t upon which the spatiotemporal region p occupies_spatiotemporal_region projects. [132-001] Domain: occurrent temporal region Axiom: Every temporal region occupies_temporal_region itself. [137-001] ] note(occupies_spatiotemporal_region)[The occupies_spatiotemporal_region and occupies_temporal_region relations are the counterpart, on the occurrent side, of the relation occupies_spatial_region.] DEFINITION: b occurs_in c iffb is a process and c is a material entity or immaterial entity& exists a spatiotemporal region r and b occupies_spatiotemporal_region r& for all t, if b exists_at t then c exists_at t & there exist spatial regions s and s' where
a(has_participant)[Domain: process] at(has_participant)[Range: independent continuant that is not a spatial region, specifically dependent continuant, generically dependent continuant] if b has_participant c at t then b is an occurrent. [087-001] ] a(has_participant)[Axiom: if b has_participant c at t then c is a continuant. [088-001] ] a(has_participant)[Axiom: if b has_participant c at t then c exists at t. [089-001] ] if b has_participant c at t & c is a specifically dependent continuant, then there is some independent continuant that is not a spatial region d, c s-depends_on d at t & b s-depends_on d at t. [090-003] ] a(has_participant)[Axiom: if b has_participant c at t & c is a generically dependent continuant, then there is some independent continuant that is not a spatial region d, and which is such that c g-depends on d at t & b s-depends_on d at t. [091-003] ] Thus both specifically and generically dependent entities participate in processes – for example when a file is copied from one hard to another – but only via the bearers of their specifically dependent concretizations. note(spatial region,has_participant)[Spatial regions do not participate in processes.] On the participation of qualities in processes see the treatment of qualitative change, below. Qualities and processes as s-dependent entities The ontological square BFO generalizes Zemach’s idea of a continuant entity by allowing not only things (such as pencils and people) as continuants, but also entities that are dependent on things, such as qualities, and dispositions. BFO thereby draws not merely on Aristotle’s distinction between universals and particulars, but also on his division of substances and accidents, which reappears in BFO as the opposition between independent and dependent continuants.
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