1 The Cornucopia of Formal- Ontological Relations Barry Smith and Pierre Grenon Institute for Formal Ontology and Medical Information Science

2 Realist Perspectivalism There is a multiplicity of ontological perspectives on reality, all equally veridical i.e. transparent to reality

3 Anatomy vs. Pathology

4 The Problem The tumor developed in John’s lung over 25 years

5 The Problem ____ developed in _____ over 25 years process state

6 The Problem The tumor developed in the lung over 25 years substances things objects continuants

7 The Problem The tumor developed in John’s lung over 25 years PARTHOOD NOT DETERMINATE

8 The Problem The tumor developed in the lung over 25 years substances GLUING THESE TOGETHER YIELDS ONTOLOGICAL MONSTERS processes

9 Substances and processes exist in time in different ways substance t i m e process

10 SNAP vs SPAN Endurants vs perdurants Continuants vs occurrents In preparing an inventory of reality we keep track of these two different kinds of entities in two different ways

11 Need for different perspectives Not one ontology, but a multiplicity of complementary ontologies Cf. particle vs. wave ontologies in quantum mechanics

12 Three kinds of SNAP entities 1.Substances 2.Dependents (SPQR… entities) 3.Spatial regions, contexts, niches, environments

13 SPQR… entities States, powers, qualities, roles … functions, dispositions, plans, shapes, status, habitus, liabilities … = dependent SNAP entities

14 SPQR… entities: one-place: your temperature, color, height my knowledge of French the whiteness of this cheese the warmth of this stone the fragility of this glass

15 relational SPQR… entities John Mary love stand in relations of one-sided dependence to a plurality of substances simultaneously specific dependence

16 Generic dependence of relational SPQR… entities legal systems languages (as systems of competences) religions (as systems of beliefs)

17 Three kinds of SNAP entities 1.Substances 2.Dependents (SPQR… entities) 3.Spatial regions, contexts, niches, environments

18 Three kinds of SNAP entities 1.Substances 2.Dependents (SPQR… entities) 3.Spatial regions, contexts, niches, environments

19 Spatial regions, contexts, niches, environments Organism species evolve into environments Domesticated spatial regions: rooms, nostrils, your alimentary tract Fiat spatial regions: JFK designated airspace

20 SNAP: Entities existing in toto at a time

21 Substances

22 SPQR …

23 Spatial regions

24 The SPAN Ontology t i m e

25 here time exists as part of the domain of the ontology The SPAN ontology

26 mereology works without restriction everywhere here t i m e clinical trial

27 Processes, too, are dependent on substances One-place vs. relational processes One-place processes: your getting warmer your getting hungrier

28 Examples of relational processes kissings, thumpings, conversations, dancings, join their carriers together into collectives of greater or lesser duration

29 SPAN: Entities extended in time

30 Two kinds of SPAN entities 1.Processes (including events: process-boundaries) 2.Spatio-temporal regions

31 Processes

32 Spatio-temporal regions

33 4-dimensional environments Lobsters have evolved into environments marked by cyclical patterns of temperature change Tudor England The Afghan winter The window of opportunity for an invasion of Iraq

34 How do you know whether an entity is SNAP or SPAN?

35 problem cases forest fire anthrax epidemic hurricane Maria traffic jam ocean wave

36 forest fire: a process a pack of monkeys jumping from tree to tree and eating up the trees as they go the Olympic flame: a process or a thing? (anthrax spores are little monkeys)

37 Formal-ontological concepts come for free do not add anything to being are domain-independent are expressed linguistically by closed- class items … HOW TO GENERATE THEM?

38 The idea (first rough version) Formal relations are those relations which are not captured by either SNAP or SPAN because they traverse the SNAP- SPAN divide they glue SNAP and SPAN entities together

39 This generates a first list of formal relations, e.g. dependence, but we find some of these relations also within SNAP or within SNAP

40 The idea (modified version) Formal relations are the relations that hold SNAP and SPAN entities/ontologies together and analogous relations

41 Example: Individuation, segmentation

42 Substances tokens separated by bona fide boundaries form natural kinds, types (universals, species + genera) separated by bona fide boundaries

43 Processes Process tokens merge into one another Process kinds merge into one another … few clean joints either between tokens or between types

44 boundaries are mostly fiat t i m e everything is flux

45 SNAP entities provide the principles of individuation/segmentation for SPAN entities No change without some THING or QUALITY which changes

46 Example: Ontological Dependence (SPAN, SNAP): process  substance The erosion of the rock necessitates the existence of the rock (SNAP, SNAP): SPQR  substance The token redness of the sand necessitates the existence of the sand

47 Generating a typology Two main types of formal relations: meta-ontological: obtain between entities of different ontologies intra-ontological: obtain between entities of the same ontology (intra- SNAP, intra-SPAN)

48 Three parameters: - the arity of the relation - the types of the relata, expressed as an ordered list, called the signature of the relation - the formal nature of the relation

49 Principal Signatures In the binary case: SNAP-SNAP - (SNAP i, SNAP i ), i = i - (SNAP i, SNAP i ), i j SPAN-SPAN SNAP-SPAN SPAN-SNAP

50 Transtemporal relations Examples: Genidentity (transtemporal generalization of identity/part-whole) Successive causality

51 Genidentity Also SPAN-SPAN? Is there a form of genidentity among processes? The such-has-to-have-come-forth-from relation. Signature: SNAP i -SNAP j Cut a chunk of matter in two, the sum of the remaining pieces is genidentical to the chunk before cutting

52 Successive Causality SNAP-SPAN: Agent causation A substance produces causally a process SPAN-SPAN: Process causation One process causes another process SPAN-SNAP: Causal repercussion A process results in the modification of a substance (always mediated by process causation) SNAP-SNAP: Causal origin One substance is the causal origin of another (mediated by other types of causal relations )

53 Successive Causality SNAP-SPAN: Agent causation SPAN-SPAN: Process causation SPAN-SNAP: Causal repercussion SNAP-SNAP: Causal origin do not apply on all levels of granularity (holds of examples given below also)

54 Our main target: Temporally extended relations Simultaneous Causality Participation (holds between a substance and a process such as an action or a life or history) Realization (holds between SPQR… entities and their SPAN expressions)

55 Simultaneous causality SPAN-SPAN The rise in temperature causes the (simultaneous) increase in pressure (Boyle’s law)

56 Substance  Process PARTICIPATION (a species of dependence)

57 Participation (SNAP-SPAN) A substance (SNAP) participates in a process (SPAN) A runner participates in a race A voter participates in an election

58 Participation x y substances x, y participate in process B time B x y SNAP-t i. time SPAN B slice of x’s life

59 Axes of variation activity/passivity (agentive) direct/mediated benefactor/malefactor (conducive to existence) [MEDICINE]

60 SNAP-SPAN Participation Perpetration (+agentive) Initiation Perpetuation Termination Influence Facilitation Hindrance Mediation Patiency (-agentive)

61 Perpetration A substance perpetrates an action (direct and agentive participation in a process): The referee fires the starting-pistol The captain gives the order

62 Initiation A substance initiates a process: The referee starts the race The attorney initiates the process of appeal

63 Perpetuation A substance sustains a process: The singer sings the song The charged filament perpetuates the emission of light

64 Termination A substance terminates a process: The operator terminates the projection of the film The judge terminates the imprisonment of the pardoned convict

65 Influence A substance (or its quality) has an effect on a process The steepness of the slope affects the movement of the troops The politicians influence the course of the war

66 Facilitation A substance plays a secondary role in a process (for example by participating in a part or layer of the process) The catalyst provides the chemical conditions for the reaction The traffic-police facilitate our rapid progress to the airport

67 Facilitation is this really a binary relation?

68 Hindrance, prevention, inhibition A substance has a negative effect on the unfolding of a process (by participating in other processes) The drug hinders the progression of the disease The strikers prevent the airplane from departing

69 Hindrance, prevention, inhibition Is this really a binary relation ? (What is the second term?)

70 Mediation A substance plays an indirect role in the unfolding of a process relating other participants: The Norwegians mediate the discussions between the warring parties

71 Patiency Dual of agentive participation John kisses [Mary] (John agent) Mary is kissed [by John] (Mary patient)

72 Signatures of meta-relations SNAP ComponentSPAN Component Substances SPQR… Space Regions Processuals Processes Events Space-Time Regions

73 Signatures of meta-relations SNAP ComponentSPAN Component Substances SPQR… Space Regions Processuals Processes Events Space-Time Regions

74 Signatures of meta-relations SNAP ComponentSPAN Component Substances SPQR… Space Regions Processuals Processes Events Space-Time Regions

75 Signatures of meta-relations SNAP ComponentSPAN Component Substances SPQR… Space Regions Processuals Processes Events Space-Time Regions

76 REALIZATION

77 Signatures of meta-relations SNAP ComponentSPAN Component Substances SPQR… Spatial Regions Processuals Processes Events Space-Time Regions participation realization

78 Realization (SPQR  process) The most general relation between a dependent (SPQR…) entity and a process The power to legislate is realized through the passing of a law The role of antibiotics in treating infections is via the killing of bacteria

79 Realization (SNAP-SPAN) the execution of a plan, algorithm the expression of a function the exercise of a role the realization of a disposition

80 SPQR… entities and their SPAN realizations plan function role disposition algorithm SNAP

81 SPQR… entities and their SPAN realizations execution expression exercise realization application course SPAN

82 Material examples: performance of a symphony projection of a film expression of an emotion utterance of a sentence application of a therapy course of a disease increase of temperature

83 SNAP  SPAN Participation Substance  Process Realization SPQR  Process

84 SPAN  SNAP Involvement

85 SPAN  SNAP Involvement Creation Sustaining in being Destruction Demarcation Blurring Degradation

86 Involvement process  substance (sometimes the converse of participation): Races involve racers (but not always): Wars involve civilians

87 Creation A process brings into being a substance: The declaration of independence creates the new state The work of the potter creates the vase

88 Sustaining in being A process sustains in being a substance: The circulation of the blood sustains the body Levying taxes sustains the army

89 Degradation A process has negative effects upon a substance Eating sugar contributes to the deterioration of your teeth. The flow of water erodes the rock

90 Destruction A process puts a substance out of existence The explosion destroys the car The falling of the vase on the floor breaks it

91 Demarcation A process creates (fiat or bona fide) boundaries of substances. The signing of the treaty establishes fixed borders between the two nations The tracing of the area of operation by the surgeon defines a boundary, the incision performed by the surgeon yet another one

92 Blurring A process destroys boundaries of substances: The military stand-off creates the no man's land The successful transplant obliterates the boundary between original and grafted tissue

93 Process  SPQR Continuation Degradation Destruction Creation Qualitative projection

94 Qualitative Projection A warming process yields a rise in temperature The tenure process yields a rise in John’s status

95 Creation A process brings into being a dependent entity The accident reshapes the car. The baking of the clay gives the vase its rigidity and color.

96 Continuation A process sustains the existence of an SPQR entity The firing of the fireworks maintains the coloration of the sky The intake of alcohol sustains the rosiness of his cheeks

97 Degradation A process affects a substance's quality or status by lowering its degree The opening of the window diminishes the temperature in the room

98 Destruction A process destroys/changes an SPQR… entity The accident destroys the car's shape The burning of the vase destroys its color The demotion relieved him of his rank as an officer

99 Varieties of projection Warming process  series of temperature qualities = qualitative projection Process  temporal interval = temporal projection

100 Spatial Projection A process occurs in a given place or area: The Revolution took place in Paris The wind blows beyond the 24th parallel

101 Starts in / ends at (spatial projection of process boundaries) A process begins/ends at a location The race started in Paris The race ended in Roubaix

102 SNAP-SPAN Participation Perpetration (+agentive) Initiation Perpetuation Termination Influence Facilitation Hindrance Mediation Patiency (-agentive)

103 SPAN-SNAP Involvement Creation Sustenance Destruction Continuation Degradation Destruction Creation Demarcation Blurring Qualitative projection Degradation

104 Varieties of Projection A process projects onto its temporal duration, onto the spatio-temporal region it occupies onto the spatial region it occupies at a given time onto the sum of its participants at a time onto the sum of the SPQR… entities realized through it at a time

105 Temporal Projection of SPAN entities onto temporal intervals of SNAP entities onto temporal intervals via their lives

106 Formal relations not dealt with so far: part-whole instantiation reference, intentionality truthmaking

107 Part-Whole Basic relation exclusively intra- ontological: either SNAP-SNAP or SPAN-SPAN. SNAP-SNAP: only if SNAP i s have the same temporal index

108 Relations crossing the SNAP/SPAN border are never part-relations John’s life substance John physiological processes sustaining in existence

109 Granularity spatial regionsubstance parts of substances are always substances

110 Granularity spatial regionsubstance parts of spatial regions are always spatial regions

111 Granularity process parts of processes are always processes

112 Intra-granular and cross-granular parthood across SNAPs: Kevin’s arm is part of Kevin Kevin’s molecule is part of Kevin across SPANs: Kevin’s leg-movement is part of Kevin’s running Kevin’s cytometabolism is part of Kevin’s running

113 The idea (a further modification) Formal relations are those relations which are not captured by either the SNAP or the SPAN ontology either because they can traverse the SNAP-SPAN divide or because they can traverse the granular divide

114 Is this Kantianism? does every ontology/perspective generate new formal-ontological relations?

115 Realist Perspectivalism There is a multiplicity of ontological perspectives on reality, all equally veridical i.e. transparent to reality

116 SNAP universals and particulars

117 What about reference, intentionality, truthmaking ?

118

119 Are there any cases of ontological dependence involving an increase in being, analogous to the increase in being between the thought and the thinker, the charge and the conductor, the swim and the swimmer between SPAN and SPAN entities? (Hypothesis: all qualities of processes are essential) Puzzle

120 Co-temporality is a requisite for most SNAP-SPAN relations (participation, realization, etc.) Exception: the memory of a process state of memory: SNAP (vs. episodic remembering: SPAN)