Conceptual Modeling and Ontological Analysis Nicola Guarino, LADSEB CNR,Italy Chris Welty, Vassar College, USA

2 Objectives Introduce the notions of formal ontology from Philosophy Present basic tools for ontology-driven conceptual analysis based on formal ontology Explore some principled guidelines for using these tools Discuss examples of using these guidelines and tools in practice

3 An Interdisciplinary Approach Towards a unified Ontology-driven Modelling Methodology for databases, knowledge bases and OO-systems –Grounded in reality –Transparent to people –Rigorous –General Based on –Logic –Philosophy –(Linguistics)

4 Summary Ontology and ontologies –Models and conceptualizations Ontology-driven conceptual modeling Formal ontological analysis –Mereology –Identity, unity, essence –Essence and rigidity –Identity and identity criteria –Unity and unity criteria –Dependence Using the formal properties –Basic property kinds –Further property kinds based on common ICs/UCs Ontology-driven modeling principles –Taxonomic relationships –An extended example –Membership relationships –Part-whole relationships A minimal top-level ontology Conclusions: some basic design principles

5 Ontology and ontologies

6 What is Ontology The study of being qua being: the study of possible The study of the nature of possible: ontology as the theory of distinctions among possibilia The study of the most general characteristics that anything must have in order to count as a (certain kind of) being or entity.

7 Definitions Ontology (capital “o”): –a philosophical discipline. An ontology (lowercase “o”): –specific artifact designed with the purpose of expressing the intended meaning of a vocabulary

8 What is an ontology? A shared vocabulary Plus … A specification (actually, a characterization) of the intended meaning of that vocabulary...i.e., an ontology accounts for the commitment of a language to a certain conceptualization “An ontology is a specification of a conceptualization” [Gruber 95]

9 Models and Conceptualizations

10 Capturing Intended Meaning First order logic is ontologically neutral Logical KBs often rely on natural language to convey intended meaning

11 Intended Models An ontology consisting of just a vocabulary is of little use - Unintended interpretations need to be excluded Models M(L) Intended models I K (L)

12 What is a conceptualization? Conceptualization of scene 1: Scene 1: blocks on a table

13 What is a conceptualization? The same conceptualization? Scene 2: a different arrangement of blocks

14 What is a conceptualization Conceptualization: the formal structure of reality as perceived and organized by an agent, independently of: –the vocabulary used (i.e., the language used) –the actual occurence of a specific situation Different situations involving the same objects, described by different vocabularies, may share the same conceptualization. apple mela same conceptualization LILI LELE

15 Relations vs. Conceptual Relations ordinary relations are defined on a domain D: conceptual relations are defined on a domain space (Montague-style semantics)

16 Ontologies constrain the intended meaning Conceptualization C Language L Commitment K= Ontology Models M(L) Intended models I K (L)

17 Levels of Ontological Depth Lexicon –Vocabulary with NL definitions Simple Taxonomy Thesaurus –Taxonomy plus related-terms Relational Model –Unconstrained use of arbitrary relations Fully Axiomatized Theory

18 Our Framework: Ontology-Driven Conceptual Modeling

19 Formal Ontology Theory of formal distinctions and connections within: –entities of the world, as we perceive it (particulars) –categories we use to talk about such entities (universals) Basic tools of formal ontological analysis: –Theory of Parts and Wholes (Mereology) –Theory of Identity, Integrity, Essence –Theory of Dependence Why formal? –Two meanings : rigorous general –Formal logic: connections between truths - neutral wrt truth –Formal ontology: connections between things - neutral wrt reality [Varzi 96] Goal: characterizing particulars and universals by means of formal properties and relations.

20 Approach Draw fundamental notions from Formal Ontology Establish a set of useful property kinds, based on behavior wrt above notions (meta- properties). Explore the constraints they impose on Information Systems design, and add further modeling principles Establish a minimal top-level ontology to drive conceptual modeling

21 Framework Formal Ontological Properties/Relations Useful Property Kinds Ontology-Driven Modeling Principles Minimal Top-Level Ontology User Conceptualization Conceptual Model Ontology Methodology

22 From Ontology to Data Reference ontology (development time) –establishes consensus about meaning of terms Application ontology (development time) –Focuses on a particular application –limited by relevance choices related to a certain application Conceptual model (run time) –implements an ontology (Tbox) –Describes constraints between terms to be checked at run time (terminological services) –limited by expressive power of implementation medium Database (Abox) (run time) –Describes a specific (epistemic) state of affairs A KB includes both

23 Formal Ontological Analysis Mereology Identity, Unity, Essence Dependence

24 Mereology

25 Mereology A possible primitive: proper part-of relation (PP) –asymmetric –transitive –Pxy = def PPxy  x=y Some further axioms: Excluded models: supplementation: PPxy   z ( PPzy  ¬ z=x) principle of sum:  z ( PPxz  PPyz  ¬  w(PPwz  ¬ (Pwx  Pwy))) extensionality: x = y  (Pwx  Pwy)

26 The problems with General Extensional Mereology Generality of mereological sums Extensionality –different identifying properties while having the same parts –different parts while having the same identifying properties Admittability of atoms

27 Part, Constitution, and Identity a + b ab Stack#1 b a ab a + b Structure may change identity K D Extensionality is lost Constitution links the two entities Constitution is asymmetric (implies dependence)

28 Identity, Unity, Essence

29  Framework Formal Ontological Properties/Relations Useful Property Kinds Ontology-Driven Modeling Principles Minimal Top-Level Ontology User Conceptualization Conceptual Model Ontology Methodology

30 Identity, Rigidity, Unity How can an entity change while keeping its identity? Under what conditions does an entity lose its identity? Do entities have any essential properties? Does a change of parts affect identity? When does an entity count as one?...How do we know the answers…

31 Identity and Unity Identity: is this my dog? Unity: is the collar part of my dog?

32 Essence and rigidity

33 Intuitive Rigidity Certain entities have essential properties. –John must have a brain. –John must be a person. Certain properties are essential to all their instances (compare being a person with having a brain). These properties are rigid - if an entity is ever an instance of a rigid property, it must always be.

34 Formal Rigidity   is rigid (+R):  x  (x)   (x) –e.g. Person, Apple   is non-rigid (-R):  x  (x)  ¬  (x) –e.g. Red, Male   is anti-rigid (~R):  x  (x)  ¬  (x) –e.g. Student, Agent

35 Identity and identity criteria

36 Synchronic Identity Criteria Material objects: same-location Immaterial objects: same-location not valid any more...

37 Diachronic Identity Requires some notion of persistence In addition, the sameness (or continuity) of certain properties is required The castle/bunch of bricks Identity is not similarity

38 Ultimately, identity criteria are the result of our conceptualization of reality. They are always related to a class of entities considered as relevant for our purposes. In general, identity can’t be defined. What we can have are just informative constraints. A priori identity?

39 Identity criteria Based on the sameness of a certain property  (x,t)   (y,t’)  ((  (x,z,t)   (y,z,t’))  x = y) t = t ’ : synchronic; t ≠ t ’ : diachronic Generalization:  (x,t)   (y,t’)   (x,y, t,t’)  x = y)

40 Necessary ICs A formula  is a necessary IC for   if  (x,t)   (y,t’)  x=y   (x,y,t,t’) … provided that: it is not equivalent to universal identity: ¬  xytt’  (x,y,t,t’)  x=y it is not trivially true of all  s: ¬  xytt’  (x,t)   (y,t’)   (x,y,t,t’)

41 Sufficient ICs A formula  is a sufficient IC of  if  (x,t)   (y,t’)   (x,y,t,t’)  x=y … provided that: it is not equivalent to universal identity: ¬  xytt’  (x,y,t,t’)  x=y it  is not trivially false:  xytt’  (x,y,t,t’)

42 Identity Meta-Properties Carrying Identity (+I) –Having an IC, either own or inherited. –Non-rigid properties must inherit ICs. –e.g. has-same-fingerprint an IC for Person Supplying Identity (+O) –having an IC that is not carried by a subsuming property –Only Rigid properties can supply ICs

43 Local Identity? Global IC: Rigid properties Local IC (+L): non-Rigid properties Local IC identifies instances of  only when they are instances of  –same-wing-pattern for Butterfly: nec & suf but only when one entity is an instance of Butterfly, but not when that entity is a caterpillar – same-registration-no. for students Only-suf: Holds only when one entity is in a certain “student experience” Global IC identifies an entity for its entire existence (only for +R properties)

44 Unity and Unity Criteria

45 Unity Analysis What counts as a whole? What makes it a whole? In which sense are its parts connected? What are the properties of the connection relation? How is the whole isolated from the background? What are its boundaries? What is the role played by the parts with respect to the whole?

46 Unity analysis and Mereotopology Primitive: topological connection (C) Some axioms: –reflexivity –symmetry –monotonicity wrt parthood: Pxy  Cxz  Cyz –external contact: everything is connected with its mereological complement Problems: –distinguish between open and closed regions? –get rid of P, defining Pxy = def Cxz  Cyz ? –different kinds of connection (line, point, surface): is C alone enough?

47 Unity Conditions An object a is a whole under  iff  is an equivalence relation such that P(y,a)  P(z,a)   y,z) but not  y,z)   x(P(y,x)  P(z,x))  can be seen as a generalized indirect connection

48 Conditions for Unity To achieve this we need –a suitable connection relation - how do we get from one part to another? –some notion of boundary - how do we know when to stop?

49 Unity and Plurality* Strong vs. weak self-connection –Piece of coal vs. lump of coal –Basic component vs. assembly –Surface connection vs. line or point connection Singular objects: strongly self-connected (may be wholes or not) Plural objects: sums of wholes –Collections (the sum is not a whole) –Plural wholes (the sum is also a whole) Mere sums

50 Unity Meta-Properties If all instances of a property  are wholes under the same relation  carries unity (+U) When at least one instance of  is not a whole, or when two instances of  are wholes under different relations,  does not carry unity (-U) When no instance of  is a whole,  carries anti-unity (~U)

51 Disjointness Theorem Properties with incompatible IC/UC are disjoint

52 Examples of identity and unity conditions An atom of matter An amount of matter A mass of matter A piece of coal A heap of coal A doughnut

53 Dependence

54 Dependence Analysis Can an entity exist alone? Does its existence imply the existence of something else? (rigid dependence) Does it imply the existence of some entities that are instances of a specific class? (generic dependence) Does a property holding for x depend on something else besides x? (property dependence)

55 Dependence Meta-Properties Our methodology currently uses only property dependence A property  is dependent (+D) if   x  (x)   y  y)  ¬ P(x,y)  ¬ C(x,y) If there is at least one instance of the property that is not dependent, the property is not dependent (-D) Also exclude qualities (i.e. Red), entities that necessarily exist (the universe), and subsumed properties.

56 Using the meta-properties

57 Framework Formal Ontological Properties/Relations Useful Property Kinds Ontology-Driven Modeling Principles Minimal Top-Level Ontology User Conceptualization Conceptual Model Ontology Methodology 

58 Motivation Our methodology will require analyzing all properties in an ontology according to these meta-properties – This is a lot of work! Why perform this analysis? –Makes modeling assumptions clear, which: helps resolve known differences helps expose unknown differences

59 Resolving known Differences Two well-known ontologies define: –Physical object is-a amount of matter (WordNet) –Amount of matter is a Physical Object (Pangloss) Which one is correct? Analyze each –Physical-object:Physical-object: –Amount of matter:Amount of matter: Result –According to the most common understanding, both ontologies are wrong, each concept is at the top-level

60 Exposing Unknown Differences Agreement: –An organization is a Social Entity Analysis: –Person 1: Social Entity +O+U+R -D –Person 2: Social Entity +O+U+R +D Problem? –Person 1: A social entity is a group of people who are together for some social reason. –Person 2: A social entity is an entity recognized by society, therefore +D

61 Property Kinds

62 Framework Formal Ontological Properties/Relations Useful Property Kinds Ontology-Driven Modeling Principles Minimal Top-Level Ontology User Conceptualization Conceptual Model Ontology Methodology 

63 Basic Property kinds

64 Sortals, categories, and other properties Sortals (horse, triangle, amount of matter, person, student...) –Carry identity –Hardly definable in terms of a few primitives –High organizational utility Categories (universal, particular, event, substance...) –No identity –Useful generalizations for sortals –Characterized by a set of (only necessary) formal properties –Good organizational utility Other non-sortals (red, big, decomposable, eatable, dependent, singular...) –No identity –Span across different sortals –Limited organizational utility (but high semantic value)

65 A formal ontology of properties Property Non-sortal -I Role ~R+D Sortal +I Formal Role Attribution -R-D Category +R Mixin -D Type +O Quasi-type -O Non-rigid -R Rigid +R Material role Anti-rigid ~R Phased sortal -D

66 Basic Property Kinds Table

67 Further Property Kinds: Common ICs/UCs

68 Ontological Levels Physical –Atomic (a minimal grain of matter) –Static (a configuration, a situation) –Mereological(an amount of matter, a collection) –Topological(a piece of matter) –Morphological(a cubic block, a constellation) Functional (an artifact, a biological organ) Biological (a human body) Intentional (a person, a robot) Social (a company) Correspond to different kinds of IC/UC All levels except the mereological one have non-extensional IC A generic dependence relation links higher levels to their immediate inferior.

69 Identity and unity conditions

70 Ontology-driven Modeling Principles

71 Framework Formal Ontological Properties/Relations Useful Property Kinds Ontology-Driven Modeling Principles Minimal Top-Level Ontology User Conceptualization Conceptual Model Ontology Methodology 

72 Re-visiting abstraction relationships Taxonomic relationships (generalization) Membership relationships (association) Part-whole relationships (aggregation)

73 Taxonomic relationships

74 Subsumption Misused To express disjunction –Person is-a Legal-Agent –Company is-a Legal-Agent To express constitution –Person is-a Amount of Matter To express multiple meanings –Book is a physical-obect –Book is a abstract-object

75 Assumptions No entity without identity Every entity must instantiate a rigid property with identity (a type)

76 Taxonomic Constraints +R  ~R -I  +I -U  +U +U  ~U -D  +D Incompatible IC’s are disjoint Incompatible UC’s are disjoint For these we introduced Common UC/IC

77 Impact of taxonomic constraints on ontology design * Stratification replaces multiple inheritance in many cases: –Simpler taxonomies –Moderate proliferation of individuals –Co-localization of entities of different kind Non-taxonomic relations become important: –Dependence –Co-localization –Constitution –Participation Type/role distinction allows for isolation of backbones in the taxonomic structure

78 Type and Role specialization* Type specialization (e.g. Living being  Person) –New features affect identity –Both necessary and sufficient ICs can be added while specializing types Polygon: same edges, same angles Triangle: two edges, one angle Living being: same DNA, etc... Zebra: same stripes Role specialization (e.g. Person  Student) –New features don’t affect identity

79 Backbone Taxonomy The most important properties in a taxonomy are types, since all entities must instantiate at least one. The rigid properties above (categories) and below (quasi-types) types taken together form the most useful structure in a taxonomy - the backbone taxonomy

80 An extended example

81 Framework Formal Ontological Properties/Relations Useful Property Kinds Ontology-Driven Modeling Principles Minimal Top-Level Ontology User Conceptualization Conceptual Model Ontology Methodology 

82 Entity Fruit Physical object Group of people Country Food Animal Legal agent Amount of matter Group Living being Location Agent Red Red apple Person Vertebrate Apple Caterpillar Butterfly Organization Social entity

83 Assign Meta-Properties

84 Property Analysis Entity, Location Entity –Everything is an entity –-I-U-D+R –Category Location –A generalized region of space. –+O: by its parts (mereologically extensional). –~U: no way to isolate a location –-D+R –Type

85 Property Analysis Amount of Matter, Red Amount of Matter –unstructured /scattered “stuff” as lumps of clay or some bricks –+O: mereologically extensional –~U: intrinsically no unity –-D+R –Type Red –Really Red-thing, the set of all red-colored entities –-I-U-D-R –Formal Attribution

86 Property Analysis Agent, Group Agent –An entity playing a part in some event –-I-U: no universal IC/UC –+D: on the event/action participating in –~R: no instance is necessarily an agent –Formal role Group –An unstructured collection of wholes –+O: same-members –~U: unstructured, no unity. – -D+R –Type

87 Property Analysis Physical Object, Living Being Physical Object –Isolated material objects. –+O: same spatial location (only synchronic, no common diachronic IC). –+U: Topological –-D+R –Type Living Being –+O: same-DNA (only nec.) –+U: biological unity –-D+R –Type

88 Property Analysis Food, Animal Food –+I-O~U: amt. of matter –+D: something that eats it. –~R: being food is not necessary... –Material Role Animal –+O: same-brain –+U: biological unity –-D+R –Type

89 Property Analysis Legal Agent, Group of People Legal Agent –A legally recognized entity –+L: All legal systems have a defined IC, has- same-legal-ID –-U: no universal unity –+D: on the legal body that recognizes it –~R: not necessary –Material Role Group of People –See Group –+I-O~U-D+R –Quasi-type

90 Property Analysis Social Entity, Organization Social Entity –A group of people together for social reasons –-I: no universal IC –+U: social-connection –-D+R –category Organization –A group of people together, with roles that define some structure –+O: same-mission and way of operating –+U: functional –-D+R –Type

91 Property Analysis Fruit Fruit –An individual fruit, such as an orange or bannana –+O: same-plant, same- shape, etc. (only nec.) –+U: topological –-D+R –Type

92 Property Analysis Apple, Red Apple Apple –+O: shape, color, skin pattern (only nec) –+U: topological –-D+R –Type Red-Apple –+I-O: from Apple –+U: from Apple –-D –~R: no red apple is necessarily red –type-attribution mixin

93 Property Analysis Vertebrate, Person Vertebrate –Really vertebrate- animal –A biological classification that adds new membership criteria (has-backbone) –+I-O: from animal –+U: from animal –-D+R –quasi-type Person –+O: same-fingerprint –+U: from animal –-D+R –Type

94 Property Analysis Butterfly, Caterpillar Butterfly –+L: same-wing-pattern –+U: biological –-D –~R: the same entity can be something else (a caterpillar) –Phased sortal Caterpillar –+L: spots, legs, color –+U: biological –-D –~R: caterpillars become butterflies and change their IC –Phased sortal

95 Property Analysis Country Country –A place recognized by convention as autonomous –+L: government, sub-regions –+U: countries are countable (heuristic) –-D –~R: some countries do not exist as countries any more (e.g. Prussia) but are still places –Phased sortal

96 Remove non-rigid properties Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Agent -I-U+D~R Apple +O+U-D+R Fruit +O+U-D+R Food +I-O~U+D~R Country +L+U-D~R Legal agent +L-U+D~R Group of people +I-O~U-D+R Red apple +I-O+U-D~R Red -I-U-D-R Vertebrate +I-O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R

97 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze taxonomic links ~U can’t subsume +U Living being can change parts and remain the same, but amounts of matter can not (incompatible ICs) Living being is constituted of matter

98 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze taxonomic links ~U can’t subsume +U Living being can change parts and remain the same, but amounts of matter can not (incompatible ICs) Living being is constituted of matter

99 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze taxonomic links ~U can’t subsume +U Physical objects can change parts and remain the same, but amounts of matter can not (incompatible ICs) Physical object is constituted of matter

100 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze taxonomic links ~U can’t subsume +U Physical objects can change parts and remain the same, but amounts of matter can not (incompatible ICs) Physical object is constituted of matter

101 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze taxonomic links Meta-properties fine Rigidity-check fails: when an entity stops being an animal, it does not stop being a physical object (when an animal dies, its body remains) Constitution again

102 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze taxonomic links Meta-properties fine Rigidity-check fails: when an entity stops being an animal, it does not stop being a physical object (when an animal dies, its body remains) Constitution again

103 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze taxonomic links ~U can’t subsume +U A group, and group of people, can’t change parts - it becomes a different group A social entity can change parts - it’s more than just a group (incompatible IC) Constitution again

104 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze taxonomic links ~U can’t subsume +U A group, and group of people, can’t change parts - it becomes a different group A social entity can change parts - it’s more than just a group (incompatible IC) Constitution again

105 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze taxonomic links ~U can’t subsume +U Same as for social entity. Note also the same group can constitute different organizations.

106 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze taxonomic links ~U can’t subsume +U Same as for social entity. Note also the same group can constitute different organizations.

107 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R

108 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze Phased Sortals For phased sortals: what do they phase into? Country is anti-rigid because it is representing multiple senses of country: a geographical region and a political entity. Split the two senses into two concepts, both rigid, both types. Country +L+U-D~R

109 Country +O+U-D+R Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze Phased Sortals There is an relationship between the two, but not subsumption. Country +L+U-D~R Geographical Region +O-U-D+R

110 Country +O+U-D+R Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze Phased Sortals Geographical Region +O-U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Caterpillar phases into butterfly - a true phased sortal There must be some property from which a single entity can uniquely claim identity across phases Define a rigid property which subsumes only the phases of the same entity. Lepidopteran +O+U-D+R

111 Country +O+U-D+R Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze Phased Sortals Geographical Region +O-U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Try for a type, may be quasi. IC for Lepidopteran could be same- cocoon Lepidopteran +O+U-D+R

112 Country +O+U-D+R Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze Roles Geographical Region +O-U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Lepidopteran +O+U-D+R Agent -I-U+D~R ~R can’t subsume +R Really want a type restriction: all agents are animals or social entities. Subsumption is not disjunction!

113 Country +O+U-D+R Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze Roles Geographical Region +O-U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Lepidopteran +O+U-D+R Agent -I-U+D~R ~R can’t subsume +R Really want a type restriction: all agents are animals or social entities. Subsumption is not disjunction!

114 Country +O+U-D+R Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze Roles Geographical Region +O-U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Lepidopteran +O+U-D+R Agent -I-U+D~R ~R can’t subsume +R Another disjunction: all legal agents are countries, persons, or organizations Legal agent +L-U+D~R

115 Country +O+U-D+R Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze Roles Geographical Region +O-U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Lepidopteran +O+U-D+R Agent -I-U+D~R ~R can’t subsume +R Another disjunction: all legal agents are countries, persons, or organizations Legal agent +L-U+D~R

116 Country +O+U-D+R Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze Roles Geographical Region +O-U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Lepidopteran +O+U-D+R Agent -I-U+D~R Legal agent +L-U+D~R ~R can’t subsume +R Apple is not necessarily food. A poison-apple, e.g., is still an apple. ~U can’t subsume +U Caterpillars are wholes, food is stuff. Food +I-O~U+D~R

117 Country +O+U-D+R Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze Roles Geographical Region +O-U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Lepidopteran +O+U-D+R Agent -I-U+D~R Legal agent +L-U+D~R ~R can’t subsume +R Apple is not necessarily food. A poison-apple, e.g., is still an apple. ~U can’t subsume +U Caterpillars are wholes, food is stuff. Food +I-O~U+D~R

118 Country +O+U-D+R Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Analyze Attributions Geographical Region +O-U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Lepidopteran +O+U-D+R Agent -I-U+D~R Legal agent +L-U+D~R No violations Attributions are discouraged, can be confusing. Often better to use attribute values (i.e. Apple Color red) Food +I-O~U+D~R Red -I-U-D-R Red apple +I-O+U-D~R

119 Country +O+U-D+R Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Lepidopteran +O+U-D+R Agent -I-U+D~R Legal agent +L-U+D~R Food +I-O~U+D~R Red -I-U-D-R Red apple +I-O+U-D~R

120 Country +O+U-D+R Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Apple +O+U-D+R Fruit +O+U-D+R Group of people +I-O~U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Lepidopteran +O+U-D+R The backbone taxonomy

121 Entity -I-U-D+R Physical object +O+U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Organization +O+U-D+R Location +O-U-D+R Living being +O+U-D+R Person +O+U-D+R Animal +O+U-D+R Social entity -I+U-D+R Agent -I-U+D~R Apple +O+U-D+R Fruit +O+U-D+R Food +I-O~U+D~R Legal agent +L-U+D~R Group of people +I-O~U-D+R Red apple +I-O+U-D~R Red -I-U-D-R Vertebrate +I-O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Country +O+U-D+R Geographical Region +O-U-D+R Lepidopteran +O+U-D+R

122 Membership relationships

123 Framework Formal Ontological Properties/Relations Useful Property Kinds Ontology-Driven Modeling Principles Minimal Top-Level Ontology User Conceptualization Conceptual Model Ontology Methodology 

124 Singular vs. Plural Singular objects: strongly self-connected Plural objects: –Collections –Plural wholes –Mere sums

125 The Instance-of Relation (1) Being instance-of something vs. being an instance. The problems of logical predication –x is an apple  Apple(x) –x is red  Red(x) Instance-of vs. class membership –John is a member of “Person”  Person(John) –Tree1 is a member of “TheForest”  TheForest(Tree1) ?? (violates usual intended interpretation of unary predicates: property shared by all instances of the corresponding class. Doesn’t pass the “is-a” test ) Temporal instances –Beethoven isn’t an “ultimate instance”, since “the young Beethoven” may be an instance of it...

126 The Instance-of Relation (2) How to decide whether something is an instance? Properties can be instances of meta-properties Hence, “being an instance” may be a subjective property But “being a particular” IS NOT! Particulars are always “ultimate” instances. Concrete entities are always particulars. So-called “temporal instances” are either temporal parts of a particular or instances of an abstract class.

127 Part-whole relationships

128 Part-of vs. part-whole relations component/integral object member/collection portion/mass stuff/object place/area feature/activity

129 Framework Formal Ontological Properties/Relations Useful Property Kinds Ontology-Driven Modeling Principles Minimal Top-Level Ontology User Conceptualization Conceptual Model Ontology Methodology 

130 A Minimal Top-level Ontology Entity Particular Concrete particular Location Object Abstract particular Set Structure … Universal Property Property Kinds... Relation

131 Well-Founded Ontologies: Some Basic Design Principles Be clear about the domain –particulars (individuals) –universals (classes and relations) –linguistic entities (nouns, verbs, adjectives...) Take identity seriously –different identity criteria imply disjoint classes Isolate a basic taxonomic structure –only sortals like “person” (as opposite to “red”) are good candidates for being taxons Make an explicit distinction between types and roles (and other property kinds)

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