Conceptual Modeling and Ontological Analysis Nicola Guarino LADSEB
Conceptual Modeling and Ontological Analysis Nicola Guarino, LADSEB CNR, Italy Chris Welty, Vassar College, USA
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 2
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) 3
Ontology and ontologies 5
What is Ontology • The study of being qua being: the study of possible • The study of the nature of possible: ontology as 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. 6
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 7
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] 8
Models and Conceptualizations 9
Capturing Intended Meaning • First order logic is ontologically neutral • Logical KBs often rely on natural language to convey intended meaning 10
Intended Models An ontology consisting of just a vocabulary is of little use Unintended interpretations need to be excluded Models M(L) Intended models IK(L) 11
What is a conceptualization? Scene 1: blocks on a table Conceptualization of scene 1: <{a, b, c, d, e }, {on, above, clear, table }> 12
What is a conceptualization? Scene 2: a different arrangement of blocks The same conceptualization? 13
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. LE apple same conceptualization LI mela 14
Relations vs. Conceptual Relations (Montague-style semantics) ordinary relations are defined on a domain D: conceptual relations are defined on a domain space <D, W> 15
Ontologies constrain the intended meaning Conceptualization C Commitment K=<C, I> Language L Models M(L) Intended models IK(L) Ontology 16
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 17
Our Framework: Ontology-Driven Conceptual Modeling 18
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. 19
Approach • Draw fundamental notions from Formal Ontology • Establish a set of useful property kinds, based on behavior wrt above notions (metaproperties). • Explore the constraints they impose on Information Systems design, and add further modeling principles • Establish a minimal top-level ontology to drive conceptual modeling 20
Framework Conceptualization Conceptual Model Ontology User Methodology Minimal Top-Level Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations 21
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 22
Formal Ontological Analysis • Mereology • Identity, Unity, Essence • Dependence 23
Mereology 24
Mereology • A possible primitive: proper part-of relation (PP) – asymmetric – transitive – Pxy =def PPxy x=y • Some further axioms: supplementation: PPxy z ( PPzy ¬ z=x) principle of sum: z ( PPxz PPyz ¬ w(PPwz ¬ (Pwx Pwy))) extensionality: x = y (Pwx Pwy) Excluded models: 25
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 26
Part, Constitution, and Identity • Structure may change identity • Extensionality is lost • Constitution links the two entities • Constitution is asymmetric (implies dependence) a+b b Stack#1 D b a K a Stack#1 a b 27
Identity, Unity, Essence 28
Framework Conceptualization Conceptual Model Ontology User Methodology Minimal Top-Level Ontology-Driven Modeling Principles Useful Property Kinds � Formal Ontological Properties/Relations 29
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… 30
Identity and Unity • Identity: is this my dog? • Unity: is the collar part of my dog? 31
Essence and rigidity 32
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. 33
Formal Rigidity · f is rigid (+R): x f(x) – e. g. Person, Apple · f is non-rigid (-R): x f(x) ¬ f(x) – e. g. Red, Male · f is anti-rigid (~R): x f(x) ¬ f(x) – e. g. Student, Agent 34
Identity and identity criteria 35
Synchronic Identity Criteria • Material objects: same-location • Immaterial objects: same-location not valid any more. . . 36
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 37
A priori identity? 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. 38
Identity criteria • Based on the sameness of a certain property f(x, t) f(y, t’) ((c(x, z, t) c(y, z, t’)) x = y) • t = t’ : synchronic; t ≠ t’ : diachronic • Generalization: f(x, t) f(y, t’) (G(x, y, t , t’) x = y) 39
Necessary ICs A formula G is a necessary IC for f if f(x, t) f(y, t’) x=y G(x, y, t, t’) … provided that: • it is not equivalent to universal identity: ¬ xytt’ G(x, y, t, t’) x=y • it is not trivially true of all fs: ¬ xytt’ f(x, t) f(y, t’) G(x, y, t, t’) 40
Sufficient ICs A formula G is a sufficient IC of f if f(x, t) f(y, t’) G(x, y, t, t’) x=y … provided that: • it is not equivalent to universal identity: ¬ xytt’ G(x, y, t, t’) x=y • it is not trivially false: xytt’ G(x, y, t, t’) 41
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 42
Local Identity? • Global IC: Rigid properties • Local IC (+L): non-Rigid properties • Local IC identifies instances of f only when they are instances of f – 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) 43
Unity and Unity Criteria 44
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? 45
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? 46
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 47
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? 48
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 49
Unity Meta-Properties • If all instances of a property f are wholes under the same relation, f carries unity (+U) • When at least one instance of f is not a whole, or when two instances of f are wholes under different relations, f does not carry unity (-U) • When no instance of f is a whole, f carries anti-unity (~U) 50
Disjointness Theorem Properties with incompatible IC/UC are disjoint 51
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 52
Dependence 53
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) 54
Dependence Meta-Properties • Our methodology currently uses only property dependence • A property f is dependent (+D) if: x f(x) y j(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. 55
Using the meta-properties 56
Framework Conceptualization Conceptual Model Ontology User � Methodology Minimal Top-Level Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations 57
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 58
Resolving known Differences • Two well-known ontologies define: – Physical object is-a amount of matter (Word. Net) – Amount of matter is a Physical Object (Pangloss) • Which one is correct? • Analyze each – Physical-object: – Amount of matter: • Result – According to the most common understanding, both ontologies are wrong, each concept is at the top-level 59
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 60
Property Kinds 61
Framework Conceptualization Conceptual Model Ontology User Methodology Minimal Top-Level Ontology-Driven Modeling Principles � Useful Property Kinds Formal Ontological Properties/Relations 62
Basic Property kinds 63
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) 64
A formal ontology of properties Category +R Non-sortal -I Attribution -R-D Role Formal Role ~R+D Property Anti-rigid Non-rigid Sortal +I ~R -R Material role Phased sortal -D Mixin -D Rigid +R Type +O Quasi-type -O 65
Basic Property Kinds Table 66
Further Property Kinds: Common ICs/UCs 67
Ontological Levels • Physical – Atomic – Static – Mereological – Topological – Morphological • Functional • Biological • Intentional • Social (a minimal grain of matter) (a configuration, a situation) (an amount of matter, a collection) (a piece of matter) (a cubic block, a constellation) (an artifact, a biological organ) (a human body) (a person, a robot) (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. 68
Identity and unity conditions 69
Ontology-driven Modeling Principles 70
Framework Conceptualization Conceptual Model Ontology User Methodology Minimal Top-Level Ontology � Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations 71
Re-visiting abstraction relationships • Taxonomic relationships (generalization) • Membership relationships (association) • Part-whole relationships (aggregation) 72
Taxonomic relationships 73
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 74
Assumptions • No entity without identity • Every entity must instantiate a rigid property with identity (a type) 75
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 76
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 77
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 78
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 79
An extended example 80
Framework Conceptualization Conceptual Model Ontology User � Methodology Minimal Top-Level Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations 81
Entity Amount of matter Location Red Physical object Fruit Agent Living being Food Group of people Social entity Animal Legal agent Apple Vertebrate Country Red apple Organization Caterpillar Butterfly Person 82
Assign Meta-Properties 83
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 84
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 85
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 86
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 87
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 88
Property Analysis Legal Agent, Group of People • Legal Agent – A legally recognized entity – +L: All legal systems have a defined IC, hassame-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 89
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 90
Property Analysis Fruit • Fruit – An individual fruit, such as an orange or bannana – +O: same-plant, sameshape, etc. (only nec. ) – +U: topological – -D+R – Type 91
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 92
Property Analysis Vertebrate, Person • Vertebrate – Really vertebrateanimal – 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 93
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 94
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 95
Entity-I-U-D+R Location Remove non-rigid properties Amount of matter +O-U-D+R +O~U-D+R Physical object +O+U-D+R Fruit +O+U-D+R Red -I-U-D-R Agent -I-U+D~R Living being Group +O~U-D+R Group of people +O+U-D+R +I-O~U-D+R Social entity Food -I+U-D+R +I-O~U+D~R Animal +O+U-D+R Legal agent +L-U+D~R Apple +O+U-D+R Vertebrate +I-O+U-D+R Country +L+U-D~R Red apple +I-O+U-D~R Caterpillar Butterfly +L+U-D~R Organization +O+U-D+R Person +O+U-D+R 96
Entity-I-U-D+R Location Analyze taxonomic links Amount of matter +O-U-D+R Group • ~U can’t subsume +U +O~U-D+R • Living being can Living being change parts. Group and of people +O+U-D+R +I-O~U-D+R remain the same, but entity can amounts. Social of matter -I+U-D+R Animal not (incompatible ICs) +O+U-D+R • Living being is constituted of matter +O~U-D+R Physical object +O+U-D+R Fruit +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R 97
Entity-I-U-D+R Location Analyze taxonomic links Amount of matter +O-U-D+R Group • ~U can’t subsume +U +O~U-D+R • Living being can Living being change parts. Group and of people +O+U-D+R +I-O~U-D+R remain the same, but entity can amounts. Social of matter -I+U-D+R Animal not (incompatible ICs) +O+U-D+R • Living being is constituted of matter +O~U-D+R Physical object +O+U-D+R Fruit +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R 98
Entity-I-U-D+R Location Analyze taxonomic links Amount of matter +O-U-D+R Group • ~U can’t subsume +U +O~U-D+R • Physical objects can Living being change parts. Group and of people +O+U-D+R +I-O~U-D+R remain the same, but entity can amounts. Social of matter -I+U-D+R Animal not (incompatible ICs) +O+U-D+R • Physical object is constituted of matter +O~U-D+R Physical object +O+U-D+R Fruit +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R 99
Entity-I-U-D+R Location Analyze taxonomic links Amount of matter +O-U-D+R Group • ~U can’t subsume +U +O~U-D+R • Physical objects can Living being change parts. Group and of people +O+U-D+R +I-O~U-D+R remain the same, but entity can amounts. Social of matter -I+U-D+R Animal not (incompatible ICs) +O+U-D+R • Physical object is constituted of matter +O~U-D+R Physical object +O+U-D+R Fruit +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R 100
Entity-I-U-D+R Location Analyze taxonomic links Amount of matter +O-U-D+R Group • Meta-properties fine +O~U-D+R • Rigidity-check fails: Living being ofstops people +O+U-D+R when an. Group entity +I-O~U-D+R being an animal, it entitybeing does. Social not stop -I+U-D+R a physical object Animal +O+U-D+R (when an animal dies, its body remains) Organization Vertebrate +I-O+U-D+R • Constitution +O+U-D+R again +O~U-D+R Physical object +O+U-D+R Fruit +O+U-D+R Apple +O+U-D+R Person +O+U-D+R 101
Entity-I-U-D+R Location Analyze taxonomic links Amount of matter +O-U-D+R Group • Meta-properties fine +O~U-D+R • Rigidity-check fails: Living being ofstops people +O+U-D+R when an. Group entity +I-O~U-D+R being an animal, it entitybeing does. Social not stop -I+U-D+R a physical object Animal +O+U-D+R (when an animal dies, its body remains) Organization Vertebrate +I-O+U-D+R • Constitution +O+U-D+R again +O~U-D+R Physical object +O+U-D+R Fruit +O+U-D+R Apple +O+U-D+R Person +O+U-D+R 102
Entity-I-U-D+R Location Analyze taxonomic links Amount of matter Group +O~U-D+R • ~U can’t subsume +U +O~U-D+R • A group, and group of Physical object Living being Group of people +O+U-D+R people, can’t change +O+U-D+R +I-O~U-D+R parts - it becomes a Social entity different group -I+U-D+R Fruit • A social entity can. Animal +O+U-D+R change parts - it’s+O+U-D+R more than Applejust a group +O+U-D+R (incompatible IC) Vertebrate Organization +I-O+U-D+R +O+U-D+R • Constitution again +O-U-D+R Person +O+U-D+R 103
Entity-I-U-D+R Location Analyze taxonomic links Amount of matter Group +O~U-D+R • ~U can’t subsume +U +O~U-D+R • A group, and group of Physical object Living being Group of people +O+U-D+R people, can’t change +O+U-D+R +I-O~U-D+R parts - it becomes a Social entity different group -I+U-D+R Fruit • A social entity can. Animal +O+U-D+R change parts - it’s+O+U-D+R more than Applejust a group +O+U-D+R (incompatible IC) Vertebrate Organization +I-O+U-D+R +O+U-D+R • Constitution again +O-U-D+R Person +O+U-D+R 104
Entity-I-U-D+R Location +O-U-D+R Analyze taxonomic links Amount of matter Group +O~U-D+R Physical object +O~U-D+R Living being • subsume +U +O+U-D+R • Same as for social entity. • Note also the same group Fruit can constitute different +O+U-D+R Animal organizations. +O+U-D+R ~U can’t Group of people +I-O~U-D+R Social entity -I+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R 105
Entity-I-U-D+R Location +O-U-D+R Analyze taxonomic links Amount of matter Group +O~U-D+R Physical object +O~U-D+R Living being • subsume +U +O+U-D+R • Same as for social entity. • Note also the same group Fruit can constitute different +O+U-D+R Animal organizations. +O+U-D+R ~U can’t Group of people +I-O~U-D+R Social entity -I+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R 106
Entity-I-U-D+R Location Amount of matter +O-U-D+R Group +O~U-D+R Physical object +O+U-D+R Fruit +O+U-D+R +O~U-D+R Living being Group of people +O+U-D+R +I-O~U-D+R Social entity -I+U-D+R Animal +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R 107
Entity-I-U-D+R Location +O-U-D+R Amount of matter Group • For phased sortals: what do they phase +O~U-D+R into? Physical object • +O+U-D+R Country is anti-rigid Living beingbecause it is +O+U-D+R representing multiple senses of country: a geographical region Social and aentity political Fruit -I+U-D+R entity. +O+U-D+R Animal Group of people • Split the two+O+U-D+R senses into two concepts, +I-O~U-D+R Apple both rigid, both types. +O~U-D+R +O+U-D+R Country Analyze Phased Sortals Vertebrate +I-O+U-D+R +L+U-D~R Person +O+U-D+R Organization +O+U-D+R 108
Entity-I-U-D+R Location Analyze Phased Sortals Amount of matter Group +O~U-D+R +O-U-D+R +O~U-D+R Physical object • There+O+U-D+R is an Living being +O+U-D+R relationship between the two, but not Social entity Fruit -I+U-D+R subsumption. +O+U-D+R Animal Group of people +O+U-D+R +I-O~U-D+R Apple +O+U-D+R Geographical Country Region Vertebrate +I-O+U-D+R Country +O+U-D+R +L+U-D~R +O-U-D+R Person +O+U-D+R Organization +O+U-D+R 109
Entity-I-U-D+R Analyze Phased Sortals • Caterpillar phases into Amount of matter Location Group butterfly - +O~U-D+R a true +O-U-D+R +O~U-D+R phased sortal • Define a rigid Physical object • There must be+O+U-D+R some Living being property which +O+U-D+R property from which a subsumes only single entity can the entity phases of the Social Fruit -I+U-D+R uniquely +O+U-D+R claim same entity. Animal +O+U-D+R identity across phases Group of people +I-O~U-D+R Apple +O+U-D+R Geographical Region +O-U-D+R Lepidopteran Vertebrate +O+U-D+R +I-O+U-D+R Caterpillar +L+U-D~R +O+U-D+R Butterfly +L+U-D~R Country Person +O+U-D+R Organization +O+U-D+R 110
Entity-I-U-D+R Location Amount of matter +O-U-D+R +O~U-D+R +O+U-D+R Fruit +O+U-D+R Apple +O+U-D+R Geographical Region Group +O~U-D+R Physical object +O-U-D+R Analyze Phased Sortals • Try for a type, Living being may be quasi. +O+U-D+R • IC for Lepidopteran Social entity -I+U-D+R could be same. Animal +O+U-D+R of people cocoon. Group +I-O~U-D+R Lepidopteran Vertebrate +O+U-D+R +I-O+U-D+R Caterpillar +L+U-D~R +O+U-D+R Butterfly +L+U-D~R Country Person +O+U-D+R Organization +O+U-D+R 111
Entity-I-U-D+R Location Analyze Roles Amount of matter Group Agent • ~R can’t subsume +O~U-D+R -I-U+D~R +R Physical object +O+U-D+R Living being • Really want a type +O+U-D+R restriction: all agents are animals Social entity Fruit -I+U-D+R +O+U-D+R or social entities. Animal Group of people • Subsumption is not +O+U-D+R +I-O~U-D+R Apple disjunction! +O+U-D+R +O-U-D+R Geographical Region +O-U-D+R +O~U-D+R Lepidopteran Vertebrate +O+U-D+R +I-O+U-D+R Caterpillar +L+U-D~R +O+U-D+R Butterfly +L+U-D~R Country Person +O+U-D+R Organization +O+U-D+R 112
Entity-I-U-D+R Location Analyze Roles Amount of matter Group Agent • ~R can’t subsume +O~U-D+R -I-U+D~R +R Physical object +O+U-D+R Living being • Really want a type +O+U-D+R restriction: all agents are animals Social entity Fruit -I+U-D+R +O+U-D+R or social entities. Animal Group of people • Subsumption is not +O+U-D+R +I-O~U-D+R Apple disjunction! +O+U-D+R +O-U-D+R Geographical Region +O-U-D+R +O~U-D+R Lepidopteran Vertebrate +O+U-D+R +I-O+U-D+R Caterpillar +L+U-D~R +O+U-D+R Butterfly +L+U-D~R Country Person +O+U-D+R Organization +O+U-D+R 113
Entity-I-U-D+R Location Analyze Roles Amount of matter Group Agent • ~R can’t subsume +R +O~U-D+R -I-U+D~R • Another. Physical disjunction: object all Living being legal agents+O+U-D+R are Legal agent +O+U-D+R +L-U+D~R countries, persons, or organizations Social entity Fruit +O-U-D+R +O~U-D+R +O+U-D+R Animal -I+U-D+R Group of people +O+U-D+R +I-O~U-D+R Apple +O+U-D+R Geographical Region +O-U-D+R Lepidopteran Vertebrate +O+U-D+R +I-O+U-D+R Caterpillar +L+U-D~R +O+U-D+R Butterfly +L+U-D~R Country Person +O+U-D+R Organization +O+U-D+R 114
Entity-I-U-D+R Location Analyze Roles Amount of matter Group Agent • ~R can’t subsume +R +O~U-D+R -I-U+D~R • Another. Physical disjunction: object all Living being legal agents+O+U-D+R are Legal agent +O+U-D+R +L-U+D~R countries, persons, or organizations Social entity Fruit +O-U-D+R +O~U-D+R +O+U-D+R Animal -I+U-D+R Group of people +O+U-D+R +I-O~U-D+R Apple +O+U-D+R Geographical Region +O-U-D+R Lepidopteran Vertebrate +O+U-D+R +I-O+U-D+R Caterpillar +L+U-D~R +O+U-D+R Butterfly +L+U-D~R Country Person +O+U-D+R Organization +O+U-D+R 115
Entity-I-U-D+R Location Analyze Roles Amount of matter +O-U-D+R +O~U-D+R Agent Group +O~U-D+R -I-U+D~R can’t subsume +R • ~R Physical object Apple is not +O+U-D+R Living • being Legalfood. agent A Food +O+U-D+R necessarily +L-U+D~R +I-O~U+D~R poison-apple, e. g. , is Social entity Fruit still -I+U-D+R an apple. +O+U-D+R Animal +O+U-D+R • ~U can’t subsume Group of+U people +I-O~U-D+R • Caterpillars are wholes, Apple +O+U-D+R food is stuff. Lepidopteran Vertebrate Geographical Region +O-U-D+R +O+U-D+R Caterpillar +L+U-D~R +I-O+U-D+R +O+U-D+R Butterfly +L+U-D~R Country Person +O+U-D+R Organization +O+U-D+R 116
Entity-I-U-D+R Location Analyze Roles Amount of matter +O-U-D+R +O~U-D+R Agent Group +O~U-D+R -I-U+D~R can’t subsume +R • ~R Physical object Apple is not +O+U-D+R Living • being Legalfood. agent A Food +O+U-D+R necessarily +L-U+D~R +I-O~U+D~R poison-apple, e. g. , is Social entity Fruit still -I+U-D+R an apple. +O+U-D+R Animal +O+U-D+R • ~U can’t subsume Group of+U people +I-O~U-D+R • Caterpillars are wholes, Apple +O+U-D+R food is stuff. Lepidopteran Vertebrate Geographical Region +O-U-D+R +O+U-D+R Caterpillar +L+U-D~R +I-O+U-D+R +O+U-D+R Butterfly +L+U-D~R Country Person +O+U-D+R Organization +O+U-D+R 117
Entity-I-U-D+R Analyze Attributions Amount of matter Location +O~U-D+R +O-U-D+R Agent Group +O~U-D+R -I-U+D~R violations • No Physical object Attributions are +O+U-D+R Living • being Legal agent Food +O+U-D+R discouraged, can be +L-U+D~R +I-O~U+D~R confusing. Red Social entity Fruit -I-U-D-R -I+U-D+R • Often better to use +O+U-D+R Animal +O+U-D+R attribute values (i. e. Group of people +I-O~U-D+R Apple Color red) Apple +O+U-D+R Geographical Region +O-U-D+R Red apple +I-O+U-D~R Lepidopteran Vertebrate +O+U-D+R +I-O+U-D+R Caterpillar +L+U-D~R +O+U-D+R Butterfly +L+U-D~R Country Person +O+U-D+R Organization +O+U-D+R 118
Entity-I-U-D+R Amount of matter Location +O~U-D+R +O-U-D+R Group Agent +O~U-D+R -I-U+D~R Physical object Food +O+U-D+R Living being +I-O~U+D~R Fruit Red +O+U-D+R Legal agent +O+U-D+R +L-U+D~R Social entity -I-U-D-R Animal -I+U-D+R Group of people +O+U-D+R +I-O~U-D+R Apple +O+U-D+R Geographical Region +O-U-D+R Red apple +I-O+U-D~R Lepidopteran Vertebrate +O+U-D+R +I-O+U-D+R Caterpillar +L+U-D~R +O+U-D+R Butterfly +L+U-D~R Country Person +O+U-D+R Organization +O+U-D+R 119
Entity-I-U-D+R Location The backbone taxonomy Amount of matter +O-U-D+R Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Social entity Fruit +O+U-D+R Animal -I+U-D+R Group of people +O+U-D+R +I-O~U-D+R Apple +O+U-D+R Geographical Region Lepidopteran Vertebrate +O+U-D+R +I-O+U-D+R Country +O+U-D+R +O-U-D+R Person +O+U-D+R Organization +O+U-D+R 120
Entity-I-U-D+R Amount of matter Location +O~U-D+R +O-U-D+R Group Agent +O~U-D+R -I-U+D~R Physical object Food +O+U-D+R Living being +I-O~U+D~R Fruit Red +O+U-D+R Legal agent +O+U-D+R +L-U+D~R Social entity -I-U-D-R Animal -I+U-D+R Group of people +O+U-D+R +I-O~U-D+R Apple +O+U-D+R Geographical Region +O-U-D+R Red apple +I-O+U-D~R Lepidopteran Vertebrate +O+U-D+R +I-O+U-D+R Caterpillar +L+U-D~R +O+U-D+R Butterfly +L+U-D~R Country Person +O+U-D+R Organization +O+U-D+R 121
Membership relationships 122
Framework Conceptualization Conceptual Model Ontology User Methodology Minimal Top-Level Ontology � Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations 123
Singular vs. Plural • Singular objects: strongly self-connected • Plural objects: – Collections – Plural wholes – Mere sums 124
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) – Tree 1 is a member of “The. Forest” The. Forest(Tree 1) ? ? (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. . . 125
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. 126
Part-whole relationships 127
Part-of vs. part-whole relations • • • component/integral object member/collection portion/mass stuff/object place/area feature/activity 128
Framework Conceptualization Conceptual Model Ontology User Methodology � Minimal Top-Level Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations 129
A Minimal Top-level Ontology Entity Particular Concrete particular Location Object Abstract particular Set Structure … Universal Property Kinds. . . Relation 130
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) 131
Ontologists Wanted!
Announcing. . . FOIS 2001 Formal Ontology in Information Systems Check out www. fois. org
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