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

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)

Ontology and ontologies

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.

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

“An ontology is a specification of a conceptualization” [Gruber 95] 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]

Models and Conceptualizations

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

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)

What is a conceptualization? Scene 1: blocks on a table Conceptualization of scene 1: <{a, b, c, d, e }, {on, above, clear, table }>

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

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 LI LE

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>

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

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 Relational model we don’t mean ER diagram

Our Framework: Ontology-Driven Conceptual Modeling

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.

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

Framework Ontology User Methodology Minimal Top-Level Ontology Conceptual Model Conceptualization Ontology User Methodology Minimal Top-Level Ontology This slide is changed from the handouts. Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations

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 This slide not in handouts

Formal Ontological Analysis Mereology Identity, Unity, Essence Dependence

Mereology

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)

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

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

Identity, Unity, Essence

Framework  Ontology User Methodology Minimal Top-Level Ontology Conceptual Model Conceptualization Ontology User Methodology Minimal Top-Level Ontology New slide added for presentation purposes Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations 

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…

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

Essence and rigidity

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.

Formal Rigidity f is rigid (+R): x f(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

Identity and identity criteria

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

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

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.

f(x,t)  f(y,t’)  (G(x,y, t ,t’) x = y) 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)

Necessary ICs A formula G is a necessary IC for f if … provided that: 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’)

f(x,t)  f(y,t’)  G(x,y,t,t’)  x=y 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’)

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 This slide is changed from the handouts.

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) This slide was not in the original handouts.

Unity and Unity Criteria

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?

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?

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

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?

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 This slide has been moved ahead and rewritten.

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)

Properties with incompatible IC/UC are disjoint Disjointness Theorem Properties with incompatible IC/UC are disjoint

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

Dependence

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)

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.

Using the meta-properties

Framework  Ontology User Methodology Minimal Top-Level Ontology Conceptual Model Conceptualization Ontology User Methodology  Minimal Top-Level Ontology New slide added for presentation purposes Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations

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

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: Amount of matter: Result According to the most common understanding, both ontologies are wrong, each concept is at the top-level

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

Property Kinds

Framework  Ontology User Methodology Minimal Top-Level Ontology Conceptual Model Conceptualization Ontology User Methodology Minimal Top-Level Ontology New slide added for presentation purposes Ontology-Driven Modeling Principles Useful Property Kinds  Formal Ontological Properties/Relations

Basic Property kinds

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)

A formal ontology of properties 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 Property

Basic Property Kinds Table

Further Property Kinds: Common ICs/UCs

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.

Identity and unity conditions

Ontology-driven Modeling Principles

Framework  Ontology User Methodology Minimal Top-Level Ontology Conceptual Model Conceptualization Ontology User Methodology Minimal Top-Level Ontology New slide added for presentation purposes Ontology-Driven Modeling Principles  Useful Property Kinds Formal Ontological Properties/Relations

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

Taxonomic relationships

Subsumption Misused To express disjunction To express constitution 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

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

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

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

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

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

An extended example

Framework  Ontology User Methodology Minimal Top-Level Ontology Conceptual Model Conceptualization Ontology User Methodology  Minimal Top-Level Ontology New slide added for presentation purposes Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations

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

Assign Meta-Properties

Property Analysis Entity, Location 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 Thsi slide is changed from the handouts

Property Analysis Amount of Matter, Red 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 Thsi slide is changed from the handouts

Property Analysis Agent, Group 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

Property Analysis Physical Object, Living Being 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

Property Analysis Food, Animal +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

Property Analysis Legal Agent, Group of People 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

Property Analysis Social Entity, Organization 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

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

Property Analysis Apple, Red 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

Property Analysis Vertebrate, Person 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

Property Analysis Butterfly, Caterpillar +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

Property Analysis 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

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

Living being is constituted of matter Entity-I-U-D+R Analyze taxonomic links Location +O-U-D+R Amount of matter +O~U-D+R ~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 Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+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

Living being is constituted of matter Entity-I-U-D+R Analyze taxonomic links Location +O-U-D+R Amount of matter +O~U-D+R ~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 Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+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

Physical object is constituted of matter Entity-I-U-D+R Analyze taxonomic links Location +O-U-D+R Amount of matter +O~U-D+R ~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 Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+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

Physical object is constituted of matter Entity-I-U-D+R Analyze taxonomic links Location +O-U-D+R Amount of matter +O~U-D+R ~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 Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+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

Entity-I-U-D+R Analyze taxonomic links Location +O-U-D+R Amount of matter +O~U-D+R 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 Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+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

Entity-I-U-D+R Analyze taxonomic links Location +O-U-D+R Amount of matter +O~U-D+R 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 Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+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

Entity-I-U-D+R Analyze taxonomic links Location +O-U-D+R Amount of matter +O~U-D+R ~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 Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+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

Entity-I-U-D+R Analyze taxonomic links Location +O-U-D+R Amount of matter +O~U-D+R ~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 Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+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

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

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

Entity-I-U-D+R Location Amount of matter Group Physical object +O-U-D+R Amount of matter +O~U-D+R Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+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

For phased sortals: what do they phase into? Entity-I-U-D+R Analyze Phased Sortals Amount of matter +O~U-D+R Location +O-U-D+R 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. Group +O~U-D+R Country +L+U-D~R Physical object +O+U-D+R Living being +O+U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Person +O+U-D+R Organization +O+U-D+R

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

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

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

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

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

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

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

Caterpillars are wholes, food is stuff. Entity-I-U-D+R Analyze Roles Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R Agent -I-U+D~R Food +I-O~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. Physical object +O+U-D+R Living being +O+U-D+R Legal agent +L-U+D~R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Lepidopteran +O+U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Country +O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Person +O+U-D+R Organization +O+U-D+R

Caterpillars are wholes, food is stuff. Entity-I-U-D+R Analyze Roles Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R Agent -I-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. Physical object +O+U-D+R Living being +O+U-D+R Food +I-O~U+D~R Legal agent +L-U+D~R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Lepidopteran +O+U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Country +O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Person +O+U-D+R Organization +O+U-D+R

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

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

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

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

Membership relationships

Framework  Ontology User Methodology Minimal Top-Level Ontology Conceptual Model Conceptualization Ontology User Methodology Minimal Top-Level Ontology New slide added for presentation purposes Ontology-Driven Modeling Principles  Useful Property Kinds Formal Ontological Properties/Relations

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

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...

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.

Part-whole relationships

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

Framework  Ontology User Methodology Minimal Top-Level Ontology Conceptual Model Conceptualization Ontology User Methodology Minimal Top-Level Ontology New slide added for presentation purposes  Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations

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

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)

Ontologists Wanted!

FOIS 2001 Formal Ontology in Information Systems Announcing... FOIS 2001 Formal Ontology in Information Systems Check out www.fois.org