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Formal Ontology. Schedule. Sep. 4: Introduction: Mereology , Dependence and Geospatial Ontology Reading: Basic Tools of Formal Ontology Ontological Tools for Geographic Representation. Schedule.

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Schedule
Schedule

  • Sep. 4: Introduction: Mereology , Dependence and Geospatial Ontology

  • Reading:

  • Basic Tools of Formal Ontology

  • Ontological Tools for Geographic Representation


Schedule1
Schedule

  • Sep. 5: (Thursday) 4pm Metaphysics talk by David Hershenov (Jointly with Philosophy Department Colloquium)

  • Sep. 11: Talk by Peter Forrest on Mereology and Time. (Jointly with Philosophy Department Colloquium)

  • Sep. 18: Truthmaking and the Semantics of Maps

  • Sep. 25: Vagueness


Schedule2
Schedule

  • Oct. 2: Granularity

  • Reading: A Theory of Granular Partitions

  • [Oct. 9 University Convocation: No meeting]

  • Oct. 16: Talk by Chuck Dement on: " The Ontology of Formal Ontology"

  • [Oct. 23 No meeting]

  • [Oct. 30 No meeting]


Schedule3
Schedule

  • Nov. 6: 2pm “SNAP and SPAN”: Cognitive Science Colloquium Talk, 280 Park

  • Nov 6: 4pm Discussion of "SNAP and SPAN“

  • Nov. 8 (Friday): 4pm Talk by Berit Brogaard


Schedule4
Schedule

  • Nov. 9 Day-long Saturday Workshop

  • 9am Achille Varzi: " From Ontology to Metaphysics"

  • 10.45 am Berit Brogaard

  • 12.30 Pizza Lunch

  • 1pm Achille Varzi: "Ontology and Logical Form"

  • 3-5pm Barry Smith

  • Nov. 13 Final Lecture


Ifomis
IFOMIS

  • Institute for Formal Ontology and Medical Information Science

  • Some background


The manchester school
The Manchester School

  • Kevin Mulligan

  • Peter Simons

  • Barry Smith

  • in Manchester 1973-76

  • working on the ontology of Edmund Husserl



Logical investigations 1900 01
Logical Investigations¸1900/01

  • the theory of part and whole

  • the theory of dependence

  • the theory of boundary, continuity and contact


Formal ontology1
Formal Ontology

  • (term coined by Husserl)

  • the theory of those ontological structures

  • (such as part-whole, universal-particular)

  • which apply to all domains whatsoever


Formal ontology vs formal logic
Formal Ontology vs. Formal Logic

  • Formal ontology deals with the interconnections of things

  • with objects and properties, parts and wholes, relations and collectives

  • Formal logic deals with the interconnections of truths

  • with consistency and validity, or and not


Formal ontology vs formal logic1
Formal Ontology vs. Formal Logic

  • Formal ontology deals with formal ontological structures

  • Formal logic deals with formal logical structures

  • ‘formal’ = obtain in all material spheres of reality


Formal ontology and symbolic logic
Formal Ontology and Symbolic Logic

  • Great advances of Frege, Russell, Wittgenstein

  • Leibnizian idea of a universal characteristic

  • …symbols are a good thing


Warning
Warning

  • don’t confuse Logical with Ontological Form

  • Russell

  • Part-whole is not a logical relation


  • for Frege, Russell, Lesniewski,

  • Wittgenstein, Quine

  • Logic is a ‘Zoology of Facts’

  • Formal theories are theories of reality

  • with one intended interpretation

  • = the world

tragically

after starting off on the right road





Ifomis ontology
IFOMIS Ontology

  • is an ontology of reality

  • Standard Information Systems Ontologies

  • are ontologies of mere 'models'


Standard information systems ontologies
Standard Information Systems Ontologies:

  • programming real ontology into computers is hard

  • therefore: we will simplify ontology

  • and not care about reality at all


Painting the emperor s palace is hard
Painting the Emperor´s Palace ishard


Therefore
therefore

  • we will not try to paint the Palace at all

  • ... we will be satisfied instead with a grainy snapshot of some other building


Ifomis strategy
IFOMIS Strategy

  • get real ontology right first

  • and then investigate ways in which this real ontology can be translated into computer-useable form later

  • NOT ALLOW ISSUES OF COMPUTER-TRACTABILITY TO DETERMINE THE CONTENT OF ONTOLOGY


A language to map these
a language to map these

  • Formal ontological structures in reality


A directly depicting language

Property

Object

a directly depicting language

  • ‘John’ ‘( ) is red’

Frege


Wittgenstein s tractatus

are pictures of

Wittgenstein’s Tractatus

  • Propositions

  • States of affairs


Parts and moments
Parts and Moments

  • in a directly depicting language

  • all well-formed parts of a true formula are also true

  • (The Oil-Painting Principle)

A new sort of mereological inference rule

– the key to the idea of a directly depicting language



A directly depicting language1
A directly depicting language

  • may contain an analogue of conjunction

  • p and q

  • _______

  • p



And also no disjunction
and also no disjunction

  • p or q

  • ______

  • p


The idea of a directly depicting language
The idea of a directly depicting language

  • suggests a new method

  • of constituent ontology:

  • to study a domain ontologically

  • is to establish the parts, qualities and processes of the domain

  • and the interrelations between them


Bfo and gol
BFO and GOL

  • Basic Formal Ontology (BFO)

  • BFO as an ontological theory of reality designed as a real constraint on domain ontologies

  • (as opposed to conceptual modeling ...)


A network of domain ontologies
A Network of Domain Ontologies

  • Material (Regional) Ontologies

Basic Formal Ontology


Ontology
Ontology

  • seeks an INVENTORY OF REALITY

  • Relevance of ontology for information systems, e.g.:

  • terminology standardization

  • taxonomy standardization

  • supports reasoning about reality


BFO

  • Basic Formal Ontology

  • = a formal ontological theory, expressed in a directly depicting language, of all non-intentional parts of reality

  • (an ontology of the whole of reality but leaving aside minds and meanings)







Extended formal ontology bfo extended by mind
Extended formal ontology(BFO Extended by Mind)







Reality3
Reality

is complicated



Anglocentric realism
Anglocentric Realism

  • We have a huge amount of knowledge of reality,

  • at many different levels of granularity,

  • from microphysics to cosmology


Anglocentric realism1
Anglocentric Realism

  • TEE = Technically Extended English

  • = English extended by the technical vocabularies of

  • meteorology, chemistry, genetics, medicine, astronomy, engineering, etc.


Anglocentric realism2
Anglocentric Realism

  • Our knowledge of reality as expressed in Technically Extended English

  • is increasing by the hour


Unfortunately
Unfortunately

  • … there are problems with TEE as a formal representation language

  • (cf. Tarski)


Nouns and verbs
Nouns and verbs

  • Substances and processes

  • Continuants and occurrents

  • In preparing an inventory of reality

  • we keep track of these two different categories of entities in two different ways


Natural language

t i m e

process

Natural language

  • glues them together indiscriminately

substance


Snapshot vs video

t i m e

process

Snapshot vs. Video

substance


Substances
Substances

  • Mesoscopic reality is

  • divided at its natural joints

  • into substances:

  • animals, bones, rocks, potatoes


The ontology of substances
The Ontology of Substances

  • Substances form natural kinds

  • (universals, species + genera)


Processes
Processes

  • Processes merge into one another

  • Process kinds merge into one another

  • … few clean joints either between instances or between types


Processes1

t i m e

Processes


Substances and processes

t i m e

process

Substances and processes

demand different sorts of inventories


Substances demand 3 d partonomies

space

Substances demand 3-D partonomies


Processes demand 4d partonomies

t i m e

Processes demand 4D-partonomies


Processes2
Processes

  • a whistling, a blushing, a speech

  • a run, the warming of this stone


Processes may have temporal parts
Processes may have temporal parts

  • The first 5 minutes of my headache is a temporal part of my headache

  • The first game of the match is a temporal part of the whole match


Substances do not have temporal parts
Substances do not have temporal parts

  • The first 5-minute phase of my existence is not a temporal part of me

  • It is a temporal part of that complex process which is my life





You are a substance
You system of representations? are a substance

  • Your life is a process

  • You are 3-dimensional

  • Your life is 4-dimensional


Substances and processes form two distinct orders of being
Substances and processes form two distinct orders of being system of representations?

  • Substances exist as a whole at every point in time at which they exist at all

  • Processes unfold through time, and are never present in full at any given instant during which they exist.

When do both exist to be inventoried together?


Main problem
Main problem system of representations?

  • English swings back and forth between two distinct depictions of reality

  • … imposing both 3-D partitions (yielding substances) and 4-D partitions (yielding processes) at the same time


Main problem1
Main problem system of representations?

  • There is a polymorphous ontological promiscuity of the English sentence,

  • which is inherited also by the form ‘F(a)’


Two alternative basic ontologies
Two alternative basic ontologies system of representations?

  • SNAP and SPAN

  • SNAP = substances plus qualities

  • SPAN = processes


These represent two views
These represent two views system of representations?

  • of the same rich and messy reality, the reality captured promiscuously by TEE


The four dimensionalist ontology

t i m e system of representations?

The Four-Dimensionalist Ontology


Boundaries are mostly fiat

t i m e system of representations?

boundaries are mostly fiat

everything is flux


Mereology works without restriction everywhere here

clinical trial system of representations?

t i m e

mereology works without restriction everywhere here


The time stamped ontology
The Time-Stamped Ontology system of representations?

t3

t2

t1

here time exists outside the ontology, as an index or time-stamp



Three views partitions of the same reality
Three views/partitions of the same reality 3-D section through reality


All contain huge amounts of knowledge of this reality
all contain huge amounts of knowledge of this reality 3-D section through reality

against Kant


Ontological zooming
Ontological Zooming 3-D section through reality

  • The dimension of granularity


Part 2

Part 2 3-D section through reality

Tools of Ontology:

Mereology, Topology, Dependence


Ontological dependence
Ontological Dependence 3-D section through reality

processes

+ qualities

substances


Ontological dependence1
Ontological Dependence 3-D section through reality

  • How to link together the domain of substances and the domain of processes?


Ontological dependence2
Ontological Dependence 3-D section through reality

  • Substances are that which can exist on their own

  • Processes require a support from substances in order to exist

  • This holds for qualities, too


Specific dependence
Specific Dependence 3-D section through reality

  • O := overlap

  • x := x is necessarily such that

  • E! := existence

  • SD(x, y) := O(x, y) x(E!x  E!y)


Mutual specific dependence
Mutual specific dependence 3-D section through reality

  • Each token of visual extension is mutually dependent on a token color quality

  • The north pole of a magnet is mutually dependent on the south pole

  • MSD(x, y) := SD(x, y)  SD(y, x)


One sided specific dependence
One-Sided Specific Dependence 3-D section through reality

  • OSD(x, y) := SD(x, y) MSD(x, y)

  • My headache is one-sidedly specifically dependent on me.


Substances qualities processes
Substances, Qualities, Processes 3-D section through reality

  • Substances are the bearers or carriers of qualities and processes,

  • … the latter are said to ‘inhere’ in their substances


Ontological dependence3
Ontological Dependence 3-D section through reality

  • Substances are such that, while remaining numerically one and the same, they can admit contrary qualities at different times

  • … I am sometimes hungry, sometimes not


Substances1
Substances 3-D section through reality

  • can also gain and lose parts

  • … as an organism may gain and lose molecules


Types of relations between parts
Types of relations between parts 3-D section through reality

  • 1. Dependence relations

  • 2. Side-by-sideness relations

  • 3. Fusion relations


Dependence
Dependence 3-D section through reality

process

a thinking

cannot exist without a thinker

substance


Theory of vagueness
Theory of vagueness 3-D section through reality

Side-by-sideness

found among substances

and among qualities and processes


Fusion
Fusion 3-D section through reality

Topology


Topology like mereology
Topology, like mereology, 3-D section through reality

  • applies both in the realm of substances and in the realms of qualities and processes


Mereotopology
Mereotopology 3-D section through reality

  • = topology on a mereological basis


Substances undetached parts and heaps
Substances, Undetached Parts and Heaps 3-D section through reality

  • Substances are unities.

  • They enjoy a natural completeness

  • in contrast to their undetached parts (arms, legs)

  • and to heaps or aggregates

  • … these are topological distinctions


substance 3-D section through reality

undetached part

collective of

substances


Special sorts of undetached parts
special sorts of undetached parts 3-D section through reality

  • ulcers

  • tumors

  • lesions


Fiat boundaries

physical (bona fide) boundary 3-D section through reality

fiat boundary

Fiat boundaries


Examples
Examples 3-D section through reality

  • of bona fide boundaries:

  • an animal’s skin, the surface of the planet

  • of fiat boundaries:

  • the boundaries of postal districts and census tracts


Mountain
Mountain 3-D section through reality

  • bona fide upper boundaries

  • with a fiat base:


Architects plan for a house
Architects Plan for a House 3-D section through reality

  • fiat upper boundaries

  • with a bona fide base:


Where does the mountain start
where does the mountain start ? 3-D section through reality

... a mountain is not a substance


nose 3-D section through reality

...and it’s not a quality, either


A substance has a complete physical boundary
A substance has a complete physical boundary 3-D section through reality

  • The latter is a special sort of part of a substance

  • … a boundary part

  • something like a maximally thin extremal slice


boundary 3-D section through reality

substance

interior


A substance takes up space
A substance takes up space. 3-D section through reality

  • A substance occupies a place or topoid (which enjoys an analogous completeness or rounded-offness)

  • A substance enjoys a place at a time


A substance has spatial parts
A substance has spatial parts 3-D section through reality

  • … perhaps also holes


Each substance is such as to have divisible bulk
Each substance is such as to have 3-D section through realitydivisible bulk:

  • it can in principle be divided into separate spatially extended substances


By virtue of their divisible bulk
By virtue of their 3-D section through realitydivisible bulk

  • substances compete for space:

  • (unlike shadows and holes)

  • no two substances can occupy the same spatial region at the same time.


Substances vs collectives
Substances vs. Collectives 3-D section through reality

  • Collectives = unified aggregates: families, jazz bands, empires

  • Collectives are real constituents of reality (contra sets)

  • but still they are not additional constituents, over and above the substances which are their parts.


Collectives inherit some but not all of the ontological marks of substances
Collectives inherit some, but not all, of the ontological marks of substances

  • They can admit contrary qualities at different times.


Collectives
Collectives, marks of substances

  • like substances,

  • may gain and lose parts or members

  • may undergo other sorts of changes through time.


Qualities and processes too may form collectives
Qualities and processes, too, may form collectives marks of substances

  • a musical chord is a collective of individual tones

  • football matches, wars, plagues are collectives of actions involving human beings


One place qualities and processes
One-place qualities and processes marks of substances

  • depend on one substance

  • (as a headache depends upon a head)


kiss marks of substances

John

Mary

  • Relational qualities and processes

stand in relations of one-sided dependence to a plurality of substances simultaneously


Examples of relational qualities and processes
Examples of relational qualities and processes marks of substances

  • kisses, thumps, conversations,

  • dances, legal systems

  • Such real relational entities

  • join their carriers together into collectives of greater or lesser duration


Mereology
Mereology marks of substances

  • ‘Entity’ = absolutely general ontological term of art

  • embracing at least: all substances, qualities, processes, and all the wholes and parts thereof, including boundaries


Primitive notion of part
Primitive notion of part marks of substances

  • ‘x is part of y’ in symbols: ‘x ≤ y’


We define overlap as the sharing of common parts
We define overlap as the sharing of common parts: marks of substances

  • O(x, y) := z(z ≤ x  z ≤ y)


Axioms for basic mereology
Axioms for basic mereology marks of substances

  • AM1 x ≤ x

  • AM2 x ≤ y  y ≤ x  x = y

  • AM3 x ≤ y  y ≤ z  x ≤ z

  • Parthood is a reflexive, antisymmetric, and transitive relation, a partial ordering.


Extensionality
Extensionality marks of substances

  • AM4 z(z ≤ x  O(z, y))  x ≤ y

  • If every part of x overlaps with y

  • then x is part of y

  • cf. status and bronze


Sum marks of substances

  • AM5 x(x) 

  • y(z(O(y,z) x(x  O(x,z))))

  • For every satisfied property or condition  there exists an entity, the sum of all the -ers


Definition of sum
Definition of Sum marks of substances

  • x(x) := yz(O(y,z) x(x  O(x,z)))

  • The sum of all the -ers is that entity which overlaps with z if and only if there is some -er which overlaps with z


Examples of sums
Examples of marks of substancessums

  • electricity, Christianity, your body’s metabolism

  • the Beatles, the population of Erie County, the species cat


Other boolean relations
Other Boolean Relations marks of substances

  • x  y := z(z ≤ x  z ≤ y) binary sum

  • x  y := z(z ≤ x  z ≤ y) product


Other boolean relations1
Other Boolean Relations marks of substances

  • x – y := z (z ≤ x  O(z, y)) difference

  • –x := z (O(z, x)) complement


What is a substance
What is a Substance? marks of substances

  • Bundle theories: a substance is a whole made up of tropes as parts.

  • What holds the tropes together?

  • ... problem of unity


Topology
Topology marks of substances

  • How can we transform a sheet of rubber in ways which do not involve cutting or tearing?


Topology1
Topology marks of substances

  • We can invert it, stretch or compress it, move it, bend it, twist it. Certain properties will be invariant under such transformations –

  • ‘topological spatial properties’


Topology2
Topology marks of substances

  • Such properties will fail to be invariant under transformations which involve cutting or tearing or gluing together of parts or the drilling of holes


Examples of topological spatial properties
Examples of topological spatial properties marks of substances

  • The property of being a (single, connected) body

  • The property of possessing holes (tunnels, internal cavities)

  • The property of being a heap

  • The property of being an undetached part of a body


Examples of topological spatial properties1
Examples of topological spatial properties marks of substances

  • It is a topological spatial property of a pack of playing cards that it consists of this or that number of separate cards

  • It is a topological spatial property of my arm that it is connected to my body.


Topological properties
Topological Properties marks of substances

  • Analogous topological properties are manifested also in the temporal realm:

  • they are those properties of temporal structures which are invariant under transformations of

  • slowing down, speeding up, temporal translocation …


Topological properties1
Topological Properties marks of substances


Topology and boundaries
Topology and Boundaries marks of substances

  • Open set: (0, 1)

  • Closed set: [0, 1]

  • Open object:

  • Closed object:


Closure
Closure marks of substances

  • = an operation which when applied to an entity x yields a whole which comprehends both x and its boundaries

  • use notion of closure to understand structure of reality in an operation-free way


Axioms for closure
Axioms for Closure marks of substances

  • AC1: each entity is part of its closure

  • AC2: the closure of the closure adds nothing to the closure of an object

  • AC3: the closure of the sum of two objects is equal to the sum of their closures


Axioms for closure1
Axioms for Closure marks of substances

  • AC1 x ≤ c(x) expansiveness

  • AC2 c(c(x)) ≤ c(x) idempotence

  • AC3 c(x  y) = c(x)  c(y) additivity


Axioms for closure2
Axioms for Closure marks of substances

  • These axioms define in mereological terms a well-known kind of structure, that of a closure algebra, which is the algebraic equivalent of the simplest kind of topological space.


Boundary
Boundary marks of substances

  • b(x) := c(x)  c(–x)

  • The boundary of an entity is also the boundary of the complement of the entity


Interior

x marks of substances

boundary

interior

Interior

  • i(x) := x – b(x)


An entity and its complement
An entity and its complement marks of substances

  • -x

x


The entity alone
The entity alone marks of substances

x


The complement alone
The complement alone marks of substances

  • -x


Closed and open objects
Closed and Open Objects marks of substances

  • x is closed := x is identical with its closure

  • x is open := x is identical with its interior

  • The complement of a closed object is open

  • The complement of an open object is closed

  • Some objects are partly open and partly closed


Definining topology
Definining Topology marks of substances

  • Topological transformations = transformations which take open objects to open objects

  • e.g. moving, shrinking

x


Closed objects
Closed Objects marks of substances

  • A closed object is an independent constituent of reality:

  • It is an object which exists on its own, without the need for any other object which would serve as its host


Contrast holes
Contrast marks of substancesholes

  • a hole requires a host


A closed object need not be connected
A closed object need not be marks of substancesconnected



Or slits
…. or slits marks of substances


Connectedness
Connectedness marks of substances

  • Definition

  • An object is connected

  • if we can proceed from any part of the object to any other

  • and remain within the confines of the object itself


Connectedness1
Connectedness marks of substances

  • A connected object is such that all ways of splitting the object into two parts yield parts whose closures overlap

  • Cn(x) :=

  • yz(x = yz w(w ≤ (c(y)c(z))))


Connectedness2
Connectedness* marks of substances

  • A connected* object is such that,

  • given any way of splitting the object into two parts x and y,

  • either x overlaps with the closure of y

  • or y overlaps with the closure of x

  • Cn*(x) := yz(x = y  z 

  • (w(w ≤ x  w ≤ c(y))  w(w ≤ y  w ≤ c(x)))


Problems
Problems marks of substances


Problem
Problem marks of substances

  • A whole made up of two adjacent spheres which are momentarily in contact with each other will satisfy either condition of connectedness

  • Strong connectedness rules out cases such as this


Strong connectedness
Strong connectedness marks of substances

  • Scn(x) := Cn*(i(x))

  • An object is strongly connected if its interior is connected*


Definition of substance
Definition of Substance marks of substances

  • A substance is a maximally strongly connected non-dependent entity:

  • S(x) := Scn(x) y(x ≤ y  Scn(y)  x = y) zSD(x, z)


More needed
More needed marks of substances

  • Substances are located in spatial regions


More needed1
More needed marks of substances

  • Some substances have a causal integrity without being completely disconnected from other substances:

  • heart

  • lung

  • Siamese twin


Time marks of substances

  • Substances can preserve their numerical identity over time

  • Full treatment needs an account of:

  • spatial location

  • transtemporal identity

  • causal integrity, matter

  • internal organization


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