Ontobras 2019 - Tutorial: Relationships and events: a general theory of reification and truthmaking
By Nicola Guarino
*My own comments are marked with an asterisk
Reifying relationships allows us to talk of:
- their nature
- the way they change in time
etc.
In Data Modeling, this has also been clear from the early stages. For instance, ER (Chen) includes a syntactical representation of relationship reification (diamond).
----
Relation vs. Relationship
- Common view: relation is a class of tuples.
- Chen: a relationship type is a set of tuples. Relationship = tuple
*more on his slide
*Relationship is what UFO calls Relator
----
He presented an example of an ER model with an association class.
Attributes in an association class are just syntactic annotations: no new entities is introduced in the domain of discourse
Constraints on the way the relation may hold cannot be expressed
----
Cardinality ambiguity is a common problem in n..n relations. This problem is targeted in the proposal of Guizzardi 2005, which defines Relators.
Example of different kinds of medical treatments, which deals with single-tuple vs. multiple-tuple cardinality constraints.
----
Linguistic evidence of property reification: adjective nominalization
E.g. Mary is beautiful
A state: Mary's being beautiful
A fact: The fact that Mary is beautiful
As a quality: Mary's beauty
Mary's being beautiful is raw and wild - we cannot say that!
But we can say: Mary's beauty is raw and wild.
Moltmann, F. (2013) Abstract Objects and the Semantics of Natural Language.
----
The truth maker of a property P, holding fo x, is a suitable y in virtue of which P(x) holds. E.g. it is because of Mary's beauty that makes Mary beautiful.
in virtue of y = in virtue of the existence of y
E.g.
rose(a) holds in virtue of the existence of a certain rose denoted by a (x = y in this case)
red(a) holds in virtue of the existence of a certain redness event (actually, a state) or the quality of being red.
*I asked if a quality could be the truth maker and he said yes, but the quality is a weak truth maker in some cases while the state is a strong one (e.g. Mary's height - remember that the mere existence of the truth maker should be enough to satisfy the true. This is not the case of height in the sentence "Mary is tall", but it is for the state of being tall).
----
Strong truth making: P(x) holds in virtue of the mere existence of a certain y
Weak truth making: P(x) holds in virtue of the way a certain y is
E.g. A Rose that in t1 is red and in a t2 is brown: different strong truth makers (the two states); same weak truth maker (the quality).
----
----
Classifying properties according to their truth makers
Descriptive properties hold in virtue of how their arguments are: Red(x), Tired(x), Married(x)
They have qualities as weak truth makers and events as strong truth makers
Non-descriptive properties hold in virtue of what their arguments are, i.e. their nature and structure: Apple(x), Person(x)
They may have objects as weak or strong truth makers, and events as strong truth makers.
Internal property vs External property
An internal property does not require external entities (e.g. Red(x), Apple(x)) while an external property do (Married(x), Father(x)).
----
He showed OntoUML models exemplifying how the color property can be reified as a Quality:
- Color (<<quality>>) inheres in Rose (<<kind>>)
Then he showed two other patterns.
- One connecting a Rose (<<kind>>) and a Color Occurrence (<<event>>)
- Complete pattern: Color (<<quality>>) inheres-in Rose(<<kind>>) participates-in Color Occurrence (<<event>>).
----
Classifying Relations
- Guizzardi's original distinction regarding relations: Material vs Formal relations
- Classifying relations according to their truth makers
Descriptive relations hold in virtue of how their arguments (relata) are: Heavier(x,y); Work(x,y)
weak truth makers: qualities inhering on the relata or their parts
possible strong truth makers: objects or events
Non-descriptive relations hold in virtue of what their arguments are, i.e. their nature and structure. E.g. Part(x,y), Depedent(x,y); inheres-in(x,y); Born-in(x,y)
weak truth makers: qualities inhering on the relata or their parts
possible strong truth makers: objects or events
Internal relations are such that each of their weak truth makers components is internal to one argument (i.e. there is no dependence in any external entity):
E.g. Heavier(x,y)
External relations are such that some of their weak truth makers components is dependent on some other argument.
E.g. Works-for(x,y)
Mathias mentioned an example that is interesting: someone is in love with a fictional character that is inside her mind. Is this an external relation? Nicola answered it is something to be reflected on, since this work is new and ongoing.
At each time, a relationship is constituted by a mereological sum fo relational qualities:
- a core nucleus of essential qualities, that can have different values (qualia) at different times;
- a shell of non-essential qualities depending on the nucleus, that can cease to exist or come into being the life of the relationship.
----
Each relationship (relator) is an instance of a rigid kind, which determines the range of values for the qualities.
----
Truth making Patterns for Internal Descriptive Relations (Comparative Relations)
(The ER 2018 explains the existing UFO-based truth making patterns)
*Important: Seeking for the truth maker is what motivates the emergence of each new pattern.
----
----
Truth making patterns for one-sided external relations (see his slide)
----
By Nicola Guarino
*My own comments are marked with an asterisk
Reifying relationships allows us to talk of:
- their nature
- the way they change in time
etc.
In Data Modeling, this has also been clear from the early stages. For instance, ER (Chen) includes a syntactical representation of relationship reification (diamond).
----
Relation vs. Relationship
- Common view: relation is a class of tuples.
- Chen: a relationship type is a set of tuples. Relationship = tuple
*more on his slide
*Relationship is what UFO calls Relator
----
He presented an example of an ER model with an association class.
Attributes in an association class are just syntactic annotations: no new entities is introduced in the domain of discourse
Constraints on the way the relation may hold cannot be expressed
----
Cardinality ambiguity is a common problem in n..n relations. This problem is targeted in the proposal of Guizzardi 2005, which defines Relators.
Example of different kinds of medical treatments, which deals with single-tuple vs. multiple-tuple cardinality constraints.
----
What to reify?
The ontological answer: those entities that are responsible for the truth of our propositions. E.g. it is the color of the rose that makes the statement "This rose is red" true.
Thus, ontological analysis is the search for truth makers
Truth making patterns: a systematic approach
- property and their truthmakers
(more in his slide)----
Linguistic evidence of property reification: adjective nominalization
E.g. Mary is beautiful
A state: Mary's being beautiful
A fact: The fact that Mary is beautiful
As a quality: Mary's beauty
Mary's being beautiful is raw and wild - we cannot say that!
But we can say: Mary's beauty is raw and wild.
Moltmann, F. (2013) Abstract Objects and the Semantics of Natural Language.
----
The truth maker of a property P, holding fo x, is a suitable y in virtue of which P(x) holds. E.g. it is because of Mary's beauty that makes Mary beautiful.
in virtue of y = in virtue of the existence of y
E.g.
rose(a) holds in virtue of the existence of a certain rose denoted by a (x = y in this case)
red(a) holds in virtue of the existence of a certain redness event (actually, a state) or the quality of being red.
*I asked if a quality could be the truth maker and he said yes, but the quality is a weak truth maker in some cases while the state is a strong one (e.g. Mary's height - remember that the mere existence of the truth maker should be enough to satisfy the true. This is not the case of height in the sentence "Mary is tall", but it is for the state of being tall).
----
Strong truth making: P(x) holds in virtue of the mere existence of a certain y
Weak truth making: P(x) holds in virtue of the way a certain y is
E.g. A Rose that in t1 is red and in a t2 is brown: different strong truth makers (the two states); same weak truth maker (the quality).
----
----
Classifying properties according to their truth makers
Descriptive properties hold in virtue of how their arguments are: Red(x), Tired(x), Married(x)
They have qualities as weak truth makers and events as strong truth makers
Non-descriptive properties hold in virtue of what their arguments are, i.e. their nature and structure: Apple(x), Person(x)
They may have objects as weak or strong truth makers, and events as strong truth makers.
Internal property vs External property
An internal property does not require external entities (e.g. Red(x), Apple(x)) while an external property do (Married(x), Father(x)).
----
He showed OntoUML models exemplifying how the color property can be reified as a Quality:
- Color (<<quality>>) inheres in Rose (<<kind>>)
Then he showed two other patterns.
- One connecting a Rose (<<kind>>) and a Color Occurrence (<<event>>)
- Complete pattern: Color (<<quality>>) inheres-in Rose(<<kind>>) participates-in Color Occurrence (<<event>>).
----
Classifying Relations
- Guizzardi's original distinction regarding relations: Material vs Formal relations
- Classifying relations according to their truth makers
Descriptive relations hold in virtue of how their arguments (relata) are: Heavier(x,y); Work(x,y)
weak truth makers: qualities inhering on the relata or their parts
possible strong truth makers: objects or events
Non-descriptive relations hold in virtue of what their arguments are, i.e. their nature and structure. E.g. Part(x,y), Depedent(x,y); inheres-in(x,y); Born-in(x,y)
weak truth makers: qualities inhering on the relata or their parts
possible strong truth makers: objects or events
Internal relations are such that each of their weak truth makers components is internal to one argument (i.e. there is no dependence in any external entity):
E.g. Heavier(x,y)
External relations are such that some of their weak truth makers components is dependent on some other argument.
E.g. Works-for(x,y)
----
Mathias mentioned an example that is interesting: someone is in love with a fictional character that is inside her mind. Is this an external relation? Nicola answered it is something to be reflected on, since this work is new and ongoing.
----
*Aspectual slice of an entity is what UFO (Guizzardi 2005) calls qua-entity
The qua-entities may evolve and change. In other words, new qualities may be included there.
----
Relationships as variable embodiments of qualities (Kit Fine)
- a core nucleus of essential qualities, that can have different values (qualia) at different times;
- a shell of non-essential qualities depending on the nucleus, that can cease to exist or come into being the life of the relationship.
----
Each relationship (relator) is an instance of a rigid kind, which determines the range of values for the qualities.
----
Truth making Patterns for Internal Descriptive Relations (Comparative Relations)
(The ER 2018 explains the existing UFO-based truth making patterns)
*Important: Seeking for the truth maker is what motivates the emergence of each new pattern.
----
*There was a lively discussion about the need for this kind of relationship (relator). Nicola gave us a good example (The distance of the moon. We can talk about this relationship, thus it may be reified).
Mathias brought a new interesting example: "Mathias is taller than Napoleon". Since Napoleon is dead, this complicates things a bit, but we are able to model it adding other concepts. Perhaps we may say there is no relationship between Mathias and Napoleon.
----
Truth making patterns for one-sided external relations (see his slide)
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Conclusions
Rather than looking mainly at reification techniques from the modeling language point of view (Olivé 1999, Dalchour&Pirotte 2002, Halpin 2006), Nicola focuses on understanding the ontological nature of what may be relied...
... by systematically investigating why and how properties of relations hold
... and providing guidelines for reification choices according to the nature of their truth makers
Crucial result: the recognition of qualities as weak truth makers
Further result: clarification of Guizzardi's distinction between formal and material relations, proposing a new classification of relations aimed at facilitating the analysis of actual modeling cases.
Proposed patterns may be easily incorporated in conceptual models based on DOLCE, UFO and BFO.
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