1. Peter Gärdenfors & Massimo Warglien Using Conceptual Spaces
to Model Actions, Events and the Semantics of Verbs

2. Conceptual spaces Information is organized by quality dimensions
… that are sorted into domains (space, time, temperature, weight, color, shape … )
Domains are endowed with a topology or metric

3. The color domain
Brightness
Yellow
Green
Intensity
Red
Blue
Hue

4. Conceptual spaces Information is organized by quality dimensions
… that are sorted into domains (space, time, temperature, weight, color, shape … )
Domains are endowed with a topology or metric
Conceptual spaces represent human cognition (not scientific models)
Similarity is represented by distance in a conceptual space

5. Properties vs. concepts
Properties: A convex region in a single domain

6. The color spindle
Brightness
Yellow
Green
Intensity
Red
Blue
Hue

7. Properties vs. concepts
Properties: A convex region in a single domain
Concepts: A number of convex regions in different domains; together with
(1) prominence values of the domains and (2) information about how the regions in different domains are correlated
Concepts ≈ frames + geometric structure

8. An example of a concept: ”Apple”
Domain Region
Color Red-green-yellow
Taste Values for sweetness, sourness etc
Shape "Round" region of shape space
Nutrition Values for sugar, vitamin C, fibres etc

9. Cognitive grounding of linguistic categories
Properties Adjectives
Concepts Nouns
There is a shape bias in children’s learning of nouns

10. Shape space according to Marr

11. How is action space structured?
We know even less about the geometry and topology of action space than we know about shape space

12. Dynamic domains
Marr & Vaina
”Walk”

13. Gunnar Johansson’s patch-light technique for analysing motion perception

14. Kinematic specification of dynamics (Runesson)
The kinematics of a movement contains sufficient information to identify the underlying dynamic force patterns.

15. Representational hypothesis
The fundamental cognitive representation of an action is the pattern of forces that generates it
Actions are more or less similar and show prototype effects
An action category is a convex region in the space of force patterns

16. A two-vector model of an event
The force vector (pattern) acts on an patient
From force space (categorized into actions)
The result vector describes the changes of the properties of the patient
Changes in location or in category space
Cognitive account, not metaphysical
(Agent)
Force
patient
Result

17. More components of events
Agent represented in agent space that contains at least the force domain
Patient represented in category space and physical space
Counterforces exerted by the Patient
Intentions of the Agent

18. Representing verb meanings
Main semantic hypothesis: A verb represents either the force vector or the result vector of an event
Explains the division of manner and result verbs
Accusative vs ergative languages

19. Manner verb: ”Push” Force applied to object
Prototypically, push leads to change in position of object
However, this change is not certain, due to counterforces
Expectations can be tested with ”but”

20. Result verbs
Describes change in object (”cut” and ”break” divide into several)
Do not say anything about the forces that lead to the change
Two basic kinds: change of position (”move”) and change of properties (”paint”)

21. Why either manner or result?
Strong support from linguistic analyses
Connection between force vector and result vector not direct (counterforces etc)
Makes it difficult to learn the mapping
Possible counterexample: ”dive”

22. Transitive/intransitive
Intransitive: walk, jump, sleep, die
In many intransitive verbs Agent = Patient
Agent applies a force to him/herself

23. Mental forces I persuade you, I scare you, I praise you, I blame you
Apply to different aspects of patient’s emotional or cognitive space
These verbs presume a sentient patient

24. State verbs E.g. be, sleep, hate
No change involved (identity vector in property space)
No force applied
Result verbs

25. Adverbs (modifying verbs)
Function as scalars to multiply force or result vectors
”He strongly pushed the door”
”She slowly opened the door”
Analogous to how adjectives modify nouns

26. Cognitive grounding of linguistic categories
Concepts Nouns
Properties Adjectives
Spatial relations Prepositions
Force and change vectors Verbs
Modifying vectors Adverbs
Events Propositions