Peter Gärdenfors&

Massimo Warglien

Using Conceptual Spaces to Model Actions, Events and the

Semantics of Verbs

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

The color domain

Intensity

Hue

Brightness

Green

Red

Yellow

Blue

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

Properties vs. concepts

Properties: A convex region in a single domain

The color spindle

Intensity

Hue

Brightness

Green

Red

Yellow

Blue

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

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

Cognitive grounding of linguistic categories

• Properties Adjectives

• Concepts Nouns

• There is a shape bias in children’s learning of nouns

Shape space according to Marr

How is action space structured?

We know even less about the geometry and topology of action space

than we know about shape space

Dynamic domains

Marr & Vaina”Walk”

Gunnar Johansson’spatch-lighttechniquefor analysingmotion perception

Kinematic specification of dynamics(Runesson)

The kinematics of a movement contains sufficient information to identify the underlying dynamic force patterns.

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

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

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

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

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”

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”)

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”

Transitive/intransitive

• Intransitive: walk, jump, sleep, die

• In many intransitive verbs Agent = Patient

• Agent applies a force to him/herself

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

State verbs

• E.g. be, sleep, hate

• No change involved (identity vector in property space)

• No force applied

• Result verbs

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

Cognitive grounding of linguistic categories

• Concepts Nouns• Properties Adjectives• Spatial relations Prepositions• Force and change vectors Verbs• Modifying vectors Adverbs• Events Propositions