Peter G

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

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The color domain
Brightness
Yellow
Green
Intensity
Red
Blue
Hue
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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

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Properties vs. concepts

• Properties A convex region in a single domain

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The color spindle
Brightness
Yellow
Green
Intensity
Red
Blue
Hue
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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
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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

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Cognitive grounding of linguistic categories

• Properties Adjectives
• Concepts Nouns
• There is a shape bias in childrens learning of
  nouns

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Shape space according to Marr
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How is action space structured?

• We know even less about the geometry and topology
  of action space than we know about shape space

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Dynamic domains
Marr Vaina Walk
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Gunnar Johanssonspatch-lighttechniquefor
analysingmotion perception
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Kinematic specification of dynamics(Runesson)
The kinematics of a movement contains sufficient
information to identify the underlying dynamic
force patterns.
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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

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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

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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

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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

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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

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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)

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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

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Transitive/intransitive

• Intransitive walk, jump, sleep, die
• In many intransitive verbs Agent Patient
• Agent applies a force to him/herself

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Mental forces

• I persuade you, I scare you, I praise you, I
  blame you
• Apply to different aspects of patients emotional
  or cognitive space
• These verbs presume a sentient patient

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State verbs

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

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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

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Cognitive grounding of linguistic categories

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