Reactive Behaviour

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Reactive Behaviour

• Patterns of behaviour (from external and internal
  viewpoint)
• stimulus-response behaviour
• delayed response behaviour
• Perspectives
• behaviourist
• functionalist

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Stimulus-response behaviour

• Most simple form of reactive behaviour
• Lets have a look at an example

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Stimulus-Response BehaviourExample Traces
 
 
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Questions

• What is the pattern behind this observed
  behaviour?
• How to characterize that pattern?
• How to generate such a pattern?
• Explanation
• Why does the agent behave this way?
• Prediction
• Can we predict what the agent will do in this
  situation?

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Specification of Input and Output

• indication of what are considered
• input ontologies and
• output ontologies
• for an agent.

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Ontologies to describes states
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Traces

• A trace is a time-indexed sequence of states
• input states - input trace
• output states - output trace
• combined states - interaction trace
• (consisting of an input part and an output part)

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Traces (cont.)
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Functional Association

• A function from the set of possible input states
  to the set of possible output states
• F Input_states ? Output_states
• However,
• mouse ? simple machine
• variations in behaviour!

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Non-Deterministic Behaviour

• Not always the same output for a given input.
• Description
• binary relation
• R Input_states Output_states

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Dynamic Property

• Definition Dynamic Property
• A temporal statement on traces.
• A dynamic property characterizes the set of all
  traces that have that property.
• Use
• A manner to characterize a pattern of behaviour
• external dynamics
• internal dynamics

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External Dynamics

• Example for stimulus-response
• ESR1
• at any point in time,
• if the agent observes that food is present at p2
  
• and it observes that no screen is present,
• then it will go to position p2

functional or non-deterministic?
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External Dynamics Graphical Form
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Internal Dynamics

• ISR1
• at any point in time,
• if the agent observes that food is present at p2
  
• then internal property b1 will hold
• ISR2
• at any point in time,
• if the agent observes that no screen is present,
• then internal property b2 will hold

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Internal Dynamics (cont.)

• So, internal state properties b1 and b2 are
  assumed with some relationships to inputs and
  outputs.
• ISR3
• at any point in time,
• if internal property b1 holds
• and internal property b2 holds,
• then the agent will go to position p2

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Internal Dynamics Graphical Form
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Explanation of Behaviour
Explanation Answer to a why-question. Why does
the animal go to p2 ? The animal goes to p2,
because .

• External perspective
• (behaviourist)

• Internal perspective
• (functionalist)

. b1 and b2 were holding Why did they
hold? b1 it observed food b2 it observed
absent screen
. it observed that food is present at p2 and
that the screen is absent
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Delayed Response Behaviour

• A more sophisticated form of reactive behaviour.
• Lets have a look at an example.
• What differences in behaviour do you see?

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Delayed Response BehaviourExample Interaction
Traces
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Questions

• What is the pattern behind this observed
  behaviour ?
• Which external dynamic properties can be
  expressed that characterize the pattern behind
  these traces ?
• Which assumed internal state properties generate
  this externally observed behaviour ?
• What is the pattern of dynamics of these internal
  state properties ?
• How can these internal dynamics be characterized
  by dynamic properties ?

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Delayed Response BehaviourExternal Dynamic
Properties (1)

• EDR1
• at any point in time,
• if the agent observes that no screen is present
• and at some earlier point in time the agent
  observed that food was present at position p2,
• then the agent will go to position p2
• Rigid form no update

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Delayed Response BehaviourExternal Dynamic
Properties (2)

• EDR1
• at any point in time t1,
• if the agent observes that no screen is present
• and at some earlier point in time t it observed
  that food was present at position p2, and at
  every point in time t' after t up to t1, it did
  not observe that no food was present at p2,
• then the agent will go to position p2
• Updating form

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Input-Output Correlation (1)

• A binary relation existing in reality between
• C Input_traces x Output_traces
• Note can be function for deterministic case.

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Input-Output Correlation (2)

• A specification of an input-output correlation C
  is called a behavioural specification.
• Behavioural specification
• external dynamic properties
• Examples
• ESR1 for the stimulus response mouse
• EDR1 for the delayed response mouse
• EAB5, EAB6, EAB7 for the adaptive agent

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Dynamic Properties and Traces

• A trace can have / satisfy a dynamic property
• A dynamic property characterizes the set of all
  traces that have that property
• A trace can have / satisfy a set of dynamic
  properties
• A trace can satisfy a behavioural specification
• A specification S is a behavioural specification
  of input-output correlation C if and only if
  for all interaction traces T the correlation C
  holds for T if and only if T satisfies S.

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Use of a Behavioural Specification

• Prediction
• prognosis of behaviour yet to come.
• Explanation
• answer to a why-question regarding observed
  behaviour.

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Prediction

• A behavioural specification of an organism
  defines an input-output correlation.
• Therefore, if the present and past inputs of an
  organism are given, a behavioural specification
  provides outputs corresponding to those of the
  organism.
• Hence it can adequately be used as an instrument
  for prediction of behaviour.

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Example on Prediction

• Do you have all the info you need to predict the
  behaviour of the mouse in this situation?
• current input cup, no_screen
• output ?

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Explanation

• Can a behavioural description also be used for
  explanation of behaviour?
• From an external perspective?
• From an internal perspective?
• When is an explanation fitting?

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Explanation of Delayed Response Behaviour

• Why does the animal go to p2 ?
• A The animal goes to p2, because it just
  observed that no screen is present, and in
  the past it observed that food was present at p2.
• B The animal goes to p2, because it just
  observed that no screen is present, and it
  believes that food is present at p2.

Intern / extern ?
Difference A, B?
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Example on Explanation

• Do you have all the elements you need to explain
  the behaviour of the delayed response mouse in
  this situation?
• current input cup, no_screen
• output goes to p2

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Explanation (cont.)

• Problem for a given input, an organisms
  behaviour can differ over time, since it also
  depends on the internal state of the organism,
  which in turn depends on the organisms past
  input.
• Therefore an adequate (causal) explanation of the
  organisms behaviour referring only to the
  immediate causes is often not possible.

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Explanation contents

• external perspective / behaviourist
• explanation needs to refer to
• present input and
• past input (indirect causes)
• internal perspective
• explanation needs to refer to
• present input (immediate causes)
• present internal states
• iterated explanation these internal states
  themselves can be explained by past inputs

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Delayed Response BehaviourInternal Dynamic
Properties (1)

• IDR1
• for all time points
• if the agent observes that food is present at
  p2,
• then internal state property b1 will hold
• IDR2
• for all time points
• if internal state property b1 holds,
• then for every later time point b1 holds

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Delayed Response BehaviourInternal Dynamic
Properties (2)

• IDR3
• at any point in time,
• if the agent observes that no screen is present
  ,
• and internal state property b1 holds,
• then the agent will go to position p2
• These dynamic properties together define the
  functional role of b1.

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Functional Role

• Note
• b1 occurs in IDR1, IDR2, and IDR3.
• There are no other internal properties.
• In other words
• IDR1, IDR2, IDR3 defines the functional role
  of b1.
• Definition Functional Role of internal property b
  is
• internal dyn prop P b occurs in P

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Delayed Response BehaviourInternal Dynamic
Properties (3)

• The internal dynamic properties together imply
  the external dynamic property EDR1 i.e.,
• IDR1 IDR2 IDR3 ? EDR1
• In other words and more general
• if a trace satisfies the internal dynamic
  properties, then it also satisfies the
  external dynamic properties.

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Graphical Form
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Graphical Form Functional Role of b1
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Executable Dynamic PropertiesDefinition

• Step Property
• If U holds
• then V will hold
• Persistence property
• If X holds
• then X will hold at all later time points,
  as long as Y does not hold
• X, Y (combinations of) state properties

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Example Persistence Property

• IDR4
• for all time points t1 and t2 with t1ltt2
• if internal state property b1 holds at t1,
• and between t1 and t2 the agent does not
  observe that food is not present at position
  p2,
• then internal state property b1 holds at t2

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Graphical Form
b1
observesno food at p2
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Executable Dynamic PropertiesAdvantages

• can be depicted in graphical form
• allow for direct implementation (in, e.g.,
  computational or natural context)
• allow for explanations based on elementary steps
  (e.g., computational or causal)