LORA

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LORA

• Dan Rochowiak
• drochowi_at_cs.uah.edu

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Rational Agents

• Psychologically and cognitively informed
• Accuracy in cognitive modeling not required
• Emphasis on rationality
• Rationality may mean logicality
• Emphasis it what ought to happen
• Accuracy in normative modeling required
• No generic and agreed to account of the norms of
  rationality
• Generic and agreed to account of logicality
• But it is knowledge soup.

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Logic of Rational Agents (LORA)

• First-order component
• Classical FoL
• Representation of properties of objects and their
  relations
• Belief-desire-intention component
• Expression of belief, desire and intention of
  agents
• Temporal component
• Represent dynamic aspects of system
• Action component
• Represent actions of agents and their effects

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First order Component

• Standard FoL
• Connectives
• Quantifiers

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BDI Component

• Modal connectives
• Binary
• Agent
• SOA, actually and formula of LORA

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Temporal Component

• Modal
• Past time is linear
• Past time is discrete sequence of states
• Future is branching
• Many possible sequences of future events

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Temporal Component
now
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Futures

• t1, t2, t5,
• t1, t2, t6,
• t1, t3, t7,
• t1, t4, t8,
• t1, t4, t9,

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Temporal Connectives

• Ne soa - soa is true next
• Ev soa - soa is eventually true
• Al soa - soa is always true
• soa1 U soa2 - soa1 is true until soa2 is true
• soa1 W soa2 - soa1 is true unless soa2 is true

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Path connectives

• Ne soa is satisfied now if soa satisfied at the
  next moment
• Ev soa is satisfied now if soa is satisfied now
  or at some future moment
• Al soa is satisfied now if soa is satisfied now
  and at all moments
• soa1 U soa2 is satisfied now soa2 is i satisfied
  at some future moment and soa1 is satisfied until
  then
• soa1 W soa2 is satisfied now if either soa1 or
  soa2 is true

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Path quantifiers

• A soa - soa is true on all paths
• E soa - soa is true on some path
• E(q U t) is true (in the example)
• since q U T is true on the path (t1,t4,t9,..)

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Action operators

• (Happens ac) - action expression ac happens next
• (Achvs ac soa) - action ac occurs and achieves
  soa
• (Agts ac g) - group g is required to do action ac

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Paths with action
a4
a2
a4
a1
a2
a5
now
a3
a6
Path(t1,t2,t5,) (Happens a2a4) is true
a3
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Pairings (constraints)

• If an agent intends something, then it desires
  it.
• If an agent desires something, then it intends
  it.
• If an agent believes something, then it desires
  it.
• If an agent desires something, then it believes
  it.

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Pairings (constraints)

• If an agent intends something, then it believes
  it.
• Rephrase as two cases
• If an agent intends something, then it believes
  it is possible.
• If an agent intends something, then it believes
  it is inevitable.
• If an agent believes something, then it intends
  it.

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Pairings (constraints)

• If an agent intends that something is inevitably
  true, then it desires that it is inevitably.
• If an agent believes that something is inevitably
  true, then it desires that it is inevitably.
• If an agent desires that something is inevitably
  true, then it believes that it is inevitably.
• If an agent intends that something is inevitably
  true, then it desires that it is inevitably.
• If an agent intends that something is inevitably
  true, then it believes that it is inevitably.
• If an agent believes that something is inevitably
  true, then it intends that it is inevitably.

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Pairings (constraints)

• If an agent intends that something be true on
  some future path, then it desires it on some
  possible path.
• If an agent desires that something be true on
  some future path, then it intends it on some
  possible path.

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Pairings (constraints)

• If an agent believes that something be true on
  some future path, then it desires it on some
  possible path.
• If an agent desires that something be true on
  some future path, then it believes it on some
  possible path.

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Pairings (constraints)

• If an agent intends that something be true on
  some future path, then it believes it on some
  possible path.
• If an agent believes that something be true on
  some future path, then it intends it on some
  possible path.

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Intention-Desire consistency

• If an agent intends something, then it is not the
  case it desires it not to be.
• If an agent desires something, then it is not the
  case that intends it not to be.
• Note that some case require reconsideration.

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Belief-Desire consistency

• If an agent believes something, then it is not
  the case it desires it not to be.
• If an agent desires something, then it is not the
  case that believes it not to be.
• Difference in context of cases calls for caution.

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Side effect problem

• It should be possible that an agent intend
  something S, believe that that S inevitably leads
  to something else C and not intend C
• It should be possible that an agent intend
  something S, desire that that S inevitably leads
  to something else C and not intend C
• It should be possible that an agent desire
  something S, believe that that S inevitably leads
  to something else C and not desire C