Agent programming in Dribble

from beliefs to goals with plans

Birna van RiemsdijkWiebe van der HoekJohn-Jules Ch. Meyer

Utrecht University John-Jules Meyer 2

Motivation

◊ Our group has done work on agent programming languages in the past– 3APL: beliefs and goals-to-do– GOAL: beliefs and goals-to-be

◊ Natural question: how to combine these?

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Answer: Dribble

◊ Dribble is an agent programming language containing:– Beliefs– Goals-to-be– Goals-to-do (Plans)

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Mental States

◊ Mental state – Belief base : set of prop. forms– Goal base : set of prop. forms– Plan : sequence of ‘basic

elements’ (imperative program)

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Belief and Goal Formulas

◊ Belief formulas• B

◊ Goal formulas

• G• logical consequences of particular goal

are also goals, if not believed

◊ Logical combinations

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Plans

◊ Plan is sequence of basic elements◊ Basic elements:

•Basic action •Abstract plan•If-then-else construct

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Basic Actions

◊ Basic action•executable •belief update•goal update: goals removed when

realised (thru commitment strategy)

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Abstract plans

◊ Abstract plan•not executable •abstraction mechanism (compare

procedures) •translation into basic actions

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If-then-else

◊ If-then-else construct if then 1 else 2 fi

•executable •plan update

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Executing Basic Actions

◊ A basic action has as effects:– Belief update

•E.g. after execution of moveLeft, the agent believes to have moved left

– Goal update•Indirect, side effect of belief update

via commitment strategy

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Commitment Strategy

◊ Commitment strategy– connection between beliefs and goals

– when are goals dropped?• when believed to have been achieved

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Goal Rules

◊ Goal rules have form – taken from GOAL : a– used for plan selection

– is condition on beliefs and/or goals• Beliefs: specify when the plan could be

executed• Goals: specify what the plan is good for

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Goal Rules (ctd)

– applicable in E iff E (selection of new plan only if current plan is empty)

– resulting mental state is (adoption of plan )

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PR Rules

◊ Practical Reasoning (PR) rules:h b

– taken from 3APL– is condition on beliefs– employed for

• Creating plans : p a;b;c

• Modifying plans : h b

• Modeling reactive behaviour : E b

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PR Rules (ctd)

– applicable in h iff h

– resulting mental state is b (adoption of plan b instead of h )

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Operational Semantics

◊ Operational semantics based on transition system

• definition of mental state transformations

◊ Transition rule for basic action execution

• T(a,) defines update of by executing action a

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Transition rules

◊ Application of goal rule g:

E EapplyRule(g)

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Transition Rules

◊ Execution of a basic action a:

T(a,) = ’_______________________aExecute(a) ’’E

where ’\’

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Summary So Far

◊ Dribble agent– Mental state

• belief base, goal base, plan

– Goal rules• plan selection

– PR rules• plan creation and modification

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Dynamic Logic

– specify and verify properties of programs

– programs: syntactic constructs in the logic

– p: possible to execute p and halt in state satisfying

– program is transformation function on states: reason about state transformations

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Logic for Dribble

◊ Dynamic logic for Dribble– transformations on mental states

caused by:• goal and PR rule application and action

execution

– reason about state transformations• reason about rule application and action

execution of meta-actions

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Syntax

◊ : sequence of meta-actions• applyRule(g), applyRule(), execute(a),

execute(if-then-else)

◊ : mental state formula• B(), G(), Com()

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Semantics

◊ r* : semantics of meta-actions• transformation function on mental states through

meta-actions ◊ interpretation of diamond formulas:

– r*

◊ Com formulas– Com’’

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Semantics

◊ Semantics of applyRule(g)

for g: ’

r* (applyRule(g)) (’

if = E and

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Correspondence

◊ Mental state transitions

- defined by transition system(meaning of Dribble agent)

- defined by actions in the logic

(by means of the r* function)

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Correspondence (ctd)

◊ Correspondence of logic and operational semantics– transition defined by actions in

the logic transition defined by transition system

– properties of actions in logic: properties of Dribble agent

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Some Validities

◊ Results of meta-actions• [applyRule(g)] Com()

• Com(h) [applyRule()]Com(b)

• Com(a;) [a] [execute(a)](Com() )

• Com(if;) [execute(if)] Com(1), where if = if then 1 else 2 fi

[Where g: and : h b]

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Some Validities (ctd)

◊ Realisability of meta-actions• Com(E) applyRule(g)T• Com(h) applyRule()

Com(b)

• Com(a;) aT execute(a)Com() • Com(if;) execute(if) T, where if = if then 1 else 2 fi

[Where g: and : h b]

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Conclusion

◊ agent programming language– incorporating goals and planning

features– formally defined semantics

◊ programming logic– a first attempt to reason about these

‘self-modifying’ programs (via meta-actions)

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Future Work

◊ incorporate first-order languages◊ selection of goal from wish base◊ explicit goal adopt and drop actions◊ drop goal when believed to be

unachievable◊ investigation of use of adding goal

formulas in PR rules