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Formal Methods in DAI : Logic-Based Representation and Reasoning

Formal Methods in DAI : Logic-Based Representation and Reasoning. 컴퓨터 공학과 이인호. 0. Contents. Introduction Logical Background Cognitive Primitives BDI Implementations Coordination Communications Social Primitives Conclusions. 1. Introduction. Agents are being used in critical situations

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Formal Methods in DAI : Logic-Based Representation and Reasoning

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  1. Formal Methods in DAI :Logic-Based Representation andReasoning 컴퓨터 공학과 이인호

  2. 0. Contents • Introduction • Logical Background • Cognitive Primitives • BDI Implementations • Coordination • Communications • Social Primitives • Conclusions

  3. 1. Introduction • Agents are being used in critical situations • Ensuring that an agent behaves correctly is important • Formal methods offer an understanding of the systems being designed at a level higher than their specific implementation

  4. 2. Logical Background (1/6) • Formalizations of agent systems are used for two quite distinct purpose • Specifying agent’s internal reasoning & action • Specifying agent’s external behavior in a dynamic environment

  5. 2. Logical Background (2/6) • Propositional Logic • Predicate Logic • Modal Logic • Possibly true / Necessarily true • Represents belief and knowledge • Deontic Logic • What an agent is obliged to do • Not mentioned in detail

  6. 2. Logical Background (3/6) • Dynamic Logic • Modal logic of action • necessity and possibility operators are based upon the kinds of actions available • a;b : doing a and b in sequence • a + b : doing either a or b, whichever works. (nondeterministic) • p? : action based on the truth value of p • a * : 0 or finitely many iterations of a

  7. 2. Logical Background (4/6) • Temporal Logic • The logic of time • Set of moments with a strict partial order, which denotes temporal precedence • Each moment is associated with a possible state of the world • A path at a moment : any maximal set of moments containing the given moment • A real path : the path on which the world progresses

  8. 2. Logical Background (5/6) • Linear Temporal Logic • pUq is true at a moment t on a path : q holds at a future moment on the given path and p holds on all moments between t and that moment • Fp : p holds sometimes in the future on the given path (true U p) • Gp : p always holds in the future on the given path (¬F¬p) • Xp : p holds in the next moment • Pq : q held in a past moment

  9. 2. Logical Background (6/6) • Branching Temporal and Action Logic • A : in all paths at the present moment • E : in some path at the present moment • R : in the real path at the present moment • x[a]p : if agent x performs action a, then p holds at the moment where a ends • x<a>p : agent x perfoms action a and p holds at the moment where a ends • (V a : p) : there is an action under which p become true

  10. 3. Cognitive Primitives (1/5) • Agents given high-level cognitive specifications such as Beliefs, Knowledge, Desires, and Intentions • Operators • Bel (Belief) • Des (Desire) • Kt (Know-that) • Kh (Know-how) • Int (Intention)

  11. 3. Cognitive Primitives (2/5) • Knowledge and Beliefs • xBelp : agent x believes p possible at the moment • xKtp : agent x know that p is true (true belief) • Desires and Goals • xDesp : agent x desires p at the moment • goal : subset of desires chosen by an agent which are both consistent and achievable

  12. 3. Cognitive Primitives (3/5) • Intentions • xIntp : agent x selected of preferred p. That is, p is inevitably hold on each of the selected paths • Satisfiability : xIntp EFp • Temporal Consistency : (xIntp xIntq)  xInt(Fp  Fq) • Persistence does not entail success : EG((xIntp)  ¬p)

  13. 3. Cognitive Primitives (4/5) • Know-how • An agent acts to satisfy their intentions, but as shown above, intentions do not ensure success • xKhp : agent x knows how to achieve p. That is, knows the action to be done to achieve p • For example, if it knows p already holds, then it knows how to achieve p(by doing nothing). • And if it knows p at a moment, then it knows how to achieve p at the moment immediately before the moment

  14. 3. Cognitive Primitives (5/5) • Reasoning with Cognitive Concepts • Using the above concepts needs efficient reasoning techniques • There are two main approaches for reasoning with a logic • Theorem Proving : establishing a given formula by following through a finite sequence of applications of axioms and inferences rules of a given logic • Model Checking :checking if a given formula is satisfied at a given model and index

  15. 4. BDI Implementations (1/8) • Basic Interpreter initialize-state(); do options := option-generator(event-queue, S) selected-poptions := deliberate(options, s); update-state(selected-options, S); execute(S); event-queue := get-new-events(); until quit.

  16. 4. BDI Implementations (2/8) • Abstract BDI-interpreter initialize-state(); do options := option-generator(event-queue, B, G, I) selected-options := deliberate(options, B, G, I); update-intentions(selected-options, I); execute(I); get-new-external-events(); drop-successful-attitudes(B, G, I); drop-impossible-attitudes(B, G, I); until quit.

  17. 4. BDI Implementations (3/8) • Practical System • To make abstract interpreter practical, some representationsla choices is needed to make option generator and deliberaton procedures fast to satisfy the realtime demands placed upon the system • Beliefs and Goals • The system operates only on explicit beliefs and goals • current : a subset of the agent’s beliefs ad goals

  18. 4. BDI Implementations (4/8) • Plans • Information about means and options as belifes can be more directly represented as plans • A plan has… • type : name of plan • body : method for executing (plan graph) • invocation condition (triggeing event) / precondition : specify when the plan may be selected • add list / delete list : atomic propositions believed or not believed upon its successful execution

  19. 4. BDI Implementation (5/8) • Whenever a plans invocation condition and precondition are satisfied, its body is believed to be an option • After successful execution, the propoitions in the add list will become true • Resulting consequences can trigger further plans

  20. 4. BDI Implementation (6/8) • Intentions • Intentions are represented as sets of hierarchically related plans • Intention frame : means (plan) - end (goal) pair with variable bindings and contorl points • An intention towards a means results in another end(subgoal) and means, thus creating another intention frame until subgoal can be directly executed as an atomic action

  21. 4. BDI Implementation (7/8) • A Practical Interpreter • option-generator(trigger-events) option := {} for trigger-event  trigger-events do for plan  plan-library do if matches(invocation(plan), trigger-event) then if provable(precondition(plan), B) then options := options U {plan}; return(options).

  22. 4. BDI Implementation (8/8) • deliberate(options) if length(options)  1 then return(options); else metalevel-options := option-generator(b-add(option-set(options))); selected-options := deliberate(metalevel-options); if null(selected-options) then return(random-choice(options)); else return(selected-options).

  23. 5. Coordination (1/3) • When agents are heterogeneous and auto-nomous, coordination becomes important • One Formal Approach developed by Singh • representing each agent as a small skeleton • each skeleton includes only the events or transitions made by the agent that are significant for coordination

  24. 5. Coordination (2/3) • Event Classes • flexible : the agent is willing to delay or omit • inevitable : the agent is willing only to delay • immediate : the agent is willing neither to delay nor to omit • triggerable : the agent is willing to perform based on external request

  25. 5. Coordination (3/3) • Common Coordination Relationships

  26. 6. Communications • Communication : a natural way in which the agents may interact with one another • Speech Act theroy : with language, we do not only make statements, but also perform actions • 3 main aspects of a speech act • locution : the string transmitted • illocution : intrinsic meaning • perlocution : possible effects on the recipients

  27. 7. Social Primitives (1/2) • Group : system of agents that are somehow constrained in their mutual interactions • Team : a group in which the agents are restricted to having a common goal of some sort

  28. 7. Social Primitives (2/2) • Mutual Belief (a) believe p, (b) believe that others believe p (c) believe that (b) holds of the others • Joint Intentions (a) each have a goal p (b) each will persist with this goal until it is mutually believed that p is achievd or that p canot be achieved (c) (a) and (b) are mutually believed

  29. 8. Conclusions • Formal mehods in DAI are still in their infancy • But, some techniques have also been used to influence a variety of practical systems • A range of future challenge : to develop formal techniques • that cover the phenomena that emerge in practice • are more accurate in real systems • can be used to analyze and design them

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