CMSC Agent Architectures Multi Agent Systems

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CMSC Agent Architectures Multi Agent Systems Powered By Docstoc
					CMSC 691M
Agent Architectures &
Multi-Agent Systems
    Spring 2002 – February 26
    Class #9 – Formal Methods for MAS
    Prof. Marie desJardins
Today’s overview

   Reading: Weiss Chap. 8, “Formal Methods in
    DAI” (Munindar P. Singh, Anand S. Rao, and Michael
    P. Georgeff)
       Why use formal methods?
       Classes of logics
       Beliefs, desires, and intentions
       Implementing BDI models
       Coordinating BDI agents
       Communicating BDI agents
       Societies of BDI agents
Why use formal methods?
   Specify properties of agents declaratively
   Provide reasoning mechanisms for agents

Benefits                    Disadvantages
+ Specify complex           - Intractable in general
  behavior at an abstract     case
  level                     - Limiting precisely
+ Validate agent              because of formalism
  behaviors                   and abstract
  What’s to be modeled?
        Propositional logic                First-order logic

           To design and implement intelligent agents,
            we may need to be able to reason about
            the truth of propositions and relations
Modal       between objects in the world, to reason
            about what may or must be true, to reason
            about how the agent’s actions affect the
            state of the world, and to reason about how
            other agents and external agents change
            the world over time.
                          Temporal logic        Dynamic logic
Classes of logics
                Wffs (syntax)          Proof theory      Model theory
                                       (inference)       (semantics)
Propositional   Atoms closed under Implication and “Meaning” of
                 and ¬            rules for  and ¬ propositions
Predicate       Adds quantifiers      Inference rules   “Meaning” of
(first-order)   and , relations,      for quantifiers   relations
                variables              and variable
Modal           Adds possibility      Inference rules   Possible worlds
                and necessity         for  and 
Dynamic         Adds sequencing,       Inference rules   Possible worlds
                branching, testing     for outcomes      with transitions
Temporal        Adds notion of time    Inference for     Possible worlds
                points or intervals,   propositions w/   with multiple
                ordering               temporal extent   transitions
Propositional logic

   L = true atomic propositions
   P is entailed iff P  L
   P  Q is entailed iff P and Q are entailed
   P is entailed iff P is not entailed
Predicate (first-order) logic

   x (Q(x)) is entailed iff Q(l) holds for every
    object l
   x (Q(x)) is entailed iff Q(l) holds for some
    object l
Modal logic

   Possible worlds semantics
   Accessibility relation R(W1, W2):
   Possibility: P is entailed in world w iff P is
    true in some possible world ( w’: R(w,w’)  P
    is entailed in w’)
   Necessity: □P is entailed in w iff P is true in
    every possible world ( w’: R(w,w’) → P is
    entailed in w’)
Dynamic logic (“modal logic of action”)
   Sequencing: a;b – do a, then do b
   Choice: a+b – do either a or b
   Testing: p? –TRUE if p, FALSE if p
       ((q?;a) + ((q?;b)) ≡ if q then a else b
   Accessibility relation RA – reachability of
    worlds via (composite) action A
Dynamic logic – modeling outcomes

   Possible outcomes
       <A>P is entailed in w iff P is entailed in some
        world reachable by applying action A
       <A>P  w’: RA(w,w’)  P entailed in w’
   Necessary outcomes
       [A]P is entailed in w iff P is entailed in all worlds
        reachable by applying action A
       [A]P w’: RA(w,w’) → P entailed in w’
Temporal logic – variations

   Linear vs. branching: modeling a single
    sequence of events/outcomes vs. modeling a
    branching series of alternative possible
   Discrete vs. dense (continuous): time treated
    as discrete intervals vs. continuously flowing
   Moment-based (point) vs. period-based
    (interval): units of time treated as points or
Discrete moment-based branching
temporal logic
   Moment in time are partially ordered
   Each moment is associated with a possible
   The actions of multiple agents can influence
    which moment (possible world) occurs next
Linear temporal logic

   p  q at moment t means that p holds from t until t’
    and q holds at t’
   X p at moment t means that p holds in the moment
    immediately following t
   P p at moment t means that p was true at t’ where t’
    is before t
   F p at moment t means that p is true at some
    moment t’ after t
   G p at moment t means that p is true at every
    moment t’ after t
Branching temporal logic

   “The present moment”
   “Reality”
   A p means that p is true in all paths at the
    present moment (i.e., no matter what may
    have gone before or will happen in the future,
    p is true now) – temporal equivalent of the
    necessity operator of modal logic
   E p means that p is true in some path at the
    present moment – temporal equivalent of
    possibility operator
Branching temporal logic II

   X<a>p is true (at a particular moment, on a
    particular path) iff p is a possible outcome of
    agent x performing action a
   X[a]p is true (at a particular moment, on a
    particular path) iff p is a necessary outcome
    of agent x performing action a
   V a : p is true (at a moment and on a path) iff
    there is some action a under which p
    becomes true
Brief commentary on logics

   Branching temporal logic is very powerful,
    and has been used to develop planners and
    other agent architectures
   Many researchers use ideas from some or all
    of these logics in their agent designs and
   Very few researchers use the full formal
    specification of these logics in building
    systems (though it isn’t uncommon to see
    them in conference and journal papers)
Beliefs, desires, and intentions

   Use modal logic to model agent’s cognitive
    attitudes: beliefs, desires, goals, know-
    how, and intentions

   X Bel p iff p is entailed in every possible
    world the agent believes it can be in
    (modeled by the B accessibility relation)
   Interestingly, although a proposition q may be
    believed by this definition, an agent may not
    believe that it believes q
       Limited rationality / limited computational
        resources means that the agent can’t derive
        everything that it “believes”

   x Des p iff p holds in all possible worlds
    reachability by the D accessibility relation
   The agent might not know how to reach the
    states it desires to be in
   An agent can desire to be in conflicting states
   Goals are the subset of the agent’s desires
    that are achievable and consistent
   x Int p iff p is true along all paths that are reachable
    by the I accessibility relation
   According to this definition, an agent can “intend”
    something it doesn’t desire
   An agent can also have an unsatisfiable intention
    (if the set of reachable paths is empty)
   An agent can intend something, and yet fail to make
    it come true (if it proceeds along a path that isn’t in
    its set of intended paths)
       Know-how models when an agent can guarantee the
        success of its actions
       More useful might be to model when an agent might be
        able to guarantee the success of its actions

   Agents that persist with their intentions (as
    long as they are satisfiable) are said to be
    committed to those intentions
   The concept of a commitment is very useful
    in modeling societies of agents
 Basic interpreter

                                                  internal state
               options := option-generator (event-queue, S);
               selected-options := deliberate (options, S);
               update-state (selected-options, S);
               execute (S);
               event-queue := get-new-events();
           until quit.
BDI interpreter
                                           Beliefs, desires (goals),
    BDI-interpreter                        and intentions
      options := option-gen (event-queue, B, G, I);
      selected-options := deliberate (options, B, G, I);
      update-intentions (selected-options, I);
      execute (I);
      event-queue := get-new-events();
                                                  satisfied or
      drop-successful-attitudes (B, G, I);        unrealizable
      drop-impossible-attitudes (B, G, I);        beliefs, goals, and
    until quit.
Issues in implementation

   Updating the BDI structures is intractable in
    the general case
   Use only explicit beliefs and goals
   Represent beliefs, goals and intentions as
    plan structures that are followed by the agent
       Support means-ends reasoning
       Hierarchically structured
Coordinating BDI agents
   Model actions of the agents in terms of how
    they can be affected by other agents’
       Flexible actions can be delayed or omitted
       Inevitable actions can be delayed but not omitted
       Immediate actions can be neither delayed nor
       Triggerable actions can be performed at the
        request of another agent
   Use a finite state automaton (skeleton) to
    model the state transitions of the agent
Coordination relationships

   Model the relationships between two agents’
       Is-required-by
       Disables
       Enables
       Conditionally enables
       (guaranteeing enablement)
       Initiates
       Jointly-required-by
       Compensates-for-failure
Communicating BDI agents

   Performative: speech act that is itself an
       Informing
       Requesting
       Promising
       Permitting
       Prohibiting
       Declaring
       Expressing
Communicating: Ontologies

   Ontology – representation of objects and
    relationships in the world
       Not quite the same as a knowledge base
       An ontology is typically the “representational” part
        of a knowledge base…
       …but sometimes axioms and rules are in an
Societies of BDI agents

   Groups of agents interact in some way
       Agents may have different roles within the group
       The agents may be heterogeneous or
   Teams of agents share (some) common
Mutual BDI

   Mutual beliefs
       Everyone believes p, believes that the others believe p,
        believes that the others believe …
       Impossible to achieve perfect mutual information in
        environments where communication can fail: “We attack at
   Joint intentions
       Everyone intends p; everyone will persist with p until
        achieved or impossible
   Shared plans: intending-to and intending-that
   Social commitments: promises and persistence
A few notes on grammar

   “Punctuation always goes inside a quote.”
   “That” is used to define; “which” is used to clarify or
       The system that Weiss describes is …
        (“that” tells which system I’m talking about)
       The PRS system, which Georgeff et al. developed, …
        (“which” tells more about the only system in question)
   Useful references:
       Strunk and White, Elements of Style
       DuPre, Bugs in Writing
       Chicago Manual of Style

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