CohenLevesque

Intention Is Commitment with Expectation: 

Intention Is Commitment with Expectation James Creel, Christopher Menzel, and Thomas Ioerger. FLAIRS-20, Key West, Florida, Monday May 7, 2007.

Outline: 

Outline Literary backdrop (1) Review of modal logic (3) Cohen & Levesque’s theory of intention (6) The problems identified by Singh (6) Solutions to the problems (5)

Cohen & Levesque’s Theory and Its Proponents: 

Cohen & Levesque’s Theory and Its Proponents C&L – Intention, joint intention, communicative acts Nick Jennings – Joint intentions in industrial robotics 1995 Milind Tambe – Toward Flexible Teamwork 1997 Michael Woolridge’s Introduction to Multiagent Systems Textbook 2002 Andreas Herzig & Dominique Longin – Reconsideration of fundamentals in 2004 And yet a disturbing criticism has long remained unaddressed…

Review of Modal Logic (1/3): 

Review of Modal Logic (1/3) A model M contains a set of worlds W and an accessibility relation ~. M, wW ╞   w s.t. w~w, M,w ╞  M, wW ╞ ◊  w s.t. w~w  M,w ╞ 

Review of Modal Logic (2/3): 

Review of Modal Logic (2/3) The two modal operators  and ◊ are duals:   ¬◊¬ ◊  ¬¬ A moment’s reflection reveals that this follows from the duality of  and .

Review of Modal Logic (3/3)Some Axioms of Modal Logic: 

Review of Modal Logic (3/3) Some Axioms of Modal Logic K is granted: ╞ (  )  (  ) B (~ symmetric): ╞   ◊ T (~ reflexive): ╞    D (~ serial): ╞   ◊ 4 (~ transitive): ╞    5 (~ Euclidean): ╞ ◊  ◊

C&L’s Theory (1/4): 

C&L’s Theory (1/4) A linear time temporal logic integrated with a KD conative logic and KD45 (weak S5) doxastic logic. B is the belief accessibility relation C is the choice accessibility relation BEL / ALLOW are the dual doxastic modalities CHOOSE / ACCEPT are the dual conative modalities

C&L’s Theory (2/4): 

C&L’s Theory (2/4) The constraint of realism: C  B Agents choose only from what they allow is possible. From realism it follows that every believed formula is chosen. From definitions, every chosen formula is accepted. Finally, from realism every accepted formula is allowed.

C&L’s Theory (3/6): 

C&L’s Theory (3/6) (HAPPENS a) (DONE a) ◊  e (HAPPENS e;?) (eventually)   ◊ (always) (LATER ) (eventually but not currently) (BEFORE , ) (should  ever come true,  comes true before  ) (A-GOAL )  (CHOOSE (LATER ))  (BEL )

C&L’s Theory (4/6) Persistent Goals (Commitments): 

C&L’s Theory (4/6) Persistent Goals (Commitments) A persistent goal (commitment) is an achievement goal that must be believed to be either achieved or impossible before it is dropped. (P-GOAL p)  (CHOOSE (LATER p))  (BEL p)  [BEFORE ((BEL p)  (BEL p)) (CHOOSE (LATER p))]

C&L’s Theory (5/6) Intention To : 

C&L’s Theory (5/6) Intention To Intention toward action is a commitment to have done the action immediately after having believed it was occurring. (INTEND1 a)  (P-GOAL (DONE (BEL (HAPPENS a))?;a))

C&L’s Theory (6/6) Intention That : 

C&L’s Theory (6/6) Intention That Intention toward a proposition is a commitment to have done some action that brings about the proposition immediately after having believed that there exists some action e that brings about the proposition and having accepted that the particular action e is the one that brings about the proposition. (INTEND2 p)  (P-GOAL e, (DONE [(BEL e, (HAPPENS e;p?))  (ACCEPT (HAPPENS e;p?))]?; e;p?))

Problems Identified By Singh (1/6): 

Problems Identified By Singh (1/6) An important assumption of C&L is ╞ ◊(CHOOSE (LATER )), which states that all achievement goals are eventually dropped. This is taken to capture both the following assumptions: Agents to not persist forever with a goal Agents do not forever defer working on their goals

Problems Identified By Singh (2/6)From Persistence to Eventualities: 

Problems Identified By Singh (2/6) From Persistence to Eventualities “If someone has a persistent goal of bringing about p, p is within his area of competence, and, before dropping his goal, the agent will not believe p will never occur, then eventually p becomes true.” ╞ (P-GOAL p)  (COMPETENT p)  [BEFORE (BEL p), (CHOOSE (LATER p))]  ◊p

Problems Identified By Singh (3/6): 

Problems Identified By Singh (3/6) The “from persistence to eventualities” theorem just stated “relates virtually trivial requirements on agents to non-trivial conditions in the world. For example, let me be the agent and let p be my favorite implausible proposition: that Helmut Kohl is on top of Mt Everest. I can easily (1) have this P-GOAL, (2) for eternity not hold the belief that Herr Kohl will not ever make it to the top of Mt Everest, and (3) be always COMPETENT about p. Therefore, by the above theorem Herr Kohl will get to the top of Mt Everest. He does not need to try; nor do I. He does not even need to know that his mountaineering feat had been my persistent goal.”

Problems Identified By Singh (4/6): 

Problems Identified By Singh (4/6) Claim: an agent who intends to do a;b also intends to do a. Counterexample: Suppose (DONE a) at the same time as INTEND1(a;b). In this case the agent cannot hold an A-GOAL about doing a because a is already done.

Problems Identified By Singh (5/6)Interleaving Plan Execution: 

Problems Identified By Singh (5/6) Interleaving Plan Execution An agent cannot intend multiple plans and flexibly interleave their executions, because if an agent does not predict (i.e. believe in) the exact course of events of an intention, the agent cannot intentionally carry out that intention.

Problems Identified By Singh (6/6): 

Problems Identified By Singh (6/6) “When asked to serve coffee, he forms an intention to do the following complex action: pick up a cup; pour coffee into it; take the cup to the table. When asked to serve tea, he forms an intention to do the corresponding action for tea. Suppose now that two orders are placed: one for tea and the other for coffee. The agent adopts two intentions as described above. The agent initially ought to pick up a cup; let us assume that this is the action he chooses and the one he believes he is about to do. However, at the time the agent picks up a cup, he might not have decided what action he will do after that, i.e. whether he will pour coffee or pour tea into the cup. Indeed, whether he pours coffee or tea into the cup might depend on other factors, e.g., which of the two brews is prepared, or whether other agents are blocking the route to one of the pots.”

Solutions (1/5): 

Solutions (1/5) Actions cannot be intentionally repeated? Key Insight: Actions are not carried out for their own sake, but for the sake of some desired outcome. Being unable to quantify over formulas, we introduce justification variables whose denotations are sets of possible worlds. A new test action s¿ succeeds if the current world is a member of s.

Solutions (2/5): 

Solutions (2/5) Intention execution cannot be interleaved? We need a notion of intention that does not require a complete plan. (WEAK-INTEND1 a)  s, (P-GOAL (DONE a;s¿)) (WEAK-INTEND2 p)  (P-GOAL a,(DONE a;p?))

Solutions (3/5): 

Solutions (3/5) In the strong sense of the word, one has a plan to carry out what one intends. (INTEND1 a)  s (P-GOAL (DONE a;s¿))  (BEL (HAPPENS a;s¿)) (INTEND2 p)  e (WEAK-INTEND p)  (BEL (HAPPENS e;p?))

Solutions (4/5): 

Solutions (4/5) Intention+No infinite persistence is too powerful. To prevent a scenario where an agent’s commitments must come about regardless of action, we need to ensure that agents do not perpetually procrastinate. ╞ (P-GOAL p)  [BEFORE (BEL p), (CHOOSE (LATER p))]  ◊(INTEND2 p)

Solutions (5/5): 

Solutions (5/5) Singh’s criticisms are addressed. In addition, we maintain the fulfillment of the desiderata that intention… poses problems to solve. provides a screen of admissibility. is tracked for successful attempts. is dropped when futile. Aaand, the case of Chisholm’s avunculicidal agent is still covered. Any questions?