A First-Order Formalization of Commitments and Goals for Planning Felipe Meneguzzi 1 , Pankaj Telang 2 and Munindar Singh 2 1 Pontifical Catholic University of Rio Grande do Sul felipe.meneguzzi@pucrs.br 2 North Carolina State University Wednesday, 17 July 13
Motivation • Commitments have been extensively studied in MAS • Encode high-level social relations between agents • Define communication protocols among agents • Previous formalizations • Operational semantics for goals and commitments, and their interaction • Propositional planning formalization Wednesday, 17 July 13
Commitment Lifecycle Expired (E) Null (N) Pending (P) • Formally reactivate create C(Debtor, suspend antecedent failure Creditor, Active (A) antecedent, Conditional (C) Detached (D) consequent) antecedent • E.g. cancel cancel ∨ consequent C(buyer,seller,goods,paid) consequent failure release Terminated (T) Satisfied (S) Violated (V) Wednesday, 17 July 13
Goal Lifecycle Null (N) • Formally consider G(Agent, pg, s, f) Inactive (I) Active (A) activate • E.g. G(buyer, suspend suspend reactivate reconsider needsgoods,goods,deadline Suspended (U) ) drop ∨ abort fail succeed Terminated (T) Failed (F) Satisfied (S) Wednesday, 17 July 13
Relating Commitments and Goals • Practical Rules relating commitments and goals • Let G = G(buyer, ⊤ ,goods, ⊥ ) and C = C (buyer, seller, goods, pay) • Entice Rule : If G is active and C is null, buyer creates C h G A , C N i create ( C ) • Motivation: Buyer can achieve its goals of goods by creating the commitment to pay for them to Seller Wednesday, 17 July 13
Hierarchical Task Network Planning • Generates a plan by successive refinement of tasks nonprimitive task • Non-primitive Tasks - abstract, high-level tasks to be method instance decomposed precond • Primitive Tasks - cannot be further primitive task primitive task decomposed (operators) operator operator • Multiple implementations instance instance (e.g. JSHOP2, SHOP2) s0 s1 s2 precond effects precond effects • Abstraction of choice for agent programming languages Wednesday, 17 July 13
HTN Planning for Commitments and Goals • Formalization of commitment protocols in terms of HTN planning Agent Commitment • Axioms enforcing state transition model Goals Protocols for goals and commitments • Planning Operators describing axioms methods operators transitions (e.g. create, suspend, etc.) HTN Planning Domain • HTN Methods for practical rules HTN Valid (e.g. entice, negotiate, etc.) Planner Enactments • Allows HTN planner to be used to validate commitment protocols Wednesday, 17 July 13
A first-order formalization • Propositional formalization had several limitations Agent Commitment • Limited expressivity Goals Protocols • New First-order formalization: domain domain domain axioms methods operators • Domain independent axioms, methods axioms methods operators and operators HTN Planning Domain • Domain dependent Multiple HTN axioms, costs, methods and operators Enactments + Planner Costs • Useful patterns of behavior Wednesday, 17 July 13
Domain Independent Axioms & Operators Commitment Axioms Goal Axioms n ull ( G, Gt, ~ Gv ) ¬ var ( G, Gt, ~ n ull ( C, Ct, ~ Cv ) ← ¬ var ( C, Ct, ~ Gv ) Cv ) i nactiveG ( G, Gt, ~ Gv ) ¬ null ( G, Gt, ~ Gv ) c onditional ( C, Ct, ~ Cv ) ← active ( C, Ct, ~ Cv ) ∧ ¬ p ( C, Ct, ~ Cv ) ^ ¬ f ( G, Gt, ~ Gv ) ^ ¬ s ( G, Gt, ~ Gv ) d etached ( C, Ct, ~ Cv ) ← active ( C, Ct, ~ Cv ) ∧ p ( C, Ct, ~ Cv ) ^ ¬ terminalG ( G, Gt, ~ Gv ) ^ ¬ suspendedG ( G, Gt, ~ Gv ) ^ ¬ activeG ( G, Gt, ~ Gv ) ~ ~ Commitment Operators Goal Operators h operator ! consider ( G, Gt, X, ~ h operator ! create ( C, Ct, De, Cr, ~ Gv ) , Cv ) , pre ( goal ( G, Gt, X ) ^ null ( G, Gt, ~ Gv ) ^ pg ( G, Gt, ~ pre ( commitment ( C, Ct, De, Cr ) ^ null ( C, Ct, ~ Gv )) , Cv )) , del () , add ( var ( G, Gt, ~ del () , add ( var ( C, Ct, ~ Gv )) i Cv )) i h operator ! activate ( G, Gt, X, ~ h operator ! suspend ( C, Ct, De, Cr, ~ Gv ) , Cv ) , pre ( goal ( G, Gt, X ) ^ inactiveG ( G, Gt, ~ pre ( commitment ( C, Ct, De, Cr ) ^ active ( C, Ct, ~ Gv )) , Cv )) , del () , add ( activatedG ( G, Gt, ~ del () , add ( pending ( C, Ct, ~ Gv )) i Cv )) i ~ suspend Wednesday, 17 July 13
Domain Dependent Definitions • Axioms plus Domain-dependent operators • Commitment Axioms formula κ we define the rules below: p ( C, Ct, ~ Cv ) ← commitment ( C, Ct, De, Cr ) ∧ ' q ( C, Ct, ~ Cv ) ← commitment ( C, Ct, De, Cr ) ∧ κ en these two basic formulas from the commitment • Goal Axioms p g ( G, Gt, ~ Gv ) goal ( G, Gt, X ) ^ $ s ( G, Gt, ~ Gv ) goal ( G, Gt, X ) ^ & f ( G, Gt, ~ Gv ) goal ( G, Gt, X ) ^ # • Axioms Generated automatically using a compilation tool • Plus any domain-specific operators (e.g. purchase, ship, etc) Wednesday, 17 July 13
Patterns of Behavior achieveGoal(G1) • Concession Pattern satisfy(C3) create(C2) create(C3) detach(C2) satisfy(C2) 2 commitments • C2 - merchant commits to delivering the pay(20, 123) pay(80, 123) !goods(123) goods upon a $20 payment from the customer !paid(20, 123) !paid(80, 123) • C3 - customer commits to pay $80 upon receiving the goods • By creating commitments C2 and C3, the customer has one possible way of achieving its goal Wednesday, 17 July 13
Conclusions and Future Work • A FO formalization of goals and commitment protocols • Multiple interacting instances of the same goals and commitments • Piecemeal progress, concession, consolidation and compensation • Future Work • Reasoning about probabilities • Modelling non-cooperative partners Wednesday, 17 July 13
Questions? Wednesday, 17 July 13
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