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Social Behavior of Agents and Stable Models

Convegno Italiano di Logica Computazionale (CILC’05) Roma, 21-22 Giugno 2005. Social Behavior of Agents and Stable Models. Francesco Buccafurri and Gianluca Caminiti DIMET, Università degli Studi “Mediterranea” di Reggio Calabria. MAS & Logic Programming. Agents  Logic Programs

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Social Behavior of Agents and Stable Models

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  1. Convegno Italiano di Logica Computazionale (CILC’05) Roma, 21-22 Giugno 2005 Social Behavior of Agents and Stable Models Francesco Buccafurri and Gianluca Caminiti DIMET, Università degli Studi “Mediterranea” di Reggio Calabria

  2. MAS & Logic Programming Agents  Logic Programs Desires/Requests  Fixpoints The behavior of one agent can depend on that of the other agents. Social Ability: interaction enables reasoning on agents’ mental states. CILC'05, Roma, 21-22 Giugno 2005

  3. Social-Oriented Reasoning/0 A a1 |A| = N CILC'05, Roma, 21-22 Giugno 2005

  4. Social-Oriented Reasoning/1 A a1 head ← [l,h]{body} CILC'05, Roma, 21-22 Giugno 2005

  5. Social-Oriented Reasoning/3 l  |S|  h A S a1 head ← [l,h]{body} CILC'05, Roma, 21-22 Giugno 2005

  6. Social-Oriented Reasoning/4 l  |S|  h A S a1 head ← [l,h]{body} CILC'05, Roma, 21-22 Giugno 2005

  7. Social-Oriented Reasoning/4 l  |S|  h A S a1 head ← [l,h]{body} CILC'05, Roma, 21-22 Giugno 2005

  8. Social-Oriented Reasoning/5 A a2 a1 head ← [a2]{body} CILC'05, Roma, 21-22 Giugno 2005

  9. Social-Oriented Reasoning/5 A a2 a1 head ← [a2]{body} CILC'05, Roma, 21-22 Giugno 2005

  10. Social-Oriented Reasoning/5 A a2 a1 head ← [a2]{body} CILC'05, Roma, 21-22 Giugno 2005

  11. Social-Oriented Reasoning/6 A a1 head ← [l1,h1]{body1, [l2,h2]{body2}} CILC'05, Roma, 21-22 Giugno 2005

  12. Social-Oriented Reasoning/6 l1  |S1|  h1 l2  |S2|  h2S2 S1 A S1 S2 a1 head ← [l1,h1]{body1, [l2,h2]{body2}} CILC'05, Roma, 21-22 Giugno 2005

  13. Example 1: a Wedding Party CILC'05, Roma, 21-22 Giugno 2005

  14. Example 1: Intended Models • {}, • {partyP1, partyP2,driveP2}, • {partyP1,partyP2, partyP3}. CILC'05, Roma, 21-22 Giugno 2005

  15. Example 2: a P2P Scenario download(X) ← [min, ]{ share(X), [1,]{not incomplete(X)} }, file(X) okay(share(X)) ← [0.33*N, ]{ share(X), [0.1*N,0.2*N]{high_bw} }, file(X) CILC'05, Roma, 21-22 Giugno 2005

  16. Syntax: Social Rules • h←body • body = b1, …, bm, s1, …, sk (m≥ 0, k ≥0) • h - literal or okay(p) • bi (1 ≤ i≤ m) - (possibly NAF) literal • sj (1≤ j ≤ k) - (possibly NAF) SSC SOLP program = set of social rules SOLP collection = set of SOLP programs CILC'05, Roma, 21-22 Giugno 2005

  17. [l, h] [agent_id] [selection_condition] Syntax: SSC [selection_condition]{body} Warning: [1, 1] ≠ [id]. Note: SSCs can be nested. CILC'05, Roma, 21-22 Giugno 2005

  18. Semantics: Autonomy P - SOLP program Var(P) - atoms occurring in P AP - autonomous reduction of P ATP - extends classical TP to social rules AFP(P) = set of autonomous fixpoints of P CILC'05, Roma, 21-22 Giugno 2005

  19. Semantics: SOLP Collection C ={P1, ..., Pn} - a SOLP collection Social Interpretation for C -I= IP1… IPnIPj - a labeled interpretation for PjC(1 ≤ j ≤ n) Candidate Social Interpretations for C –U(P1, …, Pn) = {F1P1… FnPn| FiAFP(Pi), 1 ≤ i ≤ n} CILC'05, Roma, 21-22 Giugno 2005

  20. Semantics: literals C ={P1, ..., Pn} - a SOLP collection I- a social interpretation for C aVar(Pi), PiC (resp.nota) is truew.r.t.I ifaPiI (resp.aPiI) CILC'05, Roma, 21-22 Giugno 2005

  21. Semantics: SSCs C ={P1, ..., Pn} - a SOLP collection I- a social interpretation for C • [selection_condition]{body} is truew.r.t.I • if a set of agents exists s.t. • 1) selection_conditionholds, and2) bodyistruew.r.t.I CILC'05, Roma, 21-22 Giugno 2005

  22. Semantics: Social Rules C ={P1, ..., Pn} - a SOLP collection I- a social interpretation for C h ← body- a social rule r ofPC • ris truew.r.t.I if either: • h is true w.r.t.I, or • body is false w.r.t.I. CILC'05, Roma, 21-22 Giugno 2005

  23. Semantics: Social Models C ={P1, ..., Pn} - a SOLP collection I- a social interpretation for C IU(P1, …, Pn) is a social modelof C if rP1… Pn, ris true w.r.t.I CILC'05, Roma, 21-22 Giugno 2005

  24. Translation: Overview C ={P1, ..., Pn} - a SOLP collection Goal: to build a single logic program J(C) whose stable models are in 1:1 correspondence with the social models of C. CILC'05, Roma, 21-22 Giugno 2005

  25. Translation: Step-by-step • Each SOLP program is rewritten as a classical one, P’, where the SSCs are represented by special literals. • Conventions on atom names are used in order to know which program a given atom comes from. • All the SSCs in Care rewritten as sequences of DLPAaggregate functions in a logic program S. CILC'05, Roma, 21-22 Giugno 2005

  26. Translation: Final Result J(C) = (PC P’) S Feasible in polynomial time The logic program J(C) selects, among all the candidate social interpretations for C, those w.r.t. which all the SSCs in Caretrue. CILC'05, Roma, 21-22 Giugno 2005

  27. Translation: Theorem C ={P1, ..., Pn} - a SOLP collection SOS(P1, ..., Pn) - the social models of C J(C) = (PC P’) S A one-to-one correspondence exists between the social models in SOS(P1, ..., Pn) and the stable models of J(C). CILC'05, Roma, 21-22 Giugno 2005

  28. Social Models & Joint Fixpoints COLP* program = logic program + okay rules COLP program desires/consents of a single agent Semantics of a set of COLP programs (Joint Fixpoint Semantics*): common agreement among the agents. *F. Buccafurri and G. Gottlob. Multiagent Compromises, Joint Fixpoints and Stable Models, volume 2407 of LNCS and LNAI. Springer, 2002 CILC'05, Roma, 21-22 Giugno 2005

  29. Social Semantics extends JFP From: COLP programs (JFP Semantics) To: SOLP programs (Social Semantics) Feasible in polynomial time CILC'05, Roma, 21-22 Giugno 2005

  30. Social Models & JFP: Theorem P1, ..., Pn - COLP programs Q1, ..., Qn - SOLP programs (the translation of P1, ..., Pn) A one-to-one correspondence exists between the Joint Fixpoints ofP1, ..., Pn and the social models of SOS(Q1, ..., Qn). CILC'05, Roma, 21-22 Giugno 2005

  31. SOS Existence: Theorem ProblemSOSn Instance: A SOLP collection P1, ..., Pn Question: Is SOS(P1, ..., Pn) ? Theorem The problem SOSn is NP complete. CILC'05, Roma, 21-22 Giugno 2005

  32. Conclusions • SOcial Logic Programming (SOLP) enables social behavior among a community of agents. • SOLP extends COLP. • Complexity results. CILC'05, Roma, 21-22 Giugno 2005

  33. Finally… Thank You! CILC'05, Roma, 21-22 Giugno 2005

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