Coalitional agency and evidence-based ability Nicolas Troquard ISTC-CNR (LOA group, Trento) International Workshop on The Cognitive Foundations of Group Attitudes and Social Interaction Toulouse, May 31-June 1, 2012 1 / 31
Outline Introduction 1 Elgesem’s account of individual agency and ability 2 Coalitional agency and ability 3 Meta-mathematics and reasoning about coalitional agency 4 Explicit objectives and Evidences 5 2 / 31
Formal theories of Agency Talking explicitly about action terms: using Dynamic Logics in computer science using first-order theories in the study of action sentences Actions are identified with what they bring about: St. Anselm (11th century) “seeing-to-it-that” (STIT): Chellas, Belnap and Perlo ff , ... “bringing-it-about”: Kanger, Pörn, Lindahl, Elgesem, ... 3 / 31
“bringing-it-about” in multi-agent systems (I) The bringing-it-about modality E x is popular in the MAS community to model the actions and responsibilities of acting entities: agency of an individual agent (Kanger, ...): E i ϕ ⇒ “agent i is responsible ( ex post acto ) for ϕ ” “agent i is agentive for ϕ ” “agent i brings it about that ϕ ” agency of an agent in a role (Santos and Jones, Sartor, Carmo and Pacheco, ...): E i : r ϕ ⇒ “agent i qua r is responsible for ϕ ” obligations of an agent in a role: OE i : r ϕ ⇒ “agent i playing the role r ought to achieve ϕ ” 4 / 31
“bringing-it-about” in multi-agent systems (II) Example Beliefs and expectations about other agents’ current behaviour: Bel Mary ¬ E John “dinner is ready” Obligation to do / Imperatives: E Mary O John E John “dinner is ready” Constraining a behaviour: E Mary E John “dinner is ready” Deliberate inaction: E Mary ¬ E Mary “Mary eats chocolate” 5 / 31
Outline Introduction 1 Elgesem’s account of individual agency and ability 2 Coalitional agency and ability 3 Meta-mathematics and reasoning about coalitional agency 4 Explicit objectives and Evidences 5 6 / 31
Goal-oriented (possibly non-intentional) individual agency Sommerho ff [Sommerho ff 1969]: agency is the actual bringing about of a goal towards which an activity is oriented. An agent acts to achieve a goal. But an agent is not necessarily aware of his goals, at least not in the sense that he is consciously committed to achieve them. Frankfurt [Frankfurt 1988]: the pertinent aspect of agency is the manifestation of the agent’s guidance (or control) towards a goal; not necessarily an intentional action. 7 / 31
Core principles of agency Propositional logic ⊢ ¬ E i ⊤ ⊢ E i ϕ ∧ E i ψ → E i ( ϕ ∧ ψ ) ⊢ E i ϕ → ϕ if ⊢ ϕ ↔ ψ then ⊢ E i ϕ ↔ E i ψ Example ⊢ ¬ E i ⊥ E i ϕ ∧ ¬ E i E i ϕ is satisfiable 8 / 31
Agency as the manifestation of control Elgesem observes that the manifestation of control is the exercise of a power to bring about something. Therefore, the notion of potential control of an agent for a goal should be integrated in a theory of agency. Example ([Elgesem 1998]) Bob Beamon, jumped 8.90 m (long jump) in the 1968 Olympics. If Beamon jumped that far it is that he was exercising control towards a goal. Even though this goal was probably not intentionally to jump 8.90 m, we would not take back from Beamon that on that day: he brought about the fact that he jumped that far, and he had the ability to do it. 9 / 31
Ability Elgesem then suggests: there is a more basic notion of ability than an intention-based one, and this non-intentional notion of ability is a necessary condition for agency. By bringing about something, an agent is deemed able. Similar to Mele’s simple ability in [Mele 2003, p. 448]: ”an agent’s A-ing at a time is su ffi cient for his having the simple ability to A at that time.”, and “being able to A intentionally entails having a simple ability to A and the converse is false” 10 / 31
Principles of ability ⊢ ¬ C i ⊥ ⊢ ¬ C i ⊤ ⊢ E i ϕ → C i ϕ if ⊢ ϕ ↔ ψ then ⊢ C i ϕ ↔ C i ψ Example ⊢ E i ϕ ∧ E i ψ → E i ( ϕ ∧ ψ ) → C i ( ϕ ∧ ψ ) 11 / 31
Outline Introduction 1 Elgesem’s account of individual agency and ability 2 Coalitional agency and ability 3 Meta-mathematics and reasoning about coalitional agency 4 Explicit objectives and Evidences 5 12 / 31
Joint actions and collective goals A group is a set of agents. Joint actions are a species of actions involving a group that acts towards a shared goal. S. Miller [Miller 2001] says of a joint action that it involves two co-present agents each of whom performs simultaneously with the other agent one basic individual action, and in relation to a collective goal. (Joint actions are not necessarily social actions.) “Joint actions consist of the individual actions of a number of agents directed to the realisation of a collective end. A collective end —notwithstanding its name— is a species of individual end; it is an end possessed by each of the individuals involved in the joint action.” 13 / 31
A weaker requirement than collective intentionality Despite resorting to the concept of a collective goal, Miller argues that we-intentions are not a necessary element of joint actions. Example ([Bottazzi, Ferrario]) Two scholars start chatting at a conference break and somewhat start to take a walk in the park. They respect their turn in the conversation, they synchronize their pace, and take a direction in the park without having previously agreed on it. 14 / 31
Goal-oriented non-intentional coalitional agency and ability Similar to the individual case: there is a more basic notion of coalitional goal-directed agency than an intentional one (coalitional) agency is the manifestation of an existing control that means that there is a basic notion of coalitional ability that is a necessary condition for coalitional agency 15 / 31
Inferring coalitional responsibilities and abilities In social choice theory, superadditivity is: E ff G 1 ϕ ∧ E ff G 2 ψ → E ff G 1 ∪ G 2 ( ϕ ∧ ψ ) , when G 1 ∩ G 2 = ∅ We already have the aggregation principle: E G ϕ ∧ E G ψ → E G ( ϕ ∧ ψ ) We should not have (even when G 1 ∩ G 2 = ∅ ): E G 1 ϕ ∧ E G 2 ψ → E G 1 ∪ G 2 ( ϕ ∧ ψ ) G 1 and G 2 would need to share a goal. (I’ll come back to it.) C G 1 ϕ ∧ C G 2 ψ → C G 1 ∪ G 2 ( ϕ ∧ ψ ) Ability would need some kind of context. We have something mixed (for any G 1 and G 2 ): E G 1 ϕ ∧ E G 2 ψ → C G 1 ∪ G 2 ( ϕ ∧ ψ ) 16 / 31
Principles of coalitional agency and ability For all groups G , G 1 , and G 2 and formulas ϕ and ψ : Ax0 ⊢ ϕ , when ϕ is a tautology of propositional logic Ax1 ⊢ E G ϕ ∧ E G ψ → E G ( ϕ ∧ ψ ) Ax2 ⊢ E G ϕ → ϕ Ax3 ⊢ E G ϕ → C G ϕ Ax4 ⊢ ¬ C G ⊥ Ax5 ⊢ ¬ C G ⊤ Ax6 ⊢ ¬ C ∅ ϕ Ax7 ⊢ E G 1 ϕ ∧ E G 2 ψ → C G 1 ∪ G 2 ( ϕ ∧ ψ ) MP if ⊢ ϕ and ⊢ ϕ → ψ then ⊢ ψ ERE if ⊢ ϕ ↔ ψ then ⊢ E G ϕ ↔ E G ψ ERC if ⊢ ϕ ↔ ψ then ⊢ C G ϕ ↔ C G ψ 17 / 31
Additional candidate axioms Ax8 ⊢ E G 1 ϕ → ¬ E G 2 ϕ , when G 2 ⊂ G 1 Ax9 ⊢ E G 1 E G 2 ϕ → E G 1 ϕ Ax10 ⊢ E G 1 E G 2 ϕ → E G 1 ∪ G 2 ϕ 18 / 31
Outline Introduction 1 Elgesem’s account of individual agency and ability 2 Coalitional agency and ability 3 Meta-mathematics and reasoning about coalitional agency 4 Explicit objectives and Evidences 5 19 / 31
Semantics and completeness There is a class C of neighborhood models with respect to which the Hilbert system presented on Slide 17 is sound an complete. We say that a formula ϕ is COAL-sat if there is a model in C in which ϕ is true. 20 / 31
An algorithm to decide whether ϕ is COAL-sat 1 non-deterministically guess a semi-valuation π for ϕ ; if E ∅ ψ ∈ sub ¬ ( ψ ) , then check that π ( E ∅ ψ ) = 0 ; 2 if C ∅ ψ ∈ sub ¬ ( ψ ) , then check that π ( C ∅ ψ ) = 0 ; 3 if E G ψ ∈ sub ¬ ( ϕ ) and π ( E G ψ ) = 1 , then check that π ( ψ ) = 1 ; 4 if E G ψ ∈ sub ¬ ( ϕ ) and π ( E G ψ ) = 1 , recursively check that ¬ ψ is COAL-sat; 5 if C G ψ ∈ sub ¬ ( ϕ ) and π ( C G ψ ) = 1 , recursively check that both: 6 ¬ ψ is COAL-sat; ψ is COAL-sat; if E G ψ 1 , C G ψ 2 ∈ sub ¬ ( ϕ ) , with π ( E G ψ 1 ) = 1 and π ( C G ψ 2 ) = 0 then recursively check that 7 ψ 1 ∧ ¬ ψ 2 is COAL-sat; 8 if either: E G ψ 1 , . . . , E G ψ k , E G ψ ∈ sub ¬ ( ϕ ) , with π ( E G ψ j ) = 1 for all j , and π ( E G ψ ) = 0 ; E G 1 ψ 1 , . . . , E Gk ψ k , C G ψ ∈ sub ¬ ( ϕ ) , with π ( E Gj ψ j ) = 1 for all j , π ( C G ψ ) = 0 , and G = G 1 ∪ . . . G k ; then non-deterministically and recursively check that either: � j ( ψ j ) ∧ ¬ ψ is COAL-sat ( ¬ ψ 1 ) ∧ ψ is COAL-sat; . . . ( ¬ ψ k ) ∧ ψ is COAL-sat. 21 / 31
Computational complexity of reasoning about agency The satisfiability of: the core logic of agency, Elgesem’s logic of agency and ability, and the logic of coalitional agency and ability can all be decided in space polynomial (in PSPACE). 22 / 31
Outline Introduction 1 Elgesem’s account of individual agency and ability 2 Coalitional agency and ability 3 Meta-mathematics and reasoning about coalitional agency 4 Explicit objectives and Evidences 5 23 / 31
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