Coalitional agency and evidence-based ability Nicolas Troquard - - PowerPoint PPT Presentation

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

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Outline

1

Introduction

2

Elgesem’s account of individual agency and ability

3

Coalitional agency and ability

4

Meta-mathematics and reasoning about coalitional agency

5

Explicit objectives and Evidences

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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 Perloff, ... “bringing-it-about”: Kanger, Pörn, Lindahl, Elgesem, ...

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“bringing-it-about” in multi-agent systems (I)

The bringing-it-about modality Ex is popular in the MAS community to model the actions and responsibilities of acting entities: agency of an individual agent (Kanger, ...): Eiϕ ⇒ “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, ...): Ei:rϕ ⇒ “agent i qua r is responsible for ϕ”

• bligations of an agent in a role:

OEi:rϕ ⇒ “agent i playing the role r ought to achieve ϕ”

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“bringing-it-about” in multi-agent systems (II)

Example Beliefs and expectations about other agents’ current behaviour: BelMary¬EJohn“dinner is ready” Obligation to do / Imperatives: EMaryOJohnEJohn“dinner is ready” Constraining a behaviour: EMaryEJohn“dinner is ready” Deliberate inaction: EMary¬EMary“Mary eats chocolate”

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Outline

1

Introduction

2

Elgesem’s account of individual agency and ability

3

Coalitional agency and ability

4

Meta-mathematics and reasoning about coalitional agency

5

Explicit objectives and Evidences

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Goal-oriented (possibly non-intentional) individual agency

Sommerhoff [Sommerhoff 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.

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Core principles of agency

Propositional logic ⊢ ¬Ei⊤ ⊢ Eiϕ ∧ Eiψ → Ei(ϕ ∧ ψ) ⊢ Eiϕ → ϕ if ⊢ ϕ ↔ ψ then ⊢ Eiϕ ↔ Eiψ Example ⊢ ¬Ei⊥ Eiϕ ∧ ¬EiEiϕ is satisfiable

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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.

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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 sufficient 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”

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Principles of ability

⊢ ¬Ci⊥ ⊢ ¬Ci⊤ ⊢ Eiϕ → Ciϕ if ⊢ ϕ ↔ ψ then ⊢ Ciϕ ↔ Ciψ Example ⊢ Eiϕ ∧ Eiψ → Ei(ϕ ∧ ψ) → Ci(ϕ ∧ ψ)

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Outline

1

Introduction

2

Elgesem’s account of individual agency and ability

3

Coalitional agency and ability

4

Meta-mathematics and reasoning about coalitional agency

5

Explicit objectives and Evidences

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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

• f 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.”

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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.

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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

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Inferring coalitional responsibilities and abilities

In social choice theory, superadditivity is: EffG1ϕ ∧ EffG2ψ → EffG1∪G2(ϕ ∧ ψ), when G1 ∩ G2 = ∅ We already have the aggregation principle: EGϕ ∧ EGψ → EG(ϕ ∧ ψ) We should not have (even when G1 ∩ G2 = ∅): EG1ϕ ∧ EG2ψ → EG1∪G2(ϕ ∧ ψ)

G1 and G2 would need to share a goal. (I’ll come back to it.)

CG1ϕ ∧ CG2ψ → CG1∪G2(ϕ ∧ ψ)

Ability would need some kind of context.

We have something mixed (for any G1 and G2): EG1ϕ ∧ EG2ψ → CG1∪G2(ϕ ∧ ψ)

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Principles of coalitional agency and ability

For all groups G, G1, and G2 and formulas ϕ and ψ: Ax0 ⊢ ϕ , when ϕ is a tautology of propositional logic Ax1 ⊢ EGϕ ∧ EGψ → EG(ϕ ∧ ψ) Ax2 ⊢ EGϕ → ϕ Ax3 ⊢ EGϕ → CGϕ Ax4 ⊢ ¬CG⊥ Ax5 ⊢ ¬CG⊤ Ax6 ⊢ ¬C∅ϕ Ax7 ⊢ EG1ϕ ∧ EG2ψ → CG1∪G2(ϕ ∧ ψ) MP if ⊢ ϕ and ⊢ ϕ → ψ then ⊢ ψ ERE if ⊢ ϕ ↔ ψ then ⊢ EGϕ ↔ EGψ ERC if ⊢ ϕ ↔ ψ then ⊢ CGϕ ↔ CGψ

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Additional candidate axioms

Ax8 ⊢ EG1ϕ → ¬EG2ϕ , when G2 ⊂ G1 Ax9 ⊢ EG1EG2ϕ → EG1ϕ Ax10 ⊢ EG1EG2ϕ → EG1∪G2ϕ

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Outline

1

Introduction

2

Elgesem’s account of individual agency and ability

3

Coalitional agency and ability

4

Meta-mathematics and reasoning about coalitional agency

5

Explicit objectives and Evidences

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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.

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An algorithm to decide whether ϕ is COAL-sat

1

non-deterministically guess a semi-valuation π for ϕ;

2

if E∅ψ ∈ sub¬(ψ), then check that π(E∅ψ) = 0;

3

if C∅ψ ∈ sub¬(ψ), then check that π(C∅ψ) = 0;

4

if EGψ ∈ sub¬(ϕ) and π(EGψ) = 1, then check that π(ψ) = 1;

5

if EGψ ∈ sub¬(ϕ) and π(EGψ) = 1, recursively check that ¬ψ is COAL-sat;

6

if CGψ ∈ sub¬(ϕ) and π(CGψ) = 1, recursively check that both: ¬ψ is COAL-sat; ψ is COAL-sat;

7

if EGψ1, CGψ2 ∈ sub¬(ϕ), with π(EGψ1) = 1 and π(CGψ2) = 0 then recursively check that ψ1 ∧ ¬ψ2 is COAL-sat;

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if either: EGψ1, . . . , EGψk, EGψ ∈ sub¬(ϕ), with π(EGψj) = 1 for all j, and π(EGψ) = 0; EG1 ψ1, . . . , EGk ψk, CGψ ∈ sub¬(ϕ), with π(EGj ψj) = 1 for all j, π(CGψ) = 0, and G = G1 ∪ . . . Gk; then non-deterministically and recursively check that either:

• j(ψj) ∧ ¬ψ is COAL-sat

(¬ψ1) ∧ ψ is COAL-sat; . . . (¬ψk) ∧ 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).

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Outline

1

Introduction

2

Elgesem’s account of individual agency and ability

3

Coalitional agency and ability

4

Meta-mathematics and reasoning about coalitional agency

5

Explicit objectives and Evidences

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Towards evidence-based ability

One can have the certainty that the group G is able to bring about that ϕ in only two circumstances: G is actually bringing about ϕ (axiom Ax3), or some subgroups of G1, . . . , Gk ⊆ G such that G = G1 ∪ . . . ∪ Gk are bringing about some goals ϕ1, . . . , ϕk such that ϕ ↔ ϕ1 ∧ · · · ∧ ϕk (axiom Ax7) The theory does not say what this ability becomes after the actual manifestation of the evidence. Nor does it say what it is before.

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Induction

Our notion of evidence-based ability is calling for some kind of inductive reasoning. One can acknowledge G’s ability for the goal ϕ at any time the coalition indeed brings it about, and then maintain this evidence-based ability until some further evidence falsifies it. That is, as a way to encompass Kenny’s view, we could drop the ability when the group fails to repeat their control, even when the ‘appropriate opportunity’ arises.

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Linear time and objectives

We need new primitives. Temporal features:

ϕUψ: “ϕ is true until ψ holds”.

Explicit objective for an individual agent:

Objiϕ: “i has the objective that ϕ”.

It remains to characterize: ObjGϕ: “group G has the mutual objective that ϕ”.

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Mutual objectives

Everyone’s objective. “ϕ is a shared goal/end”: O

ˆ Gϕ ↔

• i∈G

Objiϕ Mutual objective. “It is everyone’s objective that ϕ, and it is everyone’s objective that it is everyone objective that ϕ, and...” [Dunin-Ke ¸plicz & Verbrugge]: ObjGϕ ↔ O

ˆ G(ϕ ∧ ObjGϕ)

if ⊢ ϕ → O

ˆ G(ψ ∧ ϕ) then ⊢ ϕ → ObjGψ

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Relationship between objectives and agency

Goal-directed agency justifies the principle: EGϕ → ObjGϕ. Remember: We should not have (even when G1 ∩ G2 = ∅): EG1ϕ ∧ EG2ψ → EG1∪G2(ϕ ∧ ψ) because G1 and G2 would need to share a goal. Now, we can admit: EG1ϕ ∧ EG2ψ ∧ ObjG1∪G2(ϕ ∧ ψ) → EG1∪G2(ϕ ∧ ψ)

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Falsification, repeatability

We say that a situation falsifies that G is able to achieve the goal ϕ when: G has the objective that ϕ holds, but does not bring about that ϕ. This suggests the following principle: CGϕ → (CGϕ)U(ObjGϕ ∧ ¬EGϕ).

Possibly with a side condition strengthening CG: CGϕ → (CGϕ)U((ObjGϕ ∧ ¬EGϕ) ∧ ξ). Possibly with a side condition weakening CG: CGϕ → (CGϕ)U((ObjGϕ ∧ ¬EGϕ) ∨ ξ). 29 / 31

Falsification, repeatability

We say that a situation falsifies that G is able to achieve the goal ϕ when: G has the objective that ϕ holds, but does not bring about that ϕ. This suggests the following principle: CGϕ → (CGϕ)U(ObjGϕ ∧ ¬EGϕ).

Possibly with a side condition strengthening CG: CGϕ → (CGϕ)U((ObjGϕ ∧ ¬EGϕ) ∧ ξ). Possibly with a side condition weakening CG: CGϕ → (CGϕ)U((ObjGϕ ∧ ¬EGϕ) ∨ ξ). 29 / 31

Problem: showing evidence of a new ability

We should also have: ¬CGϕ → (¬CGϕ)U(“G show evidence they can bring about ϕ”). Example ¬C{i,j}(p ∧ q ∧ r) → (¬C{i,j}(p ∧ q ∧ r)U((E{i,j}(p ∧ q ∧ r))∨ (Eip ∧ Ej(q ∧ r))∨ (Ei(p ∧ q) ∧ Ejr)∨ . . . ) Possible solution:

1 capitalize on ⊢ EG1ϕ ∧ EG2ψ → CG1∪G2(ϕ ∧ ψ) (axiom Ax7) 2 enumerate the (minimal) sets of implicants of ϕ and 3 take the disjunction of all the possible ways the

subcoalitions of G could bring them about

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Summary

Elgesem: goal-oriented non-intentional agency and ability a coalitional version of bringing-it-about

but really, the logic of the modality E does not change Elgesem’s notion of ability is strengthened

complexity of reasoning is in space polynomial strengthen agency of groups

strict agency and agency by delegation capitalizing on explicit objectives

refining ability with induction

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