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Autonomous Agents and Multi-Agent Systems
Erschienen in: Autonomous Agents and Multi-Agent Systems 3/2014

01.05.2014

Reasoning about coalitional agency and ability in the logics of “bringing-it-about”

verfasst von: Nicolas Troquard

Erschienen in: Autonomous Agents and Multi-Agent Systems | Ausgabe 3/2014

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Abstract

The logics of “bringing-it-about” have been part of a prominent tradition for the formalization of individual and institutional agency. They are the logics to talk about what states of affairs an acting entity brings about while abstracting away from the means of action. Elgesem’s proposal analyzes the agency of individual agents as the goal-directed manifestation of an individual ability. It has become an authoritative modern reference. The first contribution of this paper is to extend Elgesem’s logic of individual agency and ability to coalitions. We present a general theory and later propose several possible specializations. As a second contribution, we offer algorithms to reason with the logics of bringing-it-about and we analyze their computational complexity.
Vorheriger Artikel Agent-based decentralised coordination for sensor networks using the max-sum algorithm
Nächster Artikel Majority dynamics and aggregation of information in social networks

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Fußnoten
1
We develop the research agenda presented in the earlier extended abstract published as [46].
 
2
Maybe an exception is [33]. There, the agency of a coalition is defined as adequate combinations of individual agency of its members. The additional operators with coalitions are then merely syntactic sugar, leaving the expressivity of the logic unchanged. The logic also goes beyond the Anselmian tradition by allowing explicit action terms in the language.
 
3
The main reference is [15] which unfortunately is not published. The Ref. [16] is essentially the Chapter 2 of [15].
 
4
Similar distinctions between different kinds of ability have later been made by Kapitan [27] and Mele [31]. Mele calls them simple ability to A and ability to A intentionally. He writes: “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” [31, p. 448].
 
5
Notice that \(\lnot E_x\top \) becomes redundant.
 
6
See [52] for a similar and even weaker account of ability.
 
7
Miller uses the terminology “collective end”.
 
8
This example is adapted from [5].
 
9
Observe that, as pointed out in Sect. 2.5 for Constraints 5 and 7, axiom Ax3 is redundant in presence of axiom Ax7. Given its importance in \(\mathsf{ELG }\) \(^N\), we conserve it in this axiomatization.
 
10
Contrarily to \(\mathsf{BIAT }\) \(^N\) and \(\mathsf{ELG }\) \(^N\), we need \(N\) to be finite. Our language refers to coalitions of agents that are subsets of \(N\), and the set of subsets of an enumerable infinite set is not enumerable. Hence, a logic \(\mathsf{COAL }\) \(^N\) with a possibly infinite enumerable set \(N\) of agents would not be finitely axiomatizable.
 
11
See for instance the results of the last SAT competition. http://​www.​satcompetition.​org/​.
 
12
We understand group attitude only loosely in the sense of [48].
 
13
See for instance [44].
 
14
It would just consist in rewriting the case of Constraint 9 in the proof of Theorem 4.
 
15
Nevertheless, it should be noted that bringing-it-about logics are not inherently incompatible with a refined ontology of time, as argued in [15].
 
16
A rule of thumb is that over a non-restricted language (all Boolean combinations, unbounded modal depth, etc), if a classical modal logic admits axiom Ax1 (axiom \(K\)) but does not admit \(\lnot E_x \varphi \rightarrow E_x \lnot E_x \varphi \) (axiom \(5\)), it is PSPACE-hard.
 
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Metadaten
Titel
Reasoning about coalitional agency and ability in the logics of “bringing-it-about”
verfasst von
Nicolas Troquard
Publikationsdatum
01.05.2014
Verlag
Springer US
Erschienen in
Autonomous Agents and Multi-Agent Systems / Ausgabe 3/2014
Print ISSN: 1387-2532
Elektronische ISSN: 1573-7454
DOI
https://doi.org/10.1007/s10458-013-9229-x

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