2000 ArgumentsDialogueandNegotiation
- (Amgoud et al., 2000) ⇒ Leila Amgoud, Simon Parsons, and Nicolas Maudet. (2000). “Arguments, Dialogue, and Negotiation.” In: Journal of Artificial Intelligence Research, 10(11).
Subject Headings: Negotiation, Argumentation-based Negotiation, Multi-Agent System.
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Abstract
In the past few years there have been a number of proposals for mechanisms for negotiation between agents that make use of argumentation. These proposals have largely been vague on the subject of how the generation and interpretation of arguments fits into the process of negotiation. This paper addresses this gap, proposing a particular protocol which is suitable for negotiation, and illustrating its use on an example from the literature.
1. Introduction
Negotiation is widely regarded as a key issue in building multi-agent systems. In most agent applications, the autonomous components need to interact with one another because of the inherent interdependencies which exist between them, and negotiation is the predominant mechanism for achieving this. In recent years, there have been a number of suggestions for systems of negotiation based upon argumentation, including work by Parsons and Jennings [ 7, 10], Reed [9], Sycara [11] and Tohmé [12].
All mechanisms for negotiation have at their heart an exchange of offers. Agents make offers that they find acceptable and respond to offers made to them. What distinguishes argumentation-based negotiation from other approaches is the fact that offers can be supported by arguments, which, broadly speaking, equate to explanations for why the offer was made. This permits greater flexibility than in other negotiation schemes since, for instance, it makes it possible to persuade agents to change their view of an offer by introducing new factors in the middle of a negotiation (just as a car salesperson might throw in free insurance to clinch a deal).
While this use of argumentation is a common theme in all the work mentioned above, none of those proposals explain when arguments can be used within a negotiation and how they should be dealt with by the agent that receives them. Thus the protocol for handling arguments is missing. This paper fills the gap by proposing an argumentation protocol which permits the same kind of reasoning as the system proposed in [ 7], and which can be used to underpin the negotiation illocutions introduced in [10].
2. A System of Argumentation
In this section we briefly introduce the system of argumentation which forms the backbone of our approach. This is inspired by the work of Dung [5] but goes further in dealing with preferences between arguments. Further details are available in [1]. We start with a possibly inconsistent knowledge base �with no deductive closure.
We assume � contains formulas of a propositional language L. ` stands for classical inference and �for logical equivalence.
- Definition 1
An argument is a pair (H; h) where h is a formula of L and H a subset of �such that i) H is consistent, ii) H `h and iii) H is minimal, so no subset of H satisfying both i) and ii) exists. H is called the support of the argument and h is its conclusion.
In general, since �is inconsistent, arguments in A (�), the set of all arguments which can be made from [[�]], will conflict, and we make this idea precise with the notion of undercutting:
- Definition 2
Let (H1]]; h1) and (H2; h2) be two arguments of A (�). (H1; h1) undercuts H2; h2) iff 9h 2H2such that h �:h1. In other words, an argument is undercut iff there exists an argument for the negation of an element of its support.
To capture the fact that some facts are more strongly believed (or desired, or intended, depending on the nature of the facts) we assume that any set of facts has a preference order over it which derives from the stratification of the knowledge base �into non-overlapping sets �1;:; fin such that facts in �i are all equally preferred and are more preferred than those in j where j >i. The preference level of a nonempty subset H of �, level (H), is the number of the highest numbered layer which has a member in H.
- Definition 3
Let (H1; h1) and (H2; h2) be two arguments in A (�). (H1; h1) is preferred to (H2; h2) according to Pref iff level (H1) [[� level]] (H2).
We can now define the argumentation system we will use:
- Definition 4
An argumentation system (AS) is a triple hA (�);Undercut; Pref isuch that A (�) is a set of the arguments built from [[�]], Undercut is a binary relation representing defeat relationship between arguments, Undercut �A (�) �A (�), and Pref is a (partial or complete) preordering on A (�) �A (�). �Pref stands for the strict pre-order associated with Pref.
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References
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| Author | volume | Date Value | title | type | journal | titleUrl | doi | note | year | |
|---|---|---|---|---|---|---|---|---|---|---|
| 2000 ArgumentsDialogueandNegotiation | Leila Amgoud Simon Parsons Nicolas Maudet | Arguments, Dialogue, and Negotiation | 2000 |