Ontology alignments (Section 6.2.4) can overcome the problem of semantic heterogene- ity. However, in open environments (see Section 6.2.3) it is possible that multiple alignments will exist between the ontologies of two agents. Thus, the agents need to rationally reach an agreement. Various techniques allow agents to reach an agreement, but in this thesis we focus on the use of argumentation. Argumentation is a process of systematic reasoning in support of an idea, action or theory.
Argumentation facilitates the agents in reaching an agreement over the mappings they will use to communicate. Within Artificial Intelligence it has been applied in a number of areas as a way to approach and frame problems, and to develop novel solutions. In the context of this thesis it is used as a way to bring about a mutually acceptable agreement, where agents have incomplete knowledge [84].
6.3.1 Argumentation Framework
This thesis adopts the framework used by Laeraet al.[85], which is based upon Bench- Capon’s Value-Based Argument Framework (VAF) [5], that introduces the notions of audience and preference values. An audience represents a group of agents who share the same preferences over a set of values, with a single value being assigned to each argument. The VAF is based on the seminal work by Dung [36]. Dung showed that
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many forms of non-monotonic reasoning and logic programming are special forms of his argumentation theory.
An Argumentation Framework [36] is defined as follows:
Definition (Argumentation Framework) An Argumentation Framework (AF) is a pair AF = hAR, Ai, where AR is a set of arguments A ⊂ AR×AR is the attack relation for AF. A comprises a set of ordered pairs of distinct arguments in AR. A pairhx, yi is referred to as “x attacksy”.
Let R,S be subsets of AR, we say that:
(a) s∈S isattacked by R if there is somer ∈R such thathr, si ∈A.
(b) x∈AR is acceptable with respect to S if for every y∈ ARthat attacks x there is somez∈S that attacks y.
(c) S is conflict-free if no argument inS is attacked by any other argument inS. (d) A conflict-free set isadmissible if everyy∈S is acceptable with respect to S.
(e) S is a preferred extension if it is a maximal (with respect to set inclusion, ⊆) admissible set.
A preferred extension represents a consistent position within anAF; it is defensible against all attacks and it cannot be further extended without becoming inadmissible. It is important to note thatAF can be represented as a directed graph where the vertices correspond to elements ofARand edges correspond to elements of A. For example,“x
attacks y” would give the attack graph shown in Figure 6.2.
x
y
Figure 6.2: A simple example of an attack graph.
6.3.2 Value-Based Argumentation Framework (VAF)
In Dung’s framework [36] attacks always succeed; in essence they are all given equal value. For deductive arguments this suffices, but in our scenario, ontology alignment negotiation, the persuasiveness of an argument could change depending on the audi- ence, where an audience represents a certain set of preferences. One alternative is to use an extension of Dung’s framework called Value-Based Argumentation Framework (VAF) [5], which assigns different strengths to arguments on the basis of the values
they promote and the ranking given to these values by the audience for the argument. Thus, it is possible to systematically relate strengths of arguments to their motivations and to accommodate different audience interests.
Definition (Value-Based Argumentation Framework) A Value-Based Argumen- tation Framework (VAF) is defined ashAR, A,V, ηi, where:
• hAR, Ai is an argumentation framework;
• V is a set ofkvalues which represent the types of arguments;
• η :AR→ V is a mapping that associates a value η(x) ∈ V with each argument
x∈AR.
The notion of audience is central to the VAF. Audiences are individuated by their preferences over the values. Thus, potentially, there are as many audiences as there are orderings ofV4. The set of arguments is assessed by each audience in accordance to its
preferences. An audience is defined as follows:
Definition (Audience) An audience for a VAF is a binary relation R ⊆ V × V
whose irreflexive transitive closure, R∗, is asymetric, i.e. at most one of (v, v0), (v0, v) are members ofR∗ for any distinct v, v0 ∈ V. We say that vi is preferred to vj in the
audienceR, denoted viRvj, if (vi, vj)∈ R∗
This notion allows us to consider that different agents (represented by an audience) can have different perspectives on the same candidate mapping. Thus, the VAF [5] defines what it means for an argument to be acceptable relative to some audience; it is defined as follows:
Definition (Argument Acceptability) LethAR, A,V, ηibe a VAF, withR andS
as subsets ofAR, and an audience R:
(a) For x, y∈ AR, x is a successful attack on y with respect to Rif (x, y)∈ A and
η(y)6Rη(x).
(b) x∈ARisacceptable with respect toSwith respect toRif for everyy∈ARthat successfully attacks x with respect to R, there is some z ∈ S that successfully attacksy with respect to R.
(c) S is conflict-free with respect to R if for every (x, y) ∈S×S, either (x, y) 6∈A
orη(y)Rη(x)
(d) A conflict-free setS is admissible with respect to R if everyx ∈S is acceptable toS with respect toR
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(e) S is a preferred extension for the audience R if it is a maximal admissible set with respect toR
(f) x∈ARissubjectively acceptableif and only ifxappears in the preferred extension for some specific audience.
(g) x∈ARisobjectively acceptable if and only ifxappears in the preferred extension for every specific audience.
(h) x∈ARis indefensible if it is neither subjectively nor objectively acceptable.