\subsection{Performative warrants}
\label{section 6.2}

A formal model-theoretic semantics specifies truth conditions. To fully capture the meaning of a performative, however, we need to go beyond truth-conditions, since the very same form of words may be true whoever uses them, but will only count as a performative if used by the authority it mentions. For example ÒPatrick promises...Ó uttered by Patrick is a promise - a performative act - but uttered by Christian is merely a description of the act; yet it may well still be true, and for the same reasons. We will deal with this by considering a warrant graph to be a ÔgenuineÕ warrant just when it describes its authority accurately, and to be true in any interpretation under which a genuine warrant actually exists. 

As mentioned in section 5.1. we assume that a relationship of authorizing, and sets of authorities and warrants, are taken as primitive, and we will identify them respectively with the property extension of \swp{authority} and the class extensions of \swp{Authority} and \swp{Warrant} respectively. All the remaining semantic conditions are defined in terms of these, so their correctness in any application depends on that of the interpretation of \swp{authority} together with its range and domain. Thus a triple 
\begin{rdfenv}
ex:a \swp{authority} ex:b .
\end{rdfenv}
is true in I just when I(ex:a) is a warrant which is authorized by I(ex:b). 

The performative role of a properly authorized warrant graph can then be described by simply declaring that any named graph G containing a triple

\begin{rdfenv}
name(g) \swp{authority} bbb .
\end{rdfenv}

\emph{is} a warrant. Then any interpretation I under which the graph is authorized by I(bbb) makes this triple true, and hence requires the graph g to be in ICEXT(I(\swp{Warrant})): call this an \emph{authorizing interpretation} of the graph. Any secure method for fixing the referent of the object of such a triple to be an authorizing authority thus means that the graph can be satisfied only by authorizing interpretations under which the graph is a warrant.

The self-realizing quality of performatives is extended to the triples which express propositional attitudes by making these trivially self-fulfilling when they occur under the right conditions, in an authorized warrant graph. For example if g is a warrant graph which contains a triple

\begin{rdfenv}
aaa \swp{assertedBy} bbb .
\end{rdfenv}

where I(bbb)=g, then if I is an authorizing interpretation of g, then I must satisfy that triple; similarly for \swp{quotedBy} and indeed for any other property expressing a propositional attitude of an authority towards a graph. 

Note that this does not imply that the graph g is \emph{true} in an authorizing interpretation of a warrant which asserts it. The fact of an authority asserting a graph can be true independently of the actual truth of the graph. However, the attitude expressed can be utilized by trust policies. For example, it would be appropriate to treat graphs asserted by trusted authorities as being true, but not to extend this to graphs quoted by trusted authorities. One could express this trust policy by a semantic rule to the effect that if I satisfies 

\begin{rdfenv}
aaa \swp{assertedBy} bbb .
bbb \swp{authority} ccc .
\end{rdfenv}

and I(ccc) is trusted, then I satisfies I(aaa).