active (sink x) = -deafen (x) (attend (self self (x))) attend (x)). FIGURE 14.5 Formalization of narrowcasting and selection functions in predicate calculus notation, where '-' means "not," 'N' means conjunction (logical "and"), '3' means "there exists," '=>' means "implies," and' means mutual implica- tion (equivalence). C 2009 by Taylor & Francis Group, LLC SIP Handbook: Services, Technologies, and Security (invoked on oneself) and transitive (on others), the attributes include a self flag, applied to both sources and sinks. The duality between source and sink operations is tight, and the semantics are analogous: an object is inclusively source enabled by default unless it is explicitly excluded (with mute or deafen), or, peers of the same self/non-self class are explicitly included (with sources sinks select solo or attend) when the respective object is not. Narrowcast- ing attributes are not mutually exclusive, and the dimensions are orthogo- nal. Because a source or sink is active by default, invoking exclude and include operations simultaneously on an object results in its being disabled. For instance, a sink might be first attended, perhaps as a member of some non-singleton subset of a chatspace's sinks, then later deafened, SO that both attributes are simultaneously applied. (As audibility is assumed to be a revo- cable privilege, such a seemingly conflicted attribute state disables the sink, whose receptivity would be restored upon resetting its deafen flag.) Sym- metrically, a source might be selected and then muted, akin to inclusion on a "short list" but relegated to back-up. Our system allows each user to send or receive data streams to/from a specific recipients in a session. For easier understanding, we consider only audio streams in this chapter, but the design applies to other media types. Narrowcasting audio commands are listed and their characteristics arrayed in Table 14.3. In this section, we formally define four narrowcasting commands. In the following expressions, Pa denotes the actor (cont