In the discussion so far presented, the distinguishing feature of
embodied AVAs is characterized by 
. Here we will show
that carrying a physical body has further implications.
Let 
denote an embodied AVA (Fig.
6). Then, first of all, carrying a physical body
implies that (some part of) 
can be observed from other
AVAs;
define
the physical state of its body and the body in turn can be regarded as
a part of the world. Hence, other AVAs can estimate some of
from such part of 
that represents the physical body state. indirectly reflects (i.e. is
decided depending on) even if that part of the world
does not include the physical body of an embodied AVA. For example, an
embodied AVA writes down its internal state on a blackboard, which
then is observed by other AVAs.
Figure 6: Model of an embodied AVA.
Thus, 
in equation (1) may
include . To estimate from , we define the following new function:
Note that in order for 
to function meaningfully,
must first identify the existence of and
then should have the knowledge about how is reflected
onto its physical body and/or the world.
While how to obtain such object identification and knowledge is an
important problem to be studied, here we assume they are given; and share the knowledge about the physical
reflection of . Then, can inform
of its state without sending a message:
embeds into using 
and/or 
. obtains by 
and then
extracts by applying . is used by 
to change 
, since in equation (9) contains .
followed by 
.
When is also an embodied AVA, the mutual exchange of
and can be realized without exchanging
messages. That is, the communication without message exchange can
be realized between embodied AVAs. This property is the most crucial
feature discriminating embodied from vacuous AVAs. Note that all
software agents are vacuous and lack this property.
As mentioned before, to realize the communication without message exchange, the object identification should be established and the knowledge about how the physical state reflects the internal state should be shared between AVAs. These two factors can be considered as defining the essence of Languages. In case of talking with hands, for example, the object identification implies the recognition of a ``speaker'' and the shared knowledge the specific chirology used. We believe the language is an abstract information structure used for communication and can be represented by various different media: physical bodies, sounds, visual patterns, and symbolic messages. From an information processing point of view, the complexity and efficiency of communication may depend on the media; symbolic messages seem to be more efficient and can represent more complex information than physical body actions. If so, we should use the message exchange for communication even if all AVAs are embodied.
Figure 7: Multi-channel communication between embodied AVAs.
When an embodied AVA has the message exchange capability, it has two
different ways of communication: action-perception and message
exchange (Fig. 7). Two pieces of information
carried by an action and a message should be consistent since a sender
AVA is a rational agent. This means that the former constrains the
latter and vice versa. In other words, 
constrains and
simulates 
and/or . From equation
(5), for example, can encode into 
such parts of that represent 's physical body state and/or its ``future'' action plan. Then,
using 
defined in equation (6), the
receiver changes its internal state to form
``quasi-percept'' of and/or ``expectation'' about 's body
state. The action by the sender , on the other hand, is
constrained so that its physical body action may be consistent with
the quasi-percept of and/or the expectation formed in .
This means that in some cases, the message exchange plays the same
role as the action-perception. This phenomenon has been know as
speech act in linguistics[3].
In summary, the communication between embodied AVAs is best characterized by multi-channel communication links formed by versatile combinations of perception, action and message exchange processes (Fig. 7).
