The process based definition of information differs in several respects from
Shannon’s model of information, to the extent that Shannon’s ideas about information
may be separated from those he had about communication. Shannon views
communication systems primarily as transmitting symbols between a source and a
destination. This is very different from the process model proposed above which
produces output from input, with no explicit attempt being made to encode or
represent something symbolically, or to be message based. Shannon notes that
his theory is “quite different from classical communication engineering theory
which deals with the devices employed but not with that which is communicated”
[Sha93a, p. 212]. Shannon’s focus clearly was on the message.
Unlike Shannon’s model, the process model describes information as the outcome
of any process, not just an encoding process in a symbol based communication
system. The process model of information, for example, can be used to
describe an addition process that accepts two inputs and produces the sum (information)
at the output. This output is informative about the additive process and
the inputs. This notion of aboutness is similar to Devlin’s notion of a constraint
[Dev91]. While the addition process could be interpreted as encoding the input,
that is certainly not a very natural interpretation and is certainly not a required
interpretation if we wish to understand arithmetic sums. Similarly, the process
model of information measures the information at the output as proportional to
the number of possible states and their relative frequency in the output.