- Take the protocol, examine its lexicon and syntax, and try to derive a mathematical semantics for it.
- Take an anthropological, ecological view and ask what these alien entities were trying to achieve through their communication. Then do step one.
The second approach looks to have more potential, somehow, but most natural language research has chosen the first course, on the basis that it is easier.
Back in the beginning, Montague semantics translated words, phrases and sentences of English into a massively complicated logic (higher-order with numerous modal operators capturing temporal and intentional attitudes). The semantics were standard but not recognisable as the world you and I inhabit.
Situation semantics created a richer semantic model in which the denotation of propositions was not collapsed to mere truth values, but was taken to be 'complex collections of relationships between entities and attributes at a location in time'. But still, intentionality and agency were either missing or untheorised.
I have always thought that building models of agency in paradigms drawn from economics and games theory was likely to be more promising. After all, isn't evolution just applied microeconomics? The result will be mathematical models capable of providing semantic valuations for formalised languages, but they will also constitute theories of human-style social psychology.
This must be the next big thing after todays' evolutionary psychology, surely?
A related point. Religions are also a public protocol, dual to something more hidden in the ecology of groups and social psychology. As they say, it was no accident that the great monotheistic religions developed 2-3,000 years ago at the onset of the agrarian revolution (+ the zerotheistic Buddhism and philosophical Taoism).
The God of the Old Testament (shared by Jews, Christians and Muslims) is unquestionably a muscular, patriarchic entity bestriding a dominance hierarchy - the embodiment of the agrarian pre-state embodying rules rather than the arbitrary dictates of the current warlord.
Note: Islam was later refined through a nomadic honour culture, while the New Testament represented a transactional innovation, a subversive, but constrained ideology in the interstices of the Roman Empire (Crossan). It is unlikely that Jesus would have signed up to the later evolution of 'Christianity' as an arm of that very same empire.
The principles underlying Buddhism and 'philosophical Taoism' are also transactional. Is this anything to do with the proposed greater cooperation found in east-asiatic sociaties, based on selection pressures for these traits during the time of the last ice-age (c.f. Richard Lynn, here)?