This is a personal area of interest for me, but in a slightly different way. Modern AI and AGI research has shown that first-order predicate logic (which underlies Loglan/Lojban) is unlikely to be a complete formal framework for rational thought. I am very much interested to see what a language would look like that was instead based on, e.g., probabilistic graphical models. And then see that applied to human-machine communication.
Hrm. Complete was probably the wrong word. First order logic is complete in the mathematical sense that it can be used to represent and solve any problem, but the issue with AI / AGI is one of practicality. First order logic suffers from term explosion on any non-toy problem, leading to the need for higher order logics (of which there are many), and/or integration with other kinds of systems to manage that complexity. First order logic is also not probabilistic, and dealing well with uncertainty is a hallmark of natural language. Most AGI logic systems are not first order logic, although you can implement FOL in such systems. So better summarized my research question is basically "Practical AI systems need tools beyond what first order logic provides to represent thought. I wonder what would result from applying these extra tools to a logical conlang?"
My intuition is that the right way to approach this is to ask "What would a conlang based on probabilistic graphical models look like?" The reason being that PGMs are the underlying theory for most modern approaches to concept representation and knowledge databases. Examples of PGMs are Bayes nets, Markov random fields, and restricted Boltzmann machines, aka the state of the art in modern neural networks. PGMs also underlay to a more limited degree many probabilistic concept network formulations, including the atomspace of OpenCog.
So what would a PGM-based conlang look like? I'm not sure actually, but I can tell you it probably wouldn't look much like Loglan / Lojban. It'd be easy to represent any Lojban sentence in this hypothetical PGM language, using the "first order dialect," but the converse is probably not generally true.
> Suppose that earthquakes and burglars can both set off burglar alarms. If the burglar alarm in your house goes off, it might be because of an actual burglar, but it might also be because a minor earthquake rocked your house and triggered a few sensors. Early investigators in Artificial Intelligence, who were trying to represent all high-level events using primitive tokens in a first-order logic (for reasons of historical stupidity we won't go into) were stymied by the following apparent paradox: [.. snip ..] Which represents a logical contradiction, and for a while there were attempts to develop "non-monotonic logics" so that you could retract conclusions given additional data.
1. http://lesswrong.com/lw/ev3/causal_diagrams_and_causal_model...
Thus, adding another sense (a seismograph and sightedness/touch, respectively) would seem to eliminate the problem. If this is correct, then such problems are more ones of a lack of relevant, heterogeneous information and less of a lack of logical expressiveness of probabilities.
[0] = I say "almost", because knowledge is a fundamental philosophical problem. The usual means to "almost" assurance is, as I am arguing, to employ more heterogeneous sources of information until the only logical alternatives to what you believe are absurdities (e.g. impossible).