[SiempreViernes]

>directed graph [...] containing cycles

Can you clarify what you mean with cycles? As written it sounds like you think sound arguments contain circular reasoning...

I can see a branching opening and closing in a unidirected graph being the result of a sound argument^, but since you cannot move freely in both directions I don't know if it would count as a cycle.

^ The argument being: some process has a positive an negative effect (one thing happens, another thing never happens), the positive and negative effects are observed in nature, supporting the conclusion that the process in fact is the cause of the two effects.

[TeMPOraL]

Feedback loops.

I don't think modelling "from argument X follows argument Y" is productive; what's productive is modelling that observable phenomenon X is correlated with Y, or causes Y, or has this-and-that impact on Y. At this level, things can be stuck in feedback loops, either positive or negative.

Will increase in coal exports of Poland increase Poland's CO₂ footprint? Let's try to model it the way I think about it:

     Coal exports
          ^
          | [provides Z coal to]
          |
          |     [needs α*X = A kWh for coal]
     Mining coal <---------------------\
          |                            |
          | [provides X coal to]       |
          v                            |
   Coal power plants                   |
    |     |                            |
    |     | [γ*X = Y kWh burning coal] |
    |     v                            |
    |  Electricity --------------------/
    |
    | [burned coal into β*X = N kg of CO₂]
    v
  CO₂ emissions

You have a cycle there: Mining coal -> Coal power plants -> Electricity -> Mining coal. Given A < Y, it's a negative feedback loop. It's a cycle that exists in real life (and the basis of the concept of EROI)!

If this were a reactive model, you could tweak the value of Z to see how X, Y, A and ultimately N change. But even without reactivity, you can clearly see that the answer to original question is "yes, increasing coal exports will increase Poland's carbon footprint". And there's little left open to interpretation or accusations of subjectivity.

If you don't like the answer that the model gives, it also makes some alternative strategies apparent! In this case: can we find a way to reduce α or β to compensate? Or increase γ? Or maybe add an alternative CO₂ sink for the Coal power plants -> CO₂ emissions edge? Note that these alternative strategies involve manipulating reality, not your argument.

I think we should be doing more of this kind of modelling. Building more accurate maps of the world, and reasoning straight from them, instead of trying to build complicated webs of arguments.