This excludes worlds which the deductive process has ruled out, so for example if A∨B has been proved, all worlds will have either A or B. So if you had a bet which would pay $10 on A, and a bet which would pay $2 on B, you’re treated as if you have $2 to spend.
I agree you can arbitrage inconsistencies this way, but it seems very questionable. For one, it means the market maker needs to interpret the output of the deductive process semantically. And it makes him go bankrupt if that logic is inconsistent. And there could be a case where a proposition is undecidable, and a meta-proposition about it is undecidable, and a meta-meta-propopsition about it is undecidable, all the way up, and then something bad happens, though I’m not sure what concretely.
I agree you can arbitrage inconsistencies this way, but it seems very questionable. For one, it means the market maker needs to interpret the output of the deductive process semantically. And it makes him go bankrupt if that logic is inconsistent. And there could be a case where a proposition is undecidable, and a meta-proposition about it is undecidable, and a meta-meta-propopsition about it is undecidable, all the way up, and then something bad happens, though I’m not sure what concretely.