http://cstheory.stackexchange.com/questions/18716/good-reference-about-approximate-methods-for-solving-logic-problems

I also have found several papers about it. E.g. undecidability of modalo logics can be overcome by limiting depth of nesting of modal operators. While this is not mathematically pure solution, it is very good approximation to the human reasoning that is not quite capable of self-reflection.

Are there chances that heuristic methods - e.g. genetic algorithms or neural networks can overome undecidability problem - e.g. by discovering theorems and proofs that can not be discovered by algorithmic methods?

I see big prospects for categorical logic to become the universal logic that unifies all sorts of reasoning types (human agent modelling, creativity modelling, mathematical reasoninig, legal reasoning are all types of reasoning that requires different different methods but the application borders are smooth and therefore unification is necessary) but the application will be impossible if there is no methods for handling undecidable cases. Therefore one should be able to overcome undecidability. ]]>