Microsoft is committed to the building of the scalable, industrial size topological quantum computer, Visual Studio integrated programming language and SDK will be released by the end of this year (2017). From the other side, logical/symbolic methods in computer science (natural language processing, inference, knowledge management etc.) are considered to be impractical due to high complexity/computational time, that is why subsymbolic methods (neural networks, statistical methods) are used widely today.
The question is - are there quantum algorityms for speedup of classical logical problems (i.e. all the non-quantum logics - classical, non-classical, modal, defeasible, linear, categorical, adaptable, etc.), like automated theorem proving, backward and forward reasoning and so on?
I have heard that Grover search algorithm can be used for solving Boolean satisfiability problem but are there any other quantum algorityms for logics?