Theoretical Background
The yet unproven but commonly accepted Church-Turing thesis states that a Turing machine and all equivalent formal languages such as the lambda calculus perform and represent all formal operations respectively as applied by a computing human. However the selection of adequate operations for the correct computation itself is not formally deducible, moreover it depends on the computability of the underlying problem. Tasks, such as the halting problem, may be formulated comprehensively in natural language, but the computational representation will not terminate or does not provide a usable result, which is proven by Rice's theorem. The general expression of limitations for rule based deduction by Gödel's incompleteness theorem indicates that the semantic gap is never to be fully closed. These are general statements, considering the generalized limits of computation on the highest level of abstraction where the semantic gap manifests itself. There are however lots of subsets of problems which may be translated automatically, especially in the higher numbered levels of the Chomsky hierarchy.
Read more about this topic: Semantic Gap
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