Direct machine translation systems are usually implemented as uni-directional mappings between a source and target sentence, where the accuracy of the translation is evaluated with respect to the consistency of meaning of the target with respect to the source. However, this approach does not allow us to understand how comparable the semantic representations in target and source really are, since both are described by words in different (and possibly semantically incompatible) languages. In this paper, we generalise the common method of inverting translations to generate a mapping between target and source, by proposing a new, iterative translation methodology which is based on dynamical systems theory, the Iterative Semantic Processing (ISP) Paradigm. The basic premise of this paradigm is that the preservation (or loss) of semantic representations during successive iterative translations between source and target, target and source, source and target, and so on, can be best described as one of three possible dynamical system states: point attractors (i.e., invariant semantic representations), limit cycles (i.e., steady-state variant but predictable cross-language mappings) and chaotic cycles (i.e., variant mappings with rapid short-term information loss). The mathematical properties of each of these system states as a measure of semantic stability are described in this study, and quantitative measures of semantic information loss are derived, and applied to semantic-mis-translations from a freely-available direct translation system.
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