In this thesis, a novel approach to natural language understanding inspired by quantum mechanical principle is proposed. It is based on an analogy between the physical objects at the quantum level and human's mental states. In this way, the physical and the mental phenomena are to be understood within the same framework. It is also proposed that the apparent differences between mind and matter do not lie in the fundamental differences of their properties, but in the different manifestation of macroscopic matter and macroscopic mind owing to their different composition of pure quantum eigenstates. The apparent differences are therefore quantitative rather than qualitative.
Specifically, symbols in various cognitive functions are to be treated as eigenstates with respect to a particular quantum experimental arrangement. Moreover, I claim that reasoning and inference can be treated as transformations of semiosis with symbols being the eigenstates of a particular formulation operator. The operator is the counterpart of an observable in quantum mechanics. A state of affairs (a superposition of these eigenstates) does not have well-defined physical properties until it is actually measured. Consequently the classical semantics (as classical symbols' referring to the classical physical reality) is also not well-defined and may be a misleading idea. Different from classical semantics, meaning in the quantum mechanical framework should be treated as an active measurement done on a state of affair.
Moreover, the ill-definedness also manifests itself in the cognition internal to a person if we regard memory as a language-like representational system. Nevertheless, memory, treated as a specific language system, is a largely quasi-classical phenomenon in that the chemical activities in the brain are an aggregate limiting case of quantum mechanics with a very large number of quanta. The classical ``objective'' physical reality is therefore a limiting case of quantum reality as well.
The general language in which common sense logic is embedded is then investigated and the apparent evasiveness and ambiguity of language can be accommodated in a quantum framework. This is done by postulating an analogous Uncertainty Principle and observing the implication of it. An important implication is the ``concept-symbol'' duality. As applications, the quantum mechanical formalism is applied to cognitive processes. For instance, non-monotonicity and counterfactual conditionals can be accommodated and assimilated in this framework. Specifically, the time-asymmetric property and the genuine unknown state of non-monotonic reasoning can be easily explained in quantum mechanics. This is also the case for the potentiality and actuality, which are crucial ideas for explaining counterfactual reasoning. Furthermore, causality can be regarded as a disguise of counterfactual reasoning.
The second part of the thesis is devoted to simulations and technical applications of the aforementioned principle in natural language processing. First the preliminary experiments of common sense logic are presented. These show that the ``classicization'' of common sense logic can be implemented with very simple quantum mechanical systems. Moreover, the richness of the quantum framework goes well beyond what a classical system can offer. There can be ``fine-structures'' within seemingly simple logical arguments (XOR, for example). This is also the case for non-monotonic and counterfactual reasoning.
Simple natural language tasks are also simulated based on different natural language corpora. First the syllogistic arguments embedded in natural language are simulated with a quantum system, which delivers quite remarkable results. Secondly, a monolingual syntax manipulation is implemented with a quantum system, in which the quantum mechanical approach can achieve much better performance than connectionist one. In the last experiment, a quantum mechanical architecture is trained for bilingual translation between English and German, in which there are several thorny properties in the natural language corpus, for example lexical ambiguity, separable prefixes, complicated conjugation, and non-linear translational word mappings. Nevertheless, the quantum mechanic architecture can deliver very satisfactory results.