Most expressions in our natural language are vague, a circumstance which does not cause any problem for us in our everyday life, but many if we want to understand the phenomenon of vagueness and even more if we want to understand the way humans reason in its presence.
On the one hand, there is a lively discourse on vagueness in analytic philosophy, which aims at understanding the principles of reasoning in the presence of vagueness.
On the other hand, the aim to understand the principles of reasoning in the presence of vagueness and of reasoning in general is an issue concerning also mathematicians, engineers and computer scientists.
Although reasoning seems to be a purely human ability, in this time of rapidly advancing technology the wish to create machines which imitate human behaviour has become very exigent. Therefore it is necessary to formalize the human ability of reasoning in the presence of vagueness for the purpose of automation in expert systems, computer vision, control engineering or pattern recognition, to mention just a few examples. To this end, formal languages, deductive systems and model-theoretic semantics have to be developed. However, most of the scientists and engineers working in the field of vagueness are convinced that the truth comes in degrees and support so-called degree theories.
Often they consider fuzzy logics, in particular logics based on t-norms, as the logics of vagueness as these formalisms are well-understood and have had a lot of success in the past.
The curious fact, that philosophers and computer scientists are mainly working separately from each other, shall be the point of departure for this diploma thesis, which is intended to present both points of view, pointing out the strong points and problems of every theory as well as showing possible ways of combing philosophical approaches with fuzzy logic. Concretely, the aims of the thesis are:
1) to provide an overall view of the ongoing discourse in analytic philosophy and to discuss the most important theories of vagueness, giving a useful classification; 2) to discuss fuzzy logics, the approach mostly supported by computer scientists; 3) to show different possibilities of how to derive fuzzy logic from the first principles of approximate reasoning.