Non-Axiomatic Reasoning System is an adaptive system that works with insu cient knowledge and resources. At the beginning of the paper, three binary term logics are de ned. The rst is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intension, and they also have interesting relations with Aristotle's syllogistic logic. Based on the three simple systems, a Non-Axiomatic Logic is de ned. It has a term-oriented language and an experience-grounded semantics. It can uniformly represents and processes randomness, fuzziness, and ignorance. It can also uniformly carries out deduction, abduction, induction, and revision.

proefschrift ter verkrijging van de graad van Doctor aan de Universiteit Leiden, op gezag van de Rector Magnificus Dr. D.D. Breimer, hoogleraar in de faculteit der Wiskunde en Natuurwetenschappen en die der Geneeskunde, volgens besluit van het College voor Promoties te verdedigen op woensdag 14 september 2005 klokke 15.15 uur door

at is comprehensive and satisfactory. Such a theory --- that should be stressed here and kept in mind throughout the following --- does not exist and no one has yet presented even the outlines of it --- and I shall not either. But I think that the concept of fuzzy sets may prove to serve as an at least formally satisfactory and numerically flexible link or joint to connect the two main, seemingly divergent lines of research in modern semantics: namely, the more theoretically oriented models of what formal semanticists feel an `ideal' speaker should, or would do when he produces meaningful sentences a n d the more empirically oriented methods and procedures of experimental semanticists that try to find out what real speakers actually do when they produce texts for communicative purposes. In general, most linguists will probably agree that --- whatever else has to be dealt with --- natural language meaning presents two major problems: Published