Normative arrow update logic (NAUL) is a logic that combines normative temporal logic (NTL) and arrow update logic (AUL). In NAUL, norms are interpreted as arrow updates on labeled transition systems with a CTL-like logic. We show that the satisfiability problem of NAUL is decidable with a tableau method and it is in EXPSPACE.

This thesis aims to understand Popper’s falsificationism and Lakatos’ methodology of scientific research programmes right and to grasp why and how Lakatos modifies Popper’s falsificationism to be the methodology of scientific research programmes. Firstly, it sets forth a background in which Lakatos makes the modification. The background is a basis on which we study why Lakatos modifies Popper’s falsificationism. In order to understand Lakatos’ motivation for making the modification better, the section will be described according to Lakatos’ view. It briefly (...) reviews some methodologies of science before Popper, and then explains the two phases of Popper’s methodological falsificationism--naïve methodological falsificationism and sophisticated methodological falsificationism--and makes a comparison between them. Secondly, this thesis states Lakatos’ comments about Popper’s methodological falsificationism, and then explains why and how Lakatos makes the modification and what his modification is. Moreover, it also makes a comparison between Popper’s falsificationism and the modification. Thirdly, having made comments about the influences of their theories, this thesis shows some criticisms raised by contemporary philosophers of science and discusses some of their potential problems. Finally, it makes a brief summary about the whole discussion and draws a conclusion that Lakatos modifies Popper’s falsificationism effectively and improves it more sophisticated. (shrink)

The main point of this paper is to underscore the link between simplicity and truth in an unsupervised machine learning context. More precisely, we argue that parametric and dimensional simplicity are not indicators of truth but the methodological principle that urges us to pay attention to such notions of simplicity is truth conducive. The truth that we are looking for are specific geometrical shapes and we know which algorithm can find which shapes provided that we pay attention to parametric and (...) dimensional simplicity. (shrink)