Symbolic Logic meets Machine Learning: A Brief Survey in Infinite Domains

The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence (AI). The deduction camp concerns itself with questions about the expressiveness of formal languages for capturing knowledge about the world, together with proof systems for reasoning from such knowledge bases. The learning camp attempts to generalize from examples about partial descriptions about the world. In AI, historically, these camps have loosely divided the development of the field, but advances in cross-over areas such as statistical relational learning, neuro-symbolic systems, and high-level control have illustrated that the dichotomy is not very constructive, and perhaps even ill-formed. In this article, we survey work that provides further evidence for the connections between logic and learning. Our narrative is structured in terms of three strands: logic versus learning, machine learning for logic, and logic for machine learning, but naturally, there is considerable overlap. We place an emphasis on the following "sore" point: there is a common misconception that logic is for discrete properties, whereas probability theory and machine learning, more generally, is for continuous properties. We report on results that challenge this view on the limitations of logic, and expose the role that logic can play for learning in infinite domains

Historical review of die drool phenomenon in plastics extrusion

Die drool phenomenon is defined as unwanted spontaneous accumulation of extruded plastics on die exit face(s) of extrusion die during plastics extrusion process. Such accumulated material builds up on die exit face(s) and frequently or continually sticks onto the extruded product and by this way reduces the quality of the product. When the die drool appears, the extrusion process must be shut down and the die exit face(s) must be manually cleaned, which is time consuming as well as money consuming. Die drool has been observed from the beginning of plastics extrusion and the first published remark about it was made in 1946. For a long time it was considered as only an engineering problem and even if a wide range of suppressing ideas based on modification of extrusion dies, plastics materials, and processing conditions have already been patented, its source remained unclear. During the last few years, a number of experimental as well as theoretical research papers focusing on its fundamental nature have been published. Nowadays, die drool is considered as a fundamental rheological phenomenon. The force which drives the building up of extruded plastics on die exit face(s) is negative pressure (suction) occurring in the die exit edge(s) region where the free surface of the extruded plastics is created. Moreover, two different die drool types (external and internal) exist. The formation mechanisms of external/internal die drool are based on negative pressure occurring in the die exit region together with deformation of free extrudate surface/material separation wherever inside the extrusion equipment, respectively. From the processing point of view, the internal die drool is much more problematic than the external one, primarily due to a higher build up rate and compact shapes of the accumulated drool mass. Two theories of internal die drool formation mechanism based on wall slip theories (flow-induced molecular weight fractionation and stress-induced cohesive chain disentanglement) have been recently proposed and tested. In this historically ordered review, breakthrough works in the field of die drool research are presented, many ways to suppress it are shown, techniques for its quantitative evaluation and experimental methods for its analytical investigation are introduced, external and internal die drool types are explained, and theories of external as well as internal die drool formation mechanism are presented and discussed in depth, which can be especially helpful for plastics extrusion experts as well as for the rheological community. © 2014 Taylor and Francis Group, LLC