Transformation of Refutation Graphs into Natural Deduction Proofs

Most computer generated proofs are stated in abstract representations not normally used by mathematicians. We describe a procedure to transform proofs represented as abstract refutation graphss into natural deduction proofs. The emphasis of this investigation is more on stylistic aspects rather than theoretical issues. In particular the topological properties of refutation graphs can be successfully exploited in order to obtain structured proofs

Proof Transformation with Built-in Equality Predicate

One of the main reasons why computer generated proofs are not widely accepted is often their complexity and incomprehensibility. Especially proofs of mathematical theorems with equations are normally presented in an inadequate and not intuitive way. This is even more of a problem for the presentation of inferences drawn by automated reasoning components in other AI systems. For first order logic, proof transformation procedures have been designed in order to structure proofs and state them in a formalism that is more familiar to human mathematicians. In this report we generalize these approaches, so that proofs involving equational reasoning can also be handled. To this end extended refutation graphs are introduced to represent combined resolution and paramodulation proofs. In the process of transforming these proofs into natural deduction proofs with equality, the inherent structure can also be extracted by exploiting topological properties of refutation graphs

How Do Drivers Self-Regulate their Secondary Task Engagements? The Effect of Driving Automation on Touchscreen Interactions and Glance Behavior

With ever-improving driver assistance systems and large touchscreens becoming the main in-vehicle interface, drivers are more tempted than ever to engage in distracting non-driving-related tasks. However, little research exists on how driving automation affects drivers' self-regulation when interacting with center stack touchscreens. To investigate this, we employ multilevel models on a real-world driving dataset consisting of 10,139 sequences. Our results show significant differences in drivers' interaction and glance behavior in response to varying levels of driving automation, vehicle speed, and road curvature. During partially automated driving, drivers are not only more likely to engage in secondary touchscreen tasks, but their mean glance duration toward the touchscreen also increases by 12% (Level 1) and 20% (Level 2) compared to manual driving. We further show that the effect of driving automation on drivers' self-regulation is larger than that of vehicle speed and road curvature. The derived knowledge can facilitate the safety evaluation of infotainment systems and the development of context-aware driver monitoring systems.Comment: 14th International ACM Conference on Automotive User Interfaces and Interactive Vehicular Application

Structuring Computer Generated Proofs

One of the main disadvantages of computer generated proofs of mathematical theorems is their complexity and incomprehensibility. Proof transformation procedures have been designed in order to state these proofs in a formalism that is more familiar to a human mathematician. But usually the essential idea of a proof is still not easily visible. We describe a procedure to transform proofs represented as abstract refutation graphs into natural deduction proofs. During this process topological properties of the refutation graphs can be successfully exploited in order to obtain structured proofs. It is also possible to remove trivial steps from the proof formulation

Transformation and Structuring of Computer Generated Proofs

One of the main disadvantages of computer generated proofs of mathematical theorems is often their complexity and incomprehensibility. This is even more of a problem for the presentation of inferences drawn by automated reasoning components in other AI systems. Proof transformation procedures have been designed in order to state these proofs in a formalism that is more familiar to a human mathematician. But usually the essential idea of a proof is still not easily visible. We describe a procedure to transform proofs represented as abstract refutation graphs into natural deduction proofs with a special emphasis on an “intelligent” selection of inference rules. In particular the frequent use of proofs by contradiction is avoided. During this process topological properties of the refutation graphs can be successfully exploited in order to obtain well-structured proofs. This is accomplished by dividing a large proof into a set of hierarchically arranged subproofs which are more easily comprehensible. This may be achieved by formulating lemmata that are then applied more than once in the subsequent proof, but also by simply inserting subgoals or by breaking up a substantial part of a proof into a case analysis

Presentation of Proofs in an Equational Calculus

One of the main reasons why computer generated proofs are not widely accepted is often their complexity and incomprehensibility. Especially proofs of mathematical theorems with equations are normally presented in an inadequate and not intuitive way. Often completion and rewrite proofs are only given in the form of a program trace. This is even more of a problem for the presentation of inferences drawn by automated reasoning components in other AI systems. For first order logic, proof transformation procedures have been designed in order to structure proofs and state them in a formalism that is more familiar to human mathematicians. In this report we present a method to handle equational proofs in such systems. To this end equation solution graphs are introduced to represent paramodulation or rewrite proofs. In the process of transforming these proofs into proofs with equation chains, the inherent structure can also be extracted by exploiting topological properties similar to those of refutation graphs in the pure first order case

Influence of high-energy laser therapy to the patellar tendon on its ligamentous microcirculation: An experimental intervention study.

Laser therapeutic applications, such as the use of high energy lasers (HILT), are widely used in physical therapy, but basic studies on the mechanisms of action of HILT on tendinous/ligamentous tissue are largely lacking. The aim of this study was to investigate microcirculatory changes of the patellar tendon by HILT. 21 healthy volunteers were included in the present investigation. Before and after HILT, as well as 10 minutes later, the microcirculation was measured by noninvasive laser Doppler and white light spectroscopy (O2C device). Tissue temperature was recorded at the measurement time points using thermography. Blood flow increased significantly by 86.38 arbitrary units (AU; p < 0.001) after the intervention and by 25.76 AU (p < 0.001) at follow-up. Oxygen saturation increased by 20.14% (p < 0.001) and 13.48%, respectively (p < 0.001), whereas relative hemoglobin decreased by 6.67 AU and 7.90 AU, respectively. Tendon temperature increased by 9.45° and 1.94° Celsius, respectively. Acceleration of blood flow by improving the flow properties of erythrocytes and platelets may have caused the results. HILT could be a therapeutic perspective for tendon pathologies with impaired microcirculation, although further studies are needed to validate the experimental results

Knowledge discovery standards

As knowledge discovery (KD) matures and enters the mainstream, there is an onus on the technology developers to provide the technology in a deployable, embeddable form. This transition from a stand-alone technology, in the control of the knowledgeable few, to a widely accessible and usable technology will require the development of standards. These standards need to be designed to address various aspects of KD ranging from the actual process of applying the technology in a business environment, so as to make the process more transparent and repeatable, through to the representation of knowledge generated and the support for application developers. The large variety of data and model formats that researchers and practitioners have to deal with and the lack of procedural support in KD have prompted a number of standardization efforts in recent years, led by industry and supported by the KD community at large. This paper provides an overview of the most prominent of these standards and highlights how they relate to each other using some example applications of these standards