The chapter examines the issue of civil liability in the framework of damages resulting from the use of such autonomous systems. A particular emphasis is placed on the importance of access to justice – of enhancing access for victims of harm to remedies and relief – rather than more abstract or conceptual considerations of the appropriateness of a particular regulatory solution

The topic of this chapter is the wave function – what it is, how it is to be interpreted and how information can be extracted from it. To this end, the notion of operators in quantum physics is introduced. And the statistical interpretation called the Born interpretation is discussed. This discussion also involves terms such as expectation values and standard deviations. The first part, however, is dedicated to a brief outline of how quantum theory came about – who were the key people involved, and how the theory grew out of a need for understanding certain natural phenomena. Parallels are drawn to the historical development of our understanding of light. At a time when it was generally understood that light is to be explained in terms of travelling waves, an additional understanding of light consisting of small quanta turned out to be required. It was in this context that Louis de Broglie introduced the idea that matter, which finally was known to consist of particles – atoms – must be perceived as waves as well. Finally, formal aspects such as Dirac notation and inner products are briefly addressed. And units are introduced which allow for convenient implementations in the following chapters.

The chapter begins with an introduction to the FDG theory and language model. The discussion includes some of the issues in the classification of premodifiers and compares the distinctions made in FDG with the construction-based model. The second section presents an FDG model of each of-binominal, illustrating how the model captures the differences between these constructions. By doing so, current issues in recent FDG research are addressed, such as the role of CxG like constructions in FDG, interfaces and mismatches between levels, and the distinction between operators and modifiers. One important finding is that FDG predicts the changes of premodification patterns found in Chapter 7. The historical analysis in the FDG frameworks shows that we are looking at the reduction of the internal components of the N-of-N template to a simple NP template, with a reanalyzed chunk [N of (a)], functioning first as a modifier and then as a lexical operator. Therefore, although we are structurally looking at an of-binominal, this term is actually a misnomer

This chapter deals with lexical and grammatical categories in Role and Reference Grammar (RRG). First, it discusses a range of functionally motivated, non-endocentric syntactic categories, such as the nucleus (NUC), containing the predicate, referential phrases (RPs) and modifying phrases (MPs). Although these units are typically realized by verbs, nouns and adjectives/adverbs, respectively, this is not always so, and many languages allow for non-verbal predicates, non-adjectival modifying phrases, etc., while other languages show little to no evidence for categories such as noun, verb or adjective. This is captured in RRG by assuming that NUC, RP and MP are not universally linked to particular lexical categories. The chapter also discusses grammatical categories which are referred to in RRG as operators, and which ground the clause, core or nucleus (TAM markers, evidentials, etc.), as well as categories which are primarily concerned with questions of reference, such as number, definiteness, deixis, etc., which ground the RP.

We extend the mathematical description of quantum mechanics by using operators to represent physical observables. The only possible results of measurements are the eigenvalues of operators. The eigenvectors of the operator are the basis states corresponding to each possible eigenvalue. We find the eigenvalues and eigenvectors by diagonalizing the matrix representing the operator, which allows us to predict the results of measurements. We characterize quantum mechanical measurements of an observable A by the expectation value and the uncertainty. We quantify the disturbance that measurement inflicts on quantum systems through the quantum mechanical uncertainty principle. We also introduce the projection postulate, which states how the quantum state vector is changed after a measurement.