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Causation, as any other element of an actionable tort, has to be proven in the proceedings. As pointed out in Chapter 1, the causal link is not a fact; it is indeed a connection between two known facts, also defined as 'an empirical relation between concrete conditions'. It follows that it is not subject to the same burden of proof as any other evidence submitted to the court. The causal link needs a demonstration through logic, statistics and common sense, which is supported by general scientific theories and, simultaneously, by specific justification of the singular causation. Proof of singular causation therefore needs (1) scientific validity of causal generalizations that control the condition and (2) complete instantiation of the empirical relation.
The previous chapter has presented the general proof rules of causation in competition damages actions. These standard rules burden the claimant with the proof of the essential elements of a tort, including causation. However, the claimant may find it very difficult if not impossible to prove causation, especially when information is limited or is not accessible. As observed in Chapter 5, the standard proof rules place the risk for the proof of the claim and the risk of error due to evidential uncertainty on the claimant. The rules allocating this risk are mainly the result of policy-based decisions aiming at distributing the risk fairly between the parties based on a moral statement. However, on the basis of equally justifiable policy and moral choices, it is possible to create exceptions to this rule in two cases: (1) when the information is readily available to the other party and (2) when it is fair, according to the type of responsibility, to allocate the risk differently.
Macrolophus pygmaeus, a predatory mirid used to manage greenhouse whitefly, was illegally imported into New Zealand, and for a time was reared and sold to commercial tomato growers. We designed and implemented a risk-based detection survey to determine whether M. pygmaeus was still present in New Zealand a decade later. The survey was designed to have an 80% chance of detecting a single low density (0.05 per lineal metre of host plants) population within 1 km of known points of introduction. The survey was implemented between 8 and 15 March 2018. Local habitat constraints meant that the planned sampling had to be modified but this was accounted for in the subsequent analysis. No M. pygmaeus were found in the samples, but 93 specimens from seven other mirid taxa were detected, validating the sample methods. The survey gives 60% confidence that M. pygmaeus was not present at a mean density of 0.05 per lineal metre of habitat. It gives 80% confidence that a population at 0.1 m−1 was not present and 90% confidence that no population exists at >0.18 m−1. Though there are no published data on typical field population densities of M. pygmaeus, for related species the survey would have had high confidence in detecting any medium to high density population present. Therefore, it is likely that M. pygmaeus is no longer present in New Zealand, but if extant within the sampled areas then we have high certainty that it was at low densities compared to other predaceous mirids.
Much has been said about Moore’s proof of the external world, but the notion of proof that Moore employs has been largely overlooked. I suspect that most have either found nothing wrong with it, or they have thought it somehow irrelevant to whether the proof serves its antiskeptical purpose. I show, however, that Moore’s notion of proof is highly problematic. For instance, it trivializes in the sense that any known proposition is provable. This undermines Moore’s proof as he conceives it since it introduces a skeptical regress that he goes at length to resist. I go on to consider various revisions of Moore’s notion of proof and finally settle on one that I think is adequate for Moore’s purposes and faithful to what he says concerning immediate knowledge.
None of the world’s megacities can feed themselves. Food chain risks pose imminent threat of starvation. Solutions to urban food risk. Climate-proof food supplies. Examples of novel urban food production systems. The importancve of ‘urban permaculture’. Rewilding and farmers as ‘Stewards of the Earth’. Developing wise consumers.
This article presents a new (multivalued) semantics for classical propositional logic. We begin by maximally extending the space of sequent proofs so as to admit proofs for any logical formula; then, we extract the new semantics by focusing on the axiomatic structure of proofs. In particular, the interpretation of a formula is given by the ratio between the number of identity axioms out of the total number of axioms occurring in any of its proofs. The outcome is an informational refinement of traditional Boolean semantics, obtained by breaking the symmetry between tautologies and contradictions.
Herbrand’s theorem is one of the most fundamental insights in logic. From the syntactic point of view, it suggests a compact representation of proofs in classical first- and higher-order logics by recording the information of which instances have been chosen for which quantifiers. This compact representation is known in the literature as Miller’s expansion tree proof. It is inherently analytic and hence corresponds to a cut-free sequent calculus proof. Recently several extensions of such proof representations to proofs with cuts have been proposed. These extensions are based on graphical formalisms similar to proof nets and are limited to prenex formulas.
In this paper, we present a new syntactic approach that directly extends Miller’s expansion trees by cuts and also covers non-prenex formulas. We describe a cut-elimination procedure for our expansion trees with cut that is based on the natural reduction steps and shows that it is weakly normalizing.
High-starch diets (HSDs) fed to high-producing ruminants are often responsible for rumen dysfunction and could impair animal health and production. Feeding HSDs are often characterized by transient rumen pH depression, accurate monitoring of which requires costly or invasive methods. Numerous clinical signs can be followed to monitor such diet changes but no specific indicator is able to make a statement at animal level on-farm. The aim of this pilot study was to assess a combination of non-invasive indicators in dairy cows able to monitor a HSD in experimental conditions. A longitudinal study was conducted in 11 primiparous dairy cows fed with two different diets during three successive periods: a 4-week control period (P1) with a low-starch diet (LSD; 13% starch), a 4-week period with an HSD (P2, 35% starch) and a 3-week recovery period (P3) again with the LSD. Animal behaviour was monitored throughout the experiment, and faeces, urine, saliva, milk and blood were sampled simultaneously in each animal at least once a week for analysis. A total of 136 variables were screened by successive statistical approaches including: partial least squares-discriminant analysis, multivariate analysis and mixed-effect models. Finally, 16 indicators were selected as the most representative of a HSD challenge. A generalized linear mixed model analysis was applied to highlight parsimonious combinations of indicators able to identify animals under our experimental conditions. Eighteen models were established and the combination of milk urea nitrogen, blood bicarbonate and feed intake was the best to detect the different periods of the challenge with both 100% of specificity and sensitivity. Other indicators such as the number of drinking acts, fat:protein ratio in milk, urine, and faecal pH, were the most frequently used in the proposed models. Finally, the established models highlight the necessity for animals to have more than 1 week of recovery diet to return to their initial control state after a HSD challenge. This pilot study demonstrates the interest of using combinations of non-invasive indicators to monitor feed changes from a LSD to a HSD to dairy cows in order to improve prevention of rumen dysfunction on-farm. However, the adjustment and robustness of the proposed combinations of indicators need to be challenged using a greater number of animals as well as different acidogenic conditions before being applied on-farm.
Chaucer lived in a society that was aware of childhood and adolescence as distinctive stages of human life and which inherited practices whereby young people were brought up and trained for adulthood. Informally, at home, children were introduced to social norms, religion and work. Those from wealthier families underwent more formal education, mastering literacy at home, in schools or in great households, where they learnt reading, rules of courtesy, French and, in the case of some boys, Latin. Chaucer’s works refer in passing to most of these processes, with particular attention to adolescents, including university scholars. During the fifteenth century his works in general came to be seen as having educational value. The Astrolabe, first written for his son Lewis, seems to have been used for teaching reading to other young children while his major writings were recommended as suitable literature for older ones.
This chapter examines the place of law in the England of Chaucer’s day in both the formal legal system and in popular consciousness. It considers the relation of English common law both to the overarching law of God and to other institutional legal structures, not least the canon law of the church, as well as to more informal procedures. Intrinsic contradictions in the nature of legal norms, including the tension between the needs for general certainty and individual justice, provide much scope for writers of stories. Difficulties of proof and the role of the oath are outlined and an analysis is offered of the extent to which a knowledge of the law and legal system of Chaucer’s time can add to the appreciation and understanding of his work.
This article investigates the proof theory of the Quantified Argument Calculus (Quarc) as developed and systematically studied by Hanoch Ben-Yami [3, 4]. Ben-Yami makes use of natural deduction (Suppes-Lemmon style), we, however, have chosen a sequent calculus presentation, which allows for the proofs of a multitude of significant meta-theoretic results with minor modifications to the Gentzen’s original framework, i.e., LK. As will be made clear in course of the article LK-Quarc will enjoy cut elimination and its corollaries (including subformula property and thus consistency).
By considering the new notion of the inverses of syllogisms such as Barbara and Celarent, we show how the rule of Indirect Proof, in the form (no multiple or vacuous discharges) used by Aristotle, may be dispensed with, in a system comprising four basic rules of subalternation or conversion and six basic syllogisms.
This paper clarifies that linear implication defines a branching-time preorder, preserved in all contexts, when used to compare embeddings of process in non-commutative logic. The logic considered is a first-order extension of the proof system BV featuring a de Morgan dual pair of nominal quantifiers, called BV1. An embedding of π-calculus processes as formulae in BV1 is defined, and the soundness of linear implication in BV1 with respect to a notion of weak simulation in the π -calculus is established. A novel contribution of this work is that we generalise the notion of a ‘left proof’ to a class of formulae sufficiently large to compare embeddings of processes, from which simulating execution steps are extracted. We illustrate the expressive power of BV1 by demonstrating that results extend to the internal π -calculus, where privacy of inputs is guaranteed. We also remark that linear implication is strictly finer than any interleaving preorder.