An independent axiomatisation for free short-circuit logic

Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Free short-circuit logic is the equational logic in which compound statements are evaluated from left to right, while atomic evaluations are not memorised throughout the evaluation, i.e., evaluations of distinct occurrences of an atom in a compound statement may yield different truth values. We provide a simple semantics for free SCL and an independent axiomatisation. Finally, we discuss evaluation strategies, some other SCLs, and side effects.Comment: 36 pages, 4 tables. Differences with v2: Section 2.1: theorem Thm.2.1.5 and further are renumbered; corrections: p.23, line -7, p.24, lines 3 and 7. arXiv admin note: substantial text overlap with arXiv:1010.367

Propositional logic with short-circuit evaluation: a non-commutative and a commutative variant

Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Short-circuit evaluation is widely used in programming, with sequential conjunction and disjunction as primitive connectives. We study the question which logical laws axiomatize short-circuit evaluation under the following assumptions: compound statements are evaluated from left to right, each atom (propositional variable) evaluates to either true or false, and atomic evaluations can cause a side effect. The answer to this question depends on the kind of atomic side effects that can occur and leads to different "short-circuit logics". The basic case is FSCL (free short-circuit logic), which characterizes the setting in which each atomic evaluation can cause a side effect. We recall some main results and then relate FSCL to MSCL (memorizing short-circuit logic), where in the evaluation of a compound statement, the first evaluation result of each atom is memorized. MSCL can be seen as a sequential variant of propositional logic: atomic evaluations cannot cause a side effect and the sequential connectives are not commutative. Then we relate MSCL to SSCL (static short-circuit logic), the variant of propositional logic that prescribes short-circuit evaluation with commutative sequential connectives. We present evaluation trees as an intuitive semantics for short-circuit evaluation, and simple equational axiomatizations for the short-circuit logics mentioned that use negation and the sequential connectives only.Comment: 34 pages, 6 tables. Considerable parts of the text below stem from arXiv:1206.1936, arXiv:1010.3674, and arXiv:1707.05718. Together with arXiv:1707.05718, this paper subsumes most of arXiv:1010.367

Factors Driving Duration to Cross-selling in Non-life Insurance: New Empirical Evidence from Switzerland

Customer relationship management and marketing analytics have become critical for non-life insurers operating in highly competitive markets. As it is easier to develop an existing customer than to acquire a new one, cross-selling and retention are key activities. In this research, we focus on both car and household-liability insurance products and consider the time a customer owning only a single product takes before buying the other product at the same insurer. Based on longitudinal consumer data from a Swiss insurance company covering the period from 2011 to 2015, we aim to study the factors driving the duration to cross-selling. Given the different dynamics observed in both products, we separately study the car and household-liability insurance customer cohorts. Considering the framework of survival analysis, we provide descriptive statistics and Kaplan-Meier estimates along major customer characteristics, contract history and distribution channel usage. For the econometric analysis of the duration, we compare the results from Cox and accelerated failure time models. We are able to characterize the times related to the buying behavior for both products through several covariates. Our results indicate that the policyholder age, the place of residence, the contract premium, the number of contracts held, and the initial access channel used for contracting influence the duration to cross-selling. In particular, our results underline the importance of the tied agent channel and the differences along the geographic region and the urbanicity of the place of residence. By quantifying the effects of the above factors, we extend the understanding of customer behavior and provide a basis for developing models to time marketing actions in insurance companies

Assessing the Performance of Random Forests for Modeling Claim Severity in Collision Car Insurance

For calculating non-life insurance premiums actuaries traditionally rely on separate severity and frequency models using covariates to explain the claims loss exposure. In this paper, we focus on the claim severity. First, we build two reference models, a generalized linear model and a generalized additive model, relying on a log-normal distribution of the severity and including the most significant factors. Thereby, we follow Henckaerts et al. (2018) to relate the continuous variables to the response in a nonlinear way. In the second step, we tune two random forest models, one for the claim severity and one for the log-transformed claim severity where the latter requires a transformation of the predicted results. We compare the prediction performance of the different models using the relative error, the root mean squared error and the goodness-of-lift statistics in combination with goodness-of-fit statistics (Denuit et al. 2019). In our application, we rely on a dataset of a Swiss collision insurance portfolio covering the loss exposure of the period from 2011 to 2015 and including observations from 81 309 settled claims with a total amount of CHF 184 mio. In the analysis, we use the data from 2011 to 2014 for training and from 2015 for testing. Our results indicate that the use of a log-normal transformation of the severity is not leading to performance gains with random forests. However, random forests with a log-normal transformation are the favorite choice to explain right-skewed claims. Finally, when considering all indicators, we conclude that the generalized additive model has the best overall performance

What policyholder and contract features determine the evolution of non-life insurance customer relationships? : A case study analysis

Purpose – Over the last decade, technological and social trends have significantly influenced the relationship between customers and insurers. New buying patterns, price comparison platforms and the usage of different interaction channels driving single-product purchases and impacting lapses have influenced insurers’ customer portfolios and development. The purpose of this paper is to study the features driving the customer relationship along three areas, namely, customer acquisition, development and retention. Design/methodology/approach – After defining 14 related hypotheses, the authors use econometric analyses to quantitatively support these hypotheses in the three areas of interest. The authors build on a large-scale longitudinal data set from a Swiss insurance company covering the period from 2005 to 2014 and including 2,757,000 customer-years. The data comprise information on private customers, their contract history, including coverage and losses and the channels used for buying insurance. This analysis focuses on the two most common non-life insurance products, namely, household/liability and car insurance. Findings – The authors provide descriptive statistics and results from econometric analyses to determine the significant features and patterns affecting customer development and retention. Among the main results, the authors underline the significant influence on cross-selling given by the customer’s age and the interaction channel. Customers from rural regions are more loyal and likely to conduct cross-buying when compared to their peers from urban regions. Car insurance holders are more likely to lapse than household/liability insurance clients. Finally, while newly acquired customers tend to buy only a single product, the authors show the importance of cross-selling for retaining customers. In fact, customer retention is positively influenced by the number of products hold. Research limitations/implications – This work is relevant for academics and practitioners alike, adding a quantitative basis to the understanding of managing customer relationships and for the development of further prospective models. Further work could investigate or add products, extend the study to other companies and focus on customer development with time. Originality/value – This study explores a large-scale longitudinal data set. The analyses of customer acquisition, development and retention can support insurers to construct their own models for customer relationship management

Equine-Facilitated Therapy and Trauma: Current Knowledge, Future Needs.

Equine-facilitated therapy (EFT) is a relatively new treatment for trauma and PTSD. EFT as well as animal assisted interventions in general have been introduced and implemented in mental health treatment for children and adults, though the research in support of these interventions has not kept up with practice. The purpose of this review is to examine the use of EFT for clients suffering from trauma/PTSD. Studies were included if PTSD/trauma was assessed and/or was measured as an outcome. A search of relevant databases resulted in nine peer-reviewed studies that met criteria. Studies are summarized and implications for future research are discussed. In general, findings suggest that EFT is a promising intervention for trauma/PTSD. Recommendations include a call for more research that includes veterans as well as for research that explicates the mechanisms by which EFT may be effective

The Ideological Component of Judging in the Taxation Context

Despite the vast number of systematic empirical studies of judicial behavior, we know surprisingly little about how and why judges reach decisions in the business and finance context. This void is due, in part, to scholars’ abiding focus on controversies involving civil rights and liberties; indeed, based on the extant literature, it would be easy to conclude that judges, particularly U.S. Supreme Court Justices, spend their days interpreting civil rights–type legislation to the exclusion of all other types of laws. Yet this conclusion is wide of the mark—even a simple count of the Supreme Court’s plenary docket reveals that the Court is more likely to address congressional statutes regulating business and the economy than civil rights legislation. The scholarly focus on civil rights cases, of course, is not itself problematic. The literature on judging in this area is both deep and rich; the studies are numerous and the findings robust. The problem, in our view, is that it is far from clear whether the findings in the civil rights literature can be generalized to all other areas of the law and, in particular, to cases involving statutes regulating business or the economy (“economic controversies”). To be sure, researchers find similarities in the decision making processes across issue areas, but just as often they find differences

Judging Statutes: Thoughts on Statutory Interpretation and Notes for a Project on the Internal Revenue Code

The more interesting features of the non-normative literature on statutory interpretation lie not in the distinctive conclusions it has generated, but rather in its commonalities. We see two as particularly interesting. First, many of the relevant studies focus on civil rights legislation. This holds true regardless of whether the work’s producers are legal academics or social scientists, whether the research is primarily qualitative or quantitative, or whether it finds its theoretical grounding in psychology, sociology, or economics. Second, almost all the studies—especially those of the large-n, quantitative variety—explore the outcomes reached by jurists, and not the rationale or justifications they invoke. To be sure, the outcomes under investigation differ from study to study—sometimes it is support for the government or not; in others, it is whether the judge reached a “liberal” or “conservative” decision. However, the unmistakable focus is on the result, to the neglect of the rationale. These are not criticisms of the extant literature. Quite the opposite: we firmly believe that by investigating outcomes reached in civil rights cases, this line of inquiry has revealed a great deal about the “judicial mind.” At the same time, we believe just as firmly that if we are to fully understand the determinants of statutory interpretation, then a continued emphasis on civil rights is, for reasons we specify in Part I, a potential problem. And, to the extent that we desire a more comprehensive picture of judicial behavior, an exclusive focus on outcomes is, for reasons we elaborate on in Part II, incomplete at best and misleading at worst. Accordingly, we have devised a project that aspires to address these concerns by (1) exploring Supreme Court tax opinions, a body of case law that, despite its importance, has received virtually no systematic attention, and (2) analyzing or taking into account both outcomes and rationales. At the end of the day, we hope that our attention to these matters will make a useful contribution to the literature on judging statutes

Laboratory and field measurements of enantiomeric monoterpene emissions as a function of chemotype, light and temperature

Plants emit significant amounts of monoterpenes into the earth's atmosphere, where they react rapidly to form a multitude of gas phase species and particles. Many monoterpenes exist in mirror-image forms or enantiomers. In this study the enantiomeric monoterpene profile for several representative plants (<i>Quercus ilex L., Rosmarinus officinalis L.</i>, and <i>Pinus halepensis Mill.</i>) was investigated as a function of chemotype, light and temperature both in the laboratory and in the field. Analysis of enantiomeric monoterpenes from 19 <i>Quercus ilex</i> individuals from Southern France and Spain revealed four regiospecific chemotypes (genetically fixed emission patterns). In agreement with previous work, only <i>Quercus ilex</i> emissions increased strongly with light. However, for all three plant species no consistent enantiomeric variation was observed as a function of light, and the enantiomeric ratio of &alpha;-pinene was found to vary by less than 20% from 100 and 1000 μmol m⁻² s⁻¹ PAR (photosynthetically active radiation). The rate of monoterpene emission increased with temperature from all three plant species, but little variation in the enantiomeric distribution of α-pinene was observed with temperature. There was more enantiomeric variability between individuals of the same species than could be induced by either light or temperature. Field measurements of α-pinene enantiomer mixing ratios in the air, taken at a <i>Quercus ilex</i> forest in Southern France, and several other previously reported field enantiomeric ratio diel cycle profiles are compared. All show smoothly varying diel cycles (some positive and some negative) even over changing wind directions. This is surprising in comparison with variations of enantiomeric emission patterns shown by individuals of the same species