Explicit mathematics and operational set theory: some ontological comparisons

We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.

A feasible theory of truth over combinatory algebra

We define an applicative theory of truth TPT which proves totality exactly for the polynomial time computable functions. TPT has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that have smaller length than a given word. This makes it possible to achieve the very low proof-theoretic strength. Truth induction can be allowed without any constraints. For these reasons the system TPT has the high expressive power one expects from truth theories. It allows embeddings of feasible systems of explicit mathematics and bounded arithmetic. The proof that the theory TPT is feasible is not easy. It is not possible to apply a standard realisation approach. For this reason we develop a new realisation approach whose realisation functions work on directed acyclic graphs. In this way, we can express and manipulate realisation information more efficiently.

Against Logically Possible World-Relativized Existence

The thesis that entities exist in, at, or in relation to logically possible worlds is criticized. The suggestion that actually nonexistent fictional characters might nevertheless exist in nonactual merely logically possible worlds runs afoul of the most general transworld identity requirements. An influential philosophical argument for the concept of world-relativized existence is examined in Alvin Plantinga’s formal development and explanation of modal semantic relations. Despite proposing an attractive unified semantics of alethic modality, Plantinga’s argument is rejected on formal grounds as supporting materially false actual existence assertions in the case of actually nonexistent objects in the framework of Plantinga’s own underlying classical predicate-quantificational logic.

Privacy Preserving Probabilistic Record Linkage (P3RL): a novel method for linking existing health-related data and maintaining participant confidentiality.

BACKGROUND Record linkage of existing individual health care data is an efficient way to answer important epidemiological research questions. Reuse of individual health-related data faces several problems: Either a unique personal identifier, like social security number, is not available or non-unique person identifiable information, like names, are privacy protected and cannot be accessed. A solution to protect privacy in probabilistic record linkages is to encrypt these sensitive information. Unfortunately, encrypted hash codes of two names differ completely if the plain names differ only by a single character. Therefore, standard encryption methods cannot be applied. To overcome these challenges, we developed the Privacy Preserving Probabilistic Record Linkage (P3RL) method. METHODS In this Privacy Preserving Probabilistic Record Linkage method we apply a three-party protocol, with two sites collecting individual data and an independent trusted linkage center as the third partner. Our method consists of three main steps: pre-processing, encryption and probabilistic record linkage. Data pre-processing and encryption are done at the sites by local personnel. To guarantee similar quality and format of variables and identical encryption procedure at each site, the linkage center generates semi-automated pre-processing and encryption templates. To retrieve information (i.e. data structure) for the creation of templates without ever accessing plain person identifiable information, we introduced a novel method of data masking. Sensitive string variables are encrypted using Bloom filters, which enables calculation of similarity coefficients. For date variables, we developed special encryption procedures to handle the most common date errors. The linkage center performs probabilistic record linkage with encrypted person identifiable information and plain non-sensitive variables. RESULTS In this paper we describe step by step how to link existing health-related data using encryption methods to preserve privacy of persons in the study. CONCLUSION Privacy Preserving Probabilistic Record linkage expands record linkage facilities in settings where a unique identifier is unavailable and/or regulations restrict access to the non-unique person identifiable information needed to link existing health-related data sets. Automated pre-processing and encryption fully protect sensitive information ensuring participant confidentiality. This method is suitable not just for epidemiological research but also for any setting with similar challenges.

Unfolding Feasible Arithmetic and Weak Truth

In this paper we continue Feferman’s unfolding program initiated in (Feferman, vol. 6 of Lecture Notes in Logic, 1996) which uses the concept of the unfolding U(S) of a schematic system S in order to describe those operations, predicates and principles concerning them, which are implicit in the acceptance of S. The program has been carried through for a schematic system of non-finitist arithmetic NFA in Feferman and Strahm (Ann Pure Appl Log, 104(1–3):75–96, 2000) and for a system FA (with and without Bar rule) in Feferman and Strahm (Rev Symb Log, 3(4):665–689, 2010). The present contribution elucidates the concept of unfolding for a basic schematic system FEA of feasible arithmetic. Apart from the operational unfolding U0(FEA) of FEA, we study two full unfolding notions, namely the predicate unfolding U(FEA) and a more general truth unfolding UT(FEA) of FEA, the latter making use of a truth predicate added to the language of the operational unfolding. The main results obtained are that the provably convergent functions on binary words for all three unfolding systems are precisely those being computable in polynomial time. The upper bound computations make essential use of a specific theory of truth TPT over combinatory logic, which has recently been introduced in Eberhard and Strahm (Bull Symb Log, 18(3):474–475, 2012) and Eberhard (A feasible theory of truth over combinatory logic, 2014) and whose involved proof-theoretic analysis is due to Eberhard (A feasible theory of truth over combinatory logic, 2014). The results of this paper were first announced in (Eberhard and Strahm, Bull Symb Log 18(3):474–475, 2012).

Inversion, Obviation, and Animacy in Native Languages of the Americas: Elements for a Cross-linguistic Survey

Native languages of the Americas whose predicate and clause structure reflect nominal hierarchies show an interesting range of structural diversity not only with respect to morphological makeup of their predicates and arguments but also with respect to the factors governing obviation status. The present article maps part of such diversity. The sample surveyed here includes languages with some sort of nonlocal (third person acting on third person) direction-marking system.

Privacy-preserving genomic testing in the clinic: a model using HIV treatment

PURPOSE The implementation of genomic-based medicine is hindered by unresolved questions regarding data privacy and delivery of interpreted results to health-care practitioners. We used DNA-based prediction of HIV-related outcomes as a model to explore critical issues in clinical genomics. METHODS We genotyped 4,149 markers in HIV-positive individuals. Variants allowed for prediction of 17 traits relevant to HIV medical care, inference of patient ancestry, and imputation of human leukocyte antigen (HLA) types. Genetic data were processed under a privacy-preserving framework using homomorphic encryption, and clinical reports describing potentially actionable results were delivered to health-care providers. RESULTS A total of 230 patients were included in the study. We demonstrated the feasibility of encrypting a large number of genetic markers, inferring patient ancestry, computing monogenic and polygenic trait risks, and reporting results under privacy-preserving conditions. The average execution time of a multimarker test on encrypted data was 865 ms on a standard computer. The proportion of tests returning potentially actionable genetic results ranged from 0 to 54%. CONCLUSIONS The model of implementation presented herein informs on strategies to deliver genomic test results for clinical care. Data encryption to ensure privacy helps to build patient trust, a key requirement on the road to genomic-based medicine.Genet Med advance online publication 14 January 2016Genetics in Medicine (2016); doi:10.1038/gim.2015.167.

Comparative Study of Digital Rights Management Systems for Music and Text Files

Digital Rights Management Systems (DRMS) are seen by content providers as the appropriate tool to, on the one hand, fight piracy and, on the other hand, monetize their assets. Although these systems claim to be very powerful and include multiple protection technologies, there is a lack of understanding about how such systems are currently being implemented and used by content providers. The aim of this paper is twofold. First, it provides a theoretical basis through which we present shortly the seven core protection technologies of a DRMS. Second, this paper provides empirical evidence that the seven protection technologies outlined in the first section of this paper are the most commonly used technologies. It further evaluates to what extent these technologies are being used within the music and print industry. It concludes that the three main Technologies are encryption, password, and payment systems. However, there are some industry differences: the number of protection technologies used, the requirements for a DRMS, the required investment, or the perceived success of DRMS in fighting piracy.

The Application of Digital Rights Management Systems in the Music Industry - An Empirical Investigation

Technology advances in hardware, software and IP-networks such as the Internet or peer-to-peer file sharing systems are threatening the music business. The result has been an increasing amount of illegal copies available on-line as well as off-line. With the emergence of digital rights management systems (DRMS), the music industry seems to have found the appropriate tool to simultaneously fight piracy and to monetize their assets. Although these systems are very powerful and include multiple technologies to prevent piracy, it is as of yet unknown to what extent such systems are currently being used by content providers. We provide empirical analyses, results, and conclusions related to digital rights management systems and the protection of digital content in the music industry. It shows that most content providers are protecting their digital content through a variety of technologies such as passwords or encryption. However, each protection technology has its own specific goal, and not all prevent piracy. The majority of the respondents are satisfied with their current protection but want to reinforce it for the future, due to fear of increasing piracy. Surprisingly, although encryption is seen as the core DRM technology, only few companies are currently using it. Finally, half of the respondents do not believe in the success of DRMS and their ability to reduce piracy.