Systematic construction of natural deduction systems for many-valued logics

A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems

Elimination of Cuts in First-order Finite-valued Logics

A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information

Dual Systems of Sequents and Tableaux for Many-Valued Logics

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and the exclusion of the opposite truth value describe the same situation.

Hilbert's "Verunglueckter Beweis," the first epsilon theorem, and consistency proofs

In the 1920s, Ackermann and von Neumann, in pursuit of Hilbert's Programme, were working on consistency proofs for arithmetical systems. One proposed method of giving such proofs is Hilbert's epsilon-substitution method. There was, however, a second approach which was not reflected in the publications of the Hilbert school in the 1920s, and which is a direct precursor of Hilbert's first epsilon theorem and a certain 'general consistency result' due to Bernays. An analysis of the form of this so-called 'failed proof' sheds further light on an interpretation of Hilbert's Programme as an instrumentalist enterprise with the aim of showing that whenever a `real' proposition can be proved by 'ideal' means, it can also be proved by 'real', finitary means.Comment: 18 pages, final versio

Patterns of adult sibling role involvement with brothers and sisters with intellectual and developmental disabilities

Adult siblings of individuals with intellectual and developmental disabilities (IDD) are increasingly involved in family care, yet, adult siblings consistently report needing more information and support to engage in these roles. Knowing more about which roles siblings are likely to assume may help address this need. Thus, we further examined the most common roles assumed by adult siblings (N = 171), the demographic variables related to an increased likelihood of assuming specific roles, and the potential clusters in patterns of role assumption. We transformed qualitative data from an online survey with four open-ended questions about sibling relationships and roles into quantitative presence data for role-related codes in order to examine relationships between assumed roles and demographic variables. The most common roles assumed by adult siblings were friend, advocate, caregiver, and sibling. Key demographic variables related to role assumption included disability severity, emotional closeness, and age of the brother or sister with IDD. Cluster analyses indicated five potential categories of adult sibling role involvement: Companion, Least Involved, Highly Involved, Needs Focused, and Professional. Implications and future areas of research are shared.Accepted manuscrip

An analysis of the effect of logistics involvement in cross-functional integrated new product development projects

The primary purpose of this dissertation was to empirically test the relationship between logistics involvement in new product development and improvements in new product development project performance and logistics performance. A logistics involvement new product model was developed that contained seven first order constructs: environmental uncertainty, improving information technology, time and quality based competition, global factors, cross-functional integration, new product development project performance, and logistics performance; and two second order constructs, logistics functional salience and logistics involvement

A SURVEY OF THE COMMON LOON (Gavia immer) GENOME REVEALS PATTERNS OF NATURAL SELECTION

With rapid advances in Next-Generation Sequencing technology, comparative genomics has become a viable method for studying the adaptation of species to their environment at the genome level. I investigated this in common loons (Gavia immer)—for which molecular adaptation has not been characterized—by finding signatures of positive selection as evidence for genomic adaptation. I used Illumina short read sequencing data from a single female common loon to produce a fragmented assembly of the common loon (Gavia immer) genome. The resulting assembly had a contig N50 of 814 bp, a total length of 767,326,331 bp, and 45.7 % GC content. I identified fragments of 13,821 common loon genes with known function and another 348 coding sequences of unknown function, for a total of 14,169 common loon genes. Based on estimates from well-resolved avian genomes, this figure represents 80.7% of common loon genes. I calculated dN/dS ratios between common loon and chicken (Gallus gallus) for a high confidence set of 10,106 gene fragments to find genes under positive selection. I found 490 positively selected genes in the common loon that were enriched for a number of protein classes, including those involved in muscle tissue development, immunoglobulin function, hemoglobin iron binding, nervous system development, G-protein receptors, and ATP metabolic process. The signature of positive selection in these key areas suggests common loons may have adapted for underwater diving by (1) compensations of the cardiovascular system and oxygen respiration, (2) low-light visual acuity, (3) and improved metabolism. Genes relating to immune system and neural development were also positively selected in concordance with prior research. This work represents the first effort to understand the genomic adaptations of the common loon and genus Gavia and may have implications for scholars seeking to find genes of interest for population genetic, ecological or conservation studies of the common loon

Kato-matsumoto-type results for disentanglements

We consider the possible disentanglements of holomorphic map germs f : (Cn, 0) → (CN , 0), 0 < n < N, with nonisolated locus of instability Inst(f). The aim is to achieve lower bounds for their (homological) connectiv- ity in terms of dimInst(f). Our methods apply in the case of corank 1

The Epsilon Calculus and Herbrand Complexity

Hilbert's epsilon-calculus is based on an extension of the language of predicate logic by a term-forming operator $\epsilon_{x}$. Two fundamental results about the epsilon-calculus, the first and second epsilon theorem, play a role similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential theorems obtained by this elimination procedure.Comment: 23 p