Aristotle’s Prototype Rule-Based Underlying Logic

This expository paper on Aristotle’s prototype underlying logic is intended for a broad audience that includes non-specialists. It requires as background a discussion of Aristotle’s demonstrative logic. Demonstrative logic or apodictics is the study of demonstration as opposed to persuasion. It is the subject of Aristotle’s two-volume Analytics, as its first sentence says. Many of Aristotle’s examples are geometrical. A typical geometrical demonstration requires a theorem that is to be demonstrated, known premises from which the theorem is to be deduced, and a deductive logic by which the steps of the deduction proceed. Every demonstration produces (or confirms) knowledge of (the truth of) its conclusion for every person who comprehends the demonstration. Aristotle presented a general truth-and-consequence theory of demonstration meant to apply to all demonstrations: a demonstration is an extended argumentation that begins with premises known to be truths and that involves a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In short, a demonstration is a deduction whose premises are known to be true. Aristotle’s general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining theory of deduction was meant to apply to all deductions: any deduction that is not immediately evident is an extended argumentation that involves a chaining of immediately evident steps that shows its final conclusion to follow logically from its premises. His deductions, both direct and indirect, were rule-based and not tautology-based. The idea of tautology-based deduction, which dominated modern logic in the early years of the 1900s, is nowhere to be found in Analytics. Rule-based (or “natural”) deduction was rediscovered by modern logicians. To illustrate his general theory of deduction, Aristotle presented a prototype: an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. With reference only to propositions of the four so-called categorical forms, he painstakingly worked out exactly what those immediately evident deductive steps are and how they are chained to complete deductions. In his specialized prototype theory, Aristotle explained how to deduce from a given categorical premise set, no matter how large, any categorical conclusion implied by the given set. He did not extend this treatment to non-categorical deductions, thus setting a program for future logicians. The prototype, categorical syllogistic, was seen by Boole as a “first approximation” to a comprehensive logic. Today, however it appears more as the first of the dozens of logics already created and as the first exemplification of a family that continues to expand.     

Search for lepton-flavor-violating decays of the neutral kaon

The Fermilab KTeV experiment has searched for lepton-flavor-violating decays of the K(L) meson in three decay modes. We observe no events in the signal region for any of the modes studied, and we set the following upper limits for their branching ratios at the 90% C.L.: BR(K(L) --> pi(0) micro(+/-) e(-/+)) <7.6 x 10(-11); BR(K(L) --> pi(0)pi(0) micro(+/-) e(-/+)) <1.7 x 10(-10); BR(pi(0) --> micro(+/-) e(-/+)) <3.6 x 10(-10). This result represents a factor of 82 improvement in the branching ratio limit for K(L) --> pi(0) micro(+/-) e(-/+) and is the first reported limit for K(L) --> pi(0)pi(0) micro(+/-) e(-/+).     

A performance study of radio-opaque personal protective fabrics for the reduction of transmittance of gamma-rays and neutrons

Commercial radio-opaque combat (CRC) fabrics, for incorporation into personal protective equipment used by first responders and armed forces, are marketed as having the ability to provide a level of protection against specific types of radiation. For a CRC material, a standard combat uniform and a multi-layered chemical, biological, radiological, nuclear (CBRN) protective material, the present work examines chemical composition and radiation protection against gamma-rays and neutron fluxes. Significant reduction in gamma-ray transmittance occurs only for the CRC fabric (46–514 keV) with gamma-ray attenuation coefficients of 3.10 to <0.10 cm² g⁻¹. Reduction in neutron transmittance, for all three fabrics, could not be assessed with certainty as the measured transmittance was obscured by large statistical uncertainties.     

Experimental and numerical study on the propagation of impulsive sound around buildings

Propagation of impulsive sound around buildings and induced structural loading are investigated experimentally and numerically. Experiments were conducted on a rectangular building at Virginia Tech using sonic booms generated by shaped charges with an explosive weight of 0.78 kg, constructed from detonation cord. These experiments were simulated with a three-dimensional numerical model, in the context of geometrical acoustics (GA), by combining the image source method for the reflected field (specular reflections) with an extension of the Biot–Tolstoy–Medwin (BTM) method for the diffracted field. In this model, it is assumed that the acoustic propagation is linear and that all surfaces are acoustically rigid. This numerical model is validated against a boundary element (BE) solution and experimental data, showing a good overall agreement. The key advantages of this GA modeling approach for this application include the ability to model large three-dimensional domains over a wide frequency range and also to decompose the sound field into direct, reflected, and diffracted components, thus providing a better understanding of the sound-propagation mechanisms. Finally, this validated numerical model is used to investigate sound propagation around a cluster of six rectangular buildings, for a range of elevated source positions simulating sonic booms from aircraft.     

Finding fixed-length circuits and cycles in undirected edge-weighted graphs: an application with street networks

Journal of Heuristics - This paper proposes two heuristic algorithms for finding fixed-length circuits and cycles in undirected edge-weighted graphs. It focusses particularly on a largely...     

The Impact of Research Culture on Mental Health & Diversity in STEM

The onset of COVID-19, coupled with the finer lens placed on systemic racial disparities within our society, has resulted in increased discussions around mental health. Despite this, mental health struggles in research are still often viewed as individual weaknesses and not the result of a larger dysfunctional research culture. Mental health interventions in the science, technology, engineering, and mathematics (STEM) academic community often focus on what individuals can do to improve their mental health instead of focusing on improving the research environment. In this paper, we present four aspects of research that may heavily impact mental health based on our experiences as research scientists: bullying and harassment; precarity of contracts; diversity, inclusion, and accessibility; and the competitive research landscape. Based on these aspects, we propose systemic changes that institutions must adopt to ensure their research culture is supportive and allows everyone to thrive.