Logical consequence in modal logic II: Some semantic systems for S4

ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be equivalent; but, when regarded as consequence systems (ibid., p. 157), one diverges from the others in a fashion which suggests that two standard measures of semantic complexity may not be as closely linked as previously thought. This 1974 paper uses the linear notation for natural deduction presented in [2]: each two-dimensional deduction is represented by a unique one-dimensional string of characters. Thus obviating need for two-dimensional trees, tableaux, lists, and the like—thereby facilitating electronic communication of natural deductions. The 1969 paper presents a (modal, sentential) logic which may be thought of as a partial systematization of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of this logic coincides those of standard formalizations of Lewis’s S4. Among the paper's innovations is its treatment of modal logic in the setting of natural deduction systems--as opposed to axiomatic systems. The author’s apologize for the now obsolete terminology. For example, these papers speak of “a proof of a sentence from a set of premises” where today “a deduction of a sentence from a set of premises” would be preferable. 1. Corcoran, John. 1969. Three Logical Theories, Philosophy of Science 36, 153–77. J P R 2. Corcoran, John and George Weaver. 1969. Logical Consequence in Modal Logic: Natural Deduction in S5 Notre Dame Journal of Formal Logic 10, 370–84. MR0249278 (40 #2524). 3. Weaver, George and John Corcoran. 1974. Logical Consequence in Modal Logic: Some Semantic Systems for S4, Notre Dame Journal of Formal Logic 15, 370–78. MR0351765 (50 #4253)

Deep reef fish surveys by submersible on Alderdice, McGrail, and Sonnier Banks in the Northwestern Gulf of Mexico

Submersible surveys at numerous reefs and banks in the northwestern Gulf of Mexico (NWGOM) were conducted as part of the Sustainable Seas Expedition (SSE) during July/August 2002 to identify reef fish communities, characterize benthic habitats, and identify deep coral reef ecosystems. To identify the spatial extent of hard bottom reef communities, the Flower Garden Banks National Marine Sanctuary (FGBNMS) and the U.S. Geological Survey (USGS) mapped approximately 2000 km2 of the Northwestern Gulf of Mexico (NWGOM) continental shelf during June 2002 with high-resolution multibeam bathymetry. Previous investigations conducted on the features of interest (with the exceptions of East and West Flower Garden and Sonnier Banks, accessible by SCUBA) had not been conducted since the 1970s and 1980s, and did not have the use of high-resolution maps to target survey sites. The base maps were instrumental in navigating submersibles to specific features at each study site during the Sustainable Seas Expedition (SSE)—a submersible effort culminating from a partnership between the National Atmospheric and Oceanic Administration (NOAA) and the National Geographic Society (NGS). We report the initial findings of our submersible surveys, including habitat and reef fish diversity at McGrail, Alderdice, and Sonnier Banks. A total of 120 species and 40,724 individuals were identified from video surveys at the three banks. Planktivorous fishes constituted over 87% by number for the three banks, ranging from 81.4% at Sonnier Banks to 94.3% at Alderdice Bank, indicating a direct link to pelagic prey communities, particularly in the deep reef zones. High numbers of groupers, snappers, jacks, and other fishery species were observed on all three features. These sites were nominated as Habitat Areas of Particular Concern (HAPC) by the Gulf of Mexico Fishery Council in March 2004. Data obtained during this project will contribute to benthic habitat characterization and assessment of the associated fish communities through future SCUBA, ROV, and submersible missions, and allow comparisons to other deep reef ecosystems found throughout the Gulf of Mexico and western Atlantic Ocean

Fraenkel–Carnap Questions for Equivalence Relations

An equivalence is a binary relational system A = (A,ϱA) where ϱA is an equivalence relation on A. A simple expansion of an equivalence is a system of the form (Aa1…an) were A is an equivalence and a1,…,an are members of A. It is shown that the Fraenkel-Carnap question when restricted to the class of equivalences or to the class of simple expansions of equivalences has a positive answer: that the complete second-order theory of such a system is categorical, if it is finitely axiomatizable

An Empirical Investigation of Stoltenberg\u27s Counselor Complexity Model

Supervision research has begun to focus on developmental models. The main purpose of this study was to test for possible differences in the level of self-actualization of counselor trainees who are at the four levels of counselor development as described by the counselor complexity model (Stoltenberg, 1981). Secondary questions involved the relationships between level of counselor development and the variables of trainees\u27 perceptions of themselves and amount of trainees\u27 counseling experience. Seventy-nine trainees from programs in counseling psychology, clinical psychology, educational psychology, social work, and U.S. Army mental health were used in this study. Trainees\u27 supervisors rated the trainees\u27 level of counselor development on an instrument based on the counselor complexity model (Wiley, 1983). The major findings of this study were that: (a) no relationship was found between level of counselor trainee development and a measure of self-actualization; (b) some evidence was found that a relationship existed between amount of supervised counseling experience and higher levels of counselor development; (c) from the data it was concluded that a relationship existed between amount of unsupervised counseling experience and higher levels of counselor development; (d) a relationship was also found between three measures of trainees\u27 perceptions of themselves-­ self-awareness, dependency-autonomy, theory/skill acquisition--and higher levels of counselor development. The results of this study were supportive of the counselor complexity model. Implications were discussed for developmental supervision theory and some sugges­tions were made for future research

GIS in the Field: A Path to Increasing Efficiency

GIS in the Field: The Path to Increasing Efficiency — Everyone uses GIS to display data and create maps, but it can also standardize data collection and ease data sharing. In this presentation we explore how to use GIS to collect field data; make field data accessible to the entire project team in real time; eliminate paper records; standardize data collection; and enhance flexibility by using multiple types of data, including pictures, points, lines, and polygons

The reprocessing features in the X-ray spectrum of the NELG MCG-5-23-16

We present results from the spectral analysis of the Seyfert 1.9 galaxy MCG-5-23-16, based on ASCA, BeppoSAX, Chandra and XMM-Newton observations. The spectrum of this object shows a complex iron Kalpha emission line, which is best modeled by a superposition of a narrow and a broad (possibly relativistic) iron line, together with a Compton reflection component. Comparing results from all (six) available observations, we do not find any significant variation in the flux of both line components. The moderate flux continuum variability (about 25% difference between the brightest and faintest states), however, does not permit us to infer much about the location of the line-emitting material. The amount of Compton reflection is lower than expected from the total iron line EW, implying either an iron overabundance or that one of the two line components (most likely the narrow one) originates in Compton-thin matter.Comment: Accepted for publication in A&

X-ray Outflows in the Swift Burst Alert Detected Seyfert 1s

Previous surveys of outflows in low-redshift active galactic nuclei (AGN) have relied on the analysis of sources selected primarily for their optical/X-ray brightness, and are therefore biased. Towards determining the outflow properties of local AGN, we detect warm absorption signatures of O VII and O VIII absorption edges in the available Suzaku/XMM-Newton CCD spectra of an unbiased sample of 44 Seyfert 1-1.5 sources selected in the very hard X-rays (14-195 keV) with the Swift Burst Alert Telescope. From our analysis, we find that O VII and O VIII absorption edges are present in 41% of the sample. This fraction is dependent on luminosity, with outflow detections in 60% of low luminosity and 30% of high luminosity sources. However, grating spectroscopy of the highest luminosity sources reveals that ~ 80% of these sources have ionized absorbers, but that the ionization states are higher/lower than produces the O VII and O VIII edges. This suggests that ionized absorption may be present in all local Seyfert 1s.Comment: 13 pages, 2 figures, accepted in ApJ

QUANTITY OF LIVING PLANT MATERIALS IN PRAIRIE SOILS IN RELATION TO RUN-OFF AND SOIL EROSION

The menace of soil erosion did not appear in the west until much of the prairie was broken for cropping or weakened by continuous overgrazing. The grassland sod is a great conserver of rainfall; the amount of run-off water is relatively small, and the soil is firmly held against the forces of erosion. This study is concerned with the role that the living underground plant parts play in promoting the absorption of water by the soil, and especially their importance in reducing run-off. Their holding of the soil against the forces of water erosion has been experimentally determined. A study of the quantity of living plant materials in native prairies and pastures near Lincoln, Nebraska, has just been completed. These materials-largely the underground parts of grasses-are composed of roots, rhizomes, and the bases of stems. In the case of non-grassy species or forbs, they sometimes include corms, bulbs, and certain other underground plant structures. The relation of the vegetation to the effectiveness of the precipitation in supplying water to the soil is one of great importance. When the fate of the water falling as drops of rain is studied, it is found that a part is intercepted by the vegetation and never reaches the soil. Much water is lost as run-off when absorption is not sufficiently rapid. This frequently results in erosion. Large amounts are absorbed by the soil and again used by the plant, especially when the vegetation has produced good soil structure and abundant humus. Some water may percolate beyond the depths of the roots of even the most deeply rooted species. The cover of vegetation and the amount of living and dead organic materials in the soil both play an extremely important role in all of these processes. Although this study is not concerned primarily with the effects of the cover of vegetation on soil water relations, yet plant cover is closely related to quantity of underground plant parts and to run-off. Hence, brief consideration will be given to the interception of rainfall, decrease in run-off, and promotion of absorption by the cover of vegetation

Environmental Water Quality - a guide to sampling and measurement

The guide covers the problems associated with sampling water in the field and suggestions to overcome them. The main types of water pollution that potentially occur in the south west of Western Australia are discussed and for each contaminant, the origins and environmental effects are briefly described and where available, water quality guidelines are provided for major water uses. This is followed by specific requirements of the collection, storage and analysis of samples. The guide also includes further reading and details on suppliers, analytical costs and web resources

³H-tetracycline as a proxy for ⁴¹Ca for measuring dietary perturbations of bone resorption

Our group is interested in evaluating early effects of dietary interventions on bone loss. Postmenopausal women lose bone following reduction in estrogen which leads to increased risk of fracture. Traditional means of monitoring bone loss and effectiveness of treatments include changes in bone density, which takes 6 months to years to observe effects, and changes in biochemical markers of bone turnover, which are highly variable and lack specificity. Prelabeling bone with ⁴¹Ca and measuring urinary ⁴¹Ca excretion with accelerator mass spectrometry provides a sensitive, specific, and rapid approach to evaluating effectiveness of treatment. To better understand ⁴¹Ca technology as a tool for measuring effective treatments on reducing bone resorption, we perturbed bone resorption by manipulating dietary calcium in rats. We used ³H-tetracycline (³H-TC) as a proxy for ⁴¹Ca and found that a single dose is feasible to study bone resorption. Suppression of bone resorption, as measured by urinary ³H-TC, by dietary calcium was observed in rats stabilized after ovariectomy, but not in recently ovariectomized rats