Axiomatization and completeness of uncountably valued approximation logic

A first order uncountably valued logicL _Q(0,1) for management of uncertainty is considered. It is obtained from approximation logicsL _T of any poset type (T, ) (see Rasiowa [17], [18], [19]) by assuming (T, )=(Q(0, 1), ) — whereQ(0, 1) is the set of all rational numbersq such that 0<q<1 and is the arithmetic ordering — by eliminating modal connectives and adopting a semantics based onLT-fuzzy sets (see Rasiowa and Cat Ho [20], [21]). LogicL _Q(0,1) can be treated as an important case ofLT-fuzzy logics (introduced in Rasiowa and Cat Ho [21]) for (T, )=(Q(0, 1), ), i.e. asLQ(0, 1)-fuzzy logic announced in [21] but first examined in this paper.L _Q(0,1) deals with vague concepts represented by predicate formulas and applies approximate truth-values being certain subsets ofQ(0, 1). The set of all approximate truth-values consists of the empty set ø and all non-empty subsetss ofQ(0, 1) such that ifqs andqq, thenqs. The setLQ(0, 1) of all approximate truth-values is uncountable and covers up to monomorphism the closed interval [0, 1] of the real line.LQ(0, 1) is a complete set lattice and therefore a pseudo-Boolean (Heyting) algebra. Equipped with some additional operations it is a basic plain semi-Post algebra of typeQ(0, 1) (see Rasiowa and Cat Ho [20]) and is taken as a truth-table forL _Q(0,1) logic.L _Q(0,1) can be considered as a modification of Zadeh's fuzzy logic (see Bellman and Zadeh [2] and Zadeh and Kacprzyk, eds. [29]). The aim of this paper is an axiomatization of logicL _Q(0,1) and proofs of the completeness theorem and of the theorem on the existence ofLQ(0, 1)-models (i.e. models under the semantics introduced) for consistent theories based on any denumerable set of specific axioms. Proofs apply the theory of plain semi-Post algebras investigated in Cat Ho and Rasiowa [4].Presented byCecylia Rauszer     

Compassion: An east‐west comparison

Compassion is an emotion that occupies a central position in Mahāyāna Buddhist philosophy while it is often a neglected subject in contemporary western philosophy. This essay is a comparison between an Eastern view of compassion based upon Mahāyāna Buddhist perspectives and a western view of the same emotion. Certain principles found in Mahāyāna Buddhist philosophy such as the Bodhisattva Ideal, and suffering (dukkha) to name two, are explored for the information they contain about compassion. An essay by Lawrence Blum is taken as representative of a Western view (but not exclusively) and it is analyzed for its shortcomings in light of the Buddhist view. The conclusion briefly describes the value of understanding an eastern view on compassion as a means of filling the void one finds in western medical ethics discourse which focuses so heavily, and redundantly, upon issues such as patient autonomy and paternalism.     

A faith for all seasons

A FAITH FOR ALL SEASONS:ISLAM AND WESTERN MODERNITY. By Shabbir Akhtar. London: Bellew Publishing, 1990. 251pp. Hb. £25.00. ISBN 0–947792–41–4.     

Algorithmic logic. Multiple-valued extensions

Extended algorithmic logic (EAL) as introduced in [18] is a modified version of extended ⁺-valued algorithmic logic. Only two-valued predicates and two-valued propositional variables occur in EAL. The role of the ⁺-valued logic is restricted to construct control systems (stacks) of pushdown algorithms whereas their actions are described by means of the two-valued logic. Thus EAL formalizes a programming theory with recursive procedures but without the instruction CASE.The aim of this paper is to discuss EAL and prove the completeness theorem. A complete formalization of EAL was announced in [20] but no proof of the completeness theorem was given.     

Justice in Transnational Governance

The small portion of philosophical work on global distributive justice that directly discusses particular agents, institutions or practices in global politics tends to focus on a narrow range of the existing set. The emphasis is chiefly on bilateral diplomacy or intergovernmental organisations, to the neglect of a variety of more recent forms of transnational governance, many of which incorporate non‐state actors, have more limited membership, involve informal and dynamic structures, employ cooperative and reflexive methods for ensuring compliance, and operate largely out of the public eye. This article considers how philosophers should conceive of distributive justice in relation to these neglected sites of transnational governance, using the International Organization for Standardization (ISO) as an illustration.     

Losing My Religion as a Natural Experiment: How State Pressure and Taxes Led to Church Disaffiliations between 1940 and 2010 in Germany

The sociological literature has produced a remarkably consistent picture of the quantitative patterns of religious disaffiliations in Western countries. This article argues, and demonstrates, that strong changes in a social context may lead individuals to disaffiliate rapidly, leading to very different aggregate effects from those in the “western model.” We use the unique situation of the separation of Germany from 1949 to 1989 and its subsequent reunification as a “natural experiment” to show just how much the relationships routinely found can be disrupted under changed conditions. The state socialist “treatment” affected religious disaffiliations in East Germany profoundly as it (a) made disaffiliations 10 times more probable in the East than in the West in the 1950s and 1960s, (b) shielded East German church members from factors that led to mass disaffiliations in the West in the late 1960s and early 1970s, (c) reversed the education‐disaffiliation link in the East, thus making disaffiliation more likely among the less educated, and (d) led to an especially strong increase in disaffiliations in the East right after the reunification     

Changing the Criminal Justice System Response to Sexual Assault: An Empirical Study of a Participatory Action Research Project

In jurisdictions throughout the United States, thousands of sexual assault kits (SAKs; also known as a “rape kits”) have not been submitted by the police for forensic DNA testing. DNA evidence may be helpful to sexual assault investigations and prosecutions by identifying perpetrators, revealing serial offenders through DNA matches across cases, and exonerating those who have been wrongly accused. This paper describes a longitudinal action research project conducted in Detroit, Michigan after that city discovered approximately 11,000 untested sexual assault kits in a police department storage facility. We conducted a root cause analysis to examine individual, organizational, community, and societal factors that contributed to the development of the rape kit backlog in Detroit. Based on those findings, we implemented and evaluated structural changes to increase staffing, promote kit testing, and retrain police and prosecutors so that cases could be reopened for investigation and prosecution. As we conducted this work, we also studied how this action research project impacted the Detroit criminal justice system. Participating in this project changed stakeholders’ attitudes about the utility of research to address community problems, the usefulness of DNA evidence in sexual assault cases, and the impact of trauma on survivors. The results led to new protocols for SAK testing and police investigations, and new state legislation mandating SAK forensic DNA testing.     

Fostering Well‐being through Social Support: The Role of Evangelical Communities in the Lives of Dominican Women of Haitian Descent

Women of Haitian descent living in the Dominican Republic experience oppression due to their gender, ethnicity, and economic status. They also exhibit high rates of participation in evangelical Christian communities, a paradoxical finding given the restricted roles women have traditionally played in these settings. The goals of this study were to explore the perceived benefits of participation in evangelical communities and the setting characteristics that lead to these benefits. The research team interviewed 19 current and former church participants aged 18–59. Thematic analysis revealed three perceived benefits of congregational life. Participants viewed their participation as: (a) an opportunity for personal growth and development; (b) protective against negative social influences; and (c) providing social support in the face of life challenges. In addition, dependable, expected, and reciprocal relational support was a key characteristic of evangelical communities. Findings extend the current understanding of how religious communities enhance well‐being for marginalized women through social support networks. Findings also explore the dialectical nature of settings as both empowering and disempowering. Implications for future interventions are discussed.