Merging fragments of classical logic

We investigate the possibility of extending the non-functionally complete logic of a collection of Boolean connectives by the addition of further Boolean connectives that make the resulting set of connectives functionally complete. More precisely, we will be interested in checking whether an axiomatization for Classical Propositional Logic may be produced by merging Hilbert-style calculi for two disjoint incomplete fragments of it. We will prove that the answer to that problem is a negative one, unless one of the components includes only top-like connectives.Comment: submitted to FroCoS 201

Some comments on Ian Rumfitt's bilateralism

Ian Rumfitt has proposed systems of bilateral logic for primitive speech acts of assertion and denial, with the purpose of `exploring the possibility of specifying the classically intended senses for the connectives in terms of their deductive use' (Rumfitt (2000): 810f). Rumfitt formalises two systems of bilateral logic and gives two arguments for their classical nature. I assess both arguments and conclude that only one system satisfies the meaning-theoretical requirements Rumfitt imposes in his arguments. I then formalise an intuitionist system of bilateral logic which also meets those requirements. Thus Rumfitt cannot claim that only classical bilateral rules of inference succeed in imparting a coherent sense onto the connectives. My system can be extended to classical logic by adding the intuitionistically unacceptable half of a structural rule Rumfitt uses to codify the relation between assertion and denial. Thus there is a clear sense in which, in the bilateral framework, the difference between classicism and intuitionism is not one of the rules of inference governing negation, but rather one of the relation between assertion and denial

Ethnic-minority groups in England and Wales-factors associated with the size and timing of elevated COVID-19 mortality: a retrospective cohort study linking census and death records

BACKGROUND: We estimated population-level associations between ethnicity and coronavirus disease 2019 (COVID-19) mortality using a newly linked census-based data set and investigated how ethnicity-specific mortality risk evolved during the pandemic. METHODS: We conducted a retrospective cohort study of respondents to the 2011 Census of England and Wales in private households, linked to death registrations and adjusted for emigration (n = 47 872 412). The outcome of interest was death involving COVID-19 between 2 March 2020 and 15 May 2020. We estimated hazard ratios (HRs) for ethnic-minority groups compared with the White population, controlling for individual, household and area characteristics. HRs were estimated on the full outcome period and separately for pre- and post-lockdown periods. RESULTS: In age-adjusted models, people from all ethnic-minority groups were at elevated risk of COVID-19 mortality; the HRs for Black males and females were 3.13 (95% confidence interval: 2.93 to 3.34) and 2.40 (2.20 to 2.61), respectively. However, in fully adjusted models for females, the HRs were close to unity for all ethnic groups except Black [1.29 (1.18 to 1.42)]. For males, the mortality risk remained elevated for the Black [1.76 (1.63 to 1.90)], Bangladeshi/Pakistani [1.35 (1.21 to 1.49)] and Indian [1.30 (1.19 to 1.43)] groups. The HRs decreased after lockdown for all ethnic groups, particularly Black and Bangladeshi/Pakistani females. CONCLUSION: Differences in COVID-19 mortality between ethnic groups were largely attenuated by geographical and socio-demographic factors, though some residual differences remained. Lockdown was associated with reductions in excess mortality risk in ethnic-minority populations, which has implications for a second wave of infection

Correlation Between the Deuteron Characteristics and the Low-energy Triplet np Scattering Parameters

The correlation relationship between the deuteron asymptotic normalization constant, $A_{S}$, and the triplet np scattering length, $a_{t}$, is investigated. It is found that 99.7% of the asymptotic constant $A_{S}$ is determined by the scattering length $a_{t}$. It is shown that the linear correlation relationship between the quantities $A_{S}^{-2}$ and $1/a_{t}$ provides a good test of correctness of various models of nucleon-nucleon interaction. It is revealed that, for the normalization constant $A_{S}$ and for the root-mean-square deuteron radius $r_{d}$, the results obtained with the experimental value recommended at present for the triplet scattering length $a_{t}$ are exaggerated with respect to their experimental counterparts. By using the latest experimental phase shifts of Arndt et al., we obtain, for the low-energy scattering parameters ($a_{t}$, $r_{t}$, $P_{t}$) and for the deuteron characteristics ($A_{S}$, $r_{d}$), results that comply well with experimental data.Comment: 19 pages, 1 figure, To be published in Physics of Atomic Nucle

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

Empowerment and women in adventure tourism : a negotiated journey

Women’s participation in adventure tourism is growing, yet few studies have explored this group of tourists. This conceptual paper seeks to extend our understanding of female adventure tourists by examining the empowering journey women can take through constraint negotiation to enjoy the benefits of adventure tourism. Using content analysis to review the literature on women’s adventure experiences in tourism and recreation settings reveals prominent themes that have been consolidated to propose constraint, negotiation and benefit categories. A conceptual model is presented that illustrates the opportunities for women’s empowerment within these categories and examines the interrelationships and interdependency between them. The model shows that constraints, negotiations and benefits can be experienced simultaneously, at different points in a woman’s adventure tourism journey and used as a vehicle for empowerment. Women will also re-evaluate these categories before, during and after their adventure tourism experience. Therefore, the categories are not fixed and evolve each time a woman participates in adventure tourism throughout her life. Suggestions are made for further study in this under-researched area

Bridging the Two Plans in the Semantics for Relevant Logic

Part of the Synthese Library book series (SYLI, volume 418)This paper considers how the two plans in the semantics for relevant logic are related to each other. The so-called American plan, classical-style four-valued semantics, is intuitive, but weak. The so-called Australian plan, two-valued frame semantics, is very powerful, but the semantic devices employed need some explanation. Examining R. Routley’s 1984 paper ‘American plan completed, ’ this paper argues that the American plan provides an explanatory and ontological basis for the Australian plan, and that the latter is just a developed form of the former