On the Herbrand content of LK

We present a structural representation of the Herbrand content of LK-proofs with cuts of complexity prenex Sigma-2/Pi-2. The representation takes the form of a typed non-deterministic tree grammar of order 2 which generates a finite language of first-order terms that appear in the Herbrand expansions obtained through cut-elimination. In particular, for every Gentzen-style reduction between LK-proofs we study the induced grammars and classify the cases in which language equality and inclusion hold.Comment: In Proceedings CL&C 2016, arXiv:1606.0582

Razing Lafitte: Defending Public Housing from a Hostile State

The contentious politics of the demolition of Lafitte public housing in post- Katrina New Orleans and its replacement with mixed-income properties is a telling case of the strategic conflicts housing advocates face in public housing revitalization. It reveals how the qualified outcomes of HOPE VI interact with local institutional and historical circumstances to confound the equity and social justice goals of housing and community development advocates. It shows the limits to public housing revitalization as an urban recovery strategy when hostile government leadership characterizes a region, and the state is recast as an adversary rather than revitalization partner. This case is part of a longer ethnographic project on post-Katrina New Orleans recovery

Development Of Human Brain Network Architecture Underlying Executive Function

The transition from late childhood to adulthood is characterized by refinements in brain structure and function that support the dynamic control of attention and goal-directed behavior. One broad domain of cognition that undergoes particularly protracted development is executive function, which encompasses diverse cognitive processes including working memory, inhibitory control, and task switching. Delineating how white matter architecture develops to support specialized brain circuits underlying individual differences in executive function is critical for understanding sources of risk-taking behavior and mortality during adolescence. Moreover, neuropsychiatric disorders are increasingly understood as disorders of brain development, are marked by failures of executive function, and are linked to the disruption of evolving brain connectivity. Network theory provides a parsimonious framework for modeling how anatomical white matter pathways support synchronized fluctuations in neural activity. However, only sparse data exists regarding how the maturation of white matter architecture during human brain development supports coordinated fluctuations in neural activity underlying higher-order cognitive ability. To address this gap, we capitalize on multi-modal neuroimaging and cognitive phenotyping data collected as part of the Philadelphia Neurodevelopmental Cohort (PNC), a large community-based study of brain development. First, diffusion tractography methods were applied to characterize how the development of structural brain network topology supports domain-specific improvements in cognitive ability (n=882, ages 8-22 years old). Second, structural connectivity and task-based functional connectivity approaches were integrated to describe how the development of anatomical constraints on functional communication support individual differences in executive function (n=727, ages 8-23 years old). Finally, the systematic impact of head motion artifact on measures of structural connectivity were characterized (n=949, ages 8-22 years old), providing important guidelines for studying the development of structural brain network architecture. Together, this body of work expands our understanding of how developing white matter connectivity in youth supports the emergence of functionally specialized circuits underlying executive processing. As diverse types of psychopathology are increasingly linked to atypical brain maturation, these findings could collectively lead to earlier diagnosis and personalized interventions for individuals at risk for developing mental disorders

The Church of England as a profession in Victorian England

The clergy in 1800 were by tradition part of the 'professional' world; but the professions were not large, nor were they clearly defined in terms either of their membership or of their duties and skills. Responding to both the pastoral needs and the political necessities of an industrialising, reforming nation, the Church reformed itself and greatly expanded its men and materiel. More clergy and clergy of higher calibre were ordained. At mid-century they compared well in education, zeal and rewards with the other growing and reforming professions. Various factors were to weaken this position. The need for clergy ran ahead of the capacity of the traditional source of supply, the universities, to provide them. The clergy had always tended to be recruited from the poorer university men; now many were from modest backgrounds but without the advantage of a degree. This was at a time when educational background was more and more emphasised and when connections with the old but reforming institutions of university and public school were increasingly prized. The clergy's position within the universities, particularly, was anyway less assured after 1860: there were currents of thought and opinion hostile or indifferent to religion, while at the same time more churchmen questioned the sufficiency of the university course as a training for the Church. The interests, in both senses, of the universities and of the clergy were diverging. There was, nevertheless, considerable concern in the Church at the weakening of the tie to the universities. But there was no concerted response, if only because the Church possessed no means of making such a response. Theological colleges were set up and run almost as private institutions - or at the most, episcopal ones. They were needed, yet they were resented by many clergy and church people. Gradually there developed a feeling of corporate responsibility to them; at the same time - the last quarter of the century - ordination procedures and requirements moved closer to standardisation. But even in the early 20th century there was far to go. If entry requirements seemed to be approximating slowly to the standards of other professions, in their ordained lives the clergy were ever less like other professionals. The fact that, like them, their work was more specialised than before, was outweighed by the exceptional nature of the work itself, at a time when other professions largely rested their social acceptance upon their practical utility and disinterested services. And the careers of the clergy were even more clearly anomalous. The parochial system - with its concomitants of inflexibility, widely dispersed patronage, and an arbitrarily distributed and inadequate endowment income - was incapable of providing a satisfactory 'career structure' for most clergy. The apparent stability of the Church's agricultural income, and the widespread possession of private means by the clergy, delayed full recognition of the problems. By 1900 these factors were ceasing to apply. And though the town parishes were able to benefit from increased voluntary lay contributions, it was to prove immensely difficult to change the habits and assumptions ingrained by centuries of reliance upon an independent clerical endowment. Before about 1860 the Church recruited more men than the universities could provide. Thereafter it found that a massive growth in the traditional educating institutions of the clergy was accompanied by at best a slow, and certainly a disproportionately small, growth in the number of ordinands. Doctrinal unsettlement doubtless contributed to this fact; especially as the level of religious commitment required for ordination had risen. It was also important that young men had less contact with the clergy in their school and university lives. The practical and financial problems may, however, have been the most important of all; churchmen thought that such matters weighed particularly with parents, who usually had considerable influence on the careers of their sons. For the Church already presented an unhappy compromise: it would not renounce the social and intellectual standards of the professions, but it patently did not provide, for most of its clergy, the ways and means to maintain them

The Transformation Of London's Water Supply, 1805-1821

In 1805 London was supplied with water by several old-established companies which used the traditional method of distribution by gravity, through wooden pipes, from reservoirs which were at no great elevation above the districts supplied. The New River Company was by far the largest of these. Supplies were intermittent and unreliable, and many of the suburbs had no piped water supplies at all. During the period 1805-1811 a number of new companies were set up, initially with the purpose of supplying the neglected areas on the outskirts. They used the latest technology of steam engines and cast iron pipes to give a high-pressure supply, and due to the iron pipes their supplies were more reliable, although they generally kept the intermittent system. They soon began to compete directly with the established companies, causing these to lose many customers and to experience severe financial difficulties. The new companies themselves, however, also had financial problems. They expanded their systems too rapidly, in a period of high prices, so that they needed very large capital investment, their share prices were manipulated by speculators, and no adequate return on their capitals could be gained from water charges, which were in general reduced as an inevitable result of competition. The old and new companies recognised that the competition was likely to ruin them all, and in 1815-1818 agreed boundaries giving each company an exclusive area of supply. They then substantially increased their charges, which led to furious agitation against them by groups of consumers, A Parliamentary Select Committee investigated the question in 1821 and found that the companies had generally acted reasonably. As a result of the competition and agreements among the companies, London in 1821 had a much more abundant and regular water supply, using the most up-to-date methods, than ever before

On closure ordinals for the modal mu-calculus

The closure ordinal of a formula of modal mu-calculus mu X phi is the least ordinal kappa, if it exists, such that the denotation of the formula and the kappa-th iteration of the monotone operator induced by phi coincide across all transition systems (finite and infinite). It is known that for every alpha < omega^2 there is a formula phi of modal logic such that mu X phi has closure ordinal alpha (Czarnecki 2010). We prove that the closure ordinals arising from the alternation-free fragment of modal mu-calculus (the syntactic class capturing Sigma_2 cap Pi_2) are bounded by omega^2. In this logic satisfaction can be characterised in terms of the existence of tableaux, trees generated by systematically breaking down formulae into their constituents according to the semantics of the calculus. To obtain optimal upper bounds we utilise the connection between closure ordinals of formulae and embedded order-types of the corresponding tableaux

On closure ordinals for the modal mu-calculus

The closure ordinal of a formula of modal mu-calculus mu X phi is the least ordinal kappa, if it exists, such that the denotation of the formula and the kappa-th iteration of the monotone operator induced by phi coincide across all transition systems (finite and infinite). It is known that for every alpha < omega^2 there is a formula phi of modal logic such that mu X phi has closure ordinal alpha (Czarnecki 2010). We prove that the closure ordinals arising from the alternation-free fragment of modal mu-calculus (the syntactic class capturing Sigma_2 cap Pi_2) are bounded by omega^2. In this logic satisfaction can be characterised in terms of the existence of tableaux, trees generated by systematically breaking down formulae into their constituents according to the semantics of the calculus. To obtain optimal upper bounds we utilise the connection between closure ordinals of formulae and embedded order-types of the corresponding tableaux

Finitary proof systems for Kozen’s μ.

We present three finitary cut-free sequent calculi for the modal [my]-calculus. Two of these derive annotated sequents in the style of Stirling’s ‘tableau proof system with names’ (4236) and feature special inferences that discharge open assumptions. The third system is a variant of Kozen’s axiomatisation in which cut is replaced by a strengthening of the v-induction inference rule. Soundness and completeness for the three systems is proved by establishing a sequence of embeddings between the calculi, starting at Stirling’s tableau-proofs and ending at the original axiomatisation of the [my]-calculus due to Kozen. As a corollary we obtain a completeness proof for Kozen’s axiomatisation which avoids the usual detour through automata or games

A Cyclic Proof System for Full Computation Tree Logic

Full Computation Tree Logic, commonly denoted CTL*, is the extension of Linear Temporal Logic LTL by path quantification for reasoning about branching time. In contrast to traditional Computation Tree Logic CTL, the path quantifiers are not bound to specific linear modalities, resulting in a more expressive language. We present a sound and complete hypersequent calculus for CTL*. The proof system is cyclic in the sense that proofs are finite derivation trees with back-edges. A syntactic success condition on non-axiomatic leaves guarantees soundness. Completeness is established by relating cyclic proofs to a natural ill-founded sequent calculus for the logic