AN ASSESSMENT OF THE AESTHETIC VALUE OF THE ISLAMIC UNIVERSITY MOSQUE IN CONSTANTINE

Contemporary architecture increasingly stands out as a new area of cultural heritage. The "religious patrimony of the future" is one of the principal components which fits naturally into the logical process of preservation and transfer, of the architectural heritage from one generation to the other. The patrimonial process represents the only way to identify and evaluate these "prominent qualities", through different methods of evaluation. this study aims to assess the aesthetic value, considered as one of the essential characteristics of the university mosque in Constantine. It also aims to trigger its heritage process. The methodology was for quantitative and qualitative analysis (quaternaries and formal investigation). The analysis of its outward composition and overall form fits not only into a specific theoretical framework related to the philosophy of art and the subjectivity of beauty perception but depends more on an "in situ" investigation. The evaluation criteria adopted for this study focuses on the values of balance, dominance, unity and variety as well as the parameters of rhythm, proportion and perfect angles. The finding of this study reveals that these criteria made evident different constructive logics used at this university mosque such as the use of Doric proportions and privileged angles, which could serve as an objective argument in according aesthetic value to this mosque in Constantine and prepare its patrimonial future as a religious heritage for future generations.

Coinductive predicates and final sequences in a fibration

Coinductive predicates express persisting ‘safety’ specifications of transition systems. Previous observations by Hermida and Jacobs identify coinductive predicates as suitable final coalgebras in a fibration – a categorical abstraction of predicate logic. In this paper, we follow the spirit of a seminal work by Worrell and study final sequences in a fibration. Our main contribution is to identify some categorical ‘size restriction’ axioms that guarantee stabilization of final sequences after ω steps. In its course, we develop a relevant categorical infrastructure that relates fibrations and locally presentable categories, a combination that does not seem to be studied a lot. The genericity of our fibrational framework can be exploited for binary relations (i.e. the logic of ‘binary predicates’) for which a coinductive predicate is bisimilarity, constructive logics (where interests are growing in coinductive predicates) and logics for name-passing processes.

From Compound Houses to Villas: The Incremental Transformation of Dakar’s Urban Landscape

This paper examines the transformation of the housing typology in informal neighbourhoods located on the periphery of Dakar, Senegal. More specifically, it documents the spatial logics and factors guiding the construction of new multi-storey houses called “villas”, which are significantly transforming the landscape of the city. Studies have thus far examined villas through the lenses of migrants’ investments and lifestyles, associating these houses with new functions and decorative elements and materials inspired by time spent abroad, with innovative ways of building and dwelling that disrupt more popular housing practices. Based upon an architectural survey of seventeen houses and the detailed stories of their construction, this paper argues that while the Senegalese villa is influenced by global networks and symbols of success, it is also deeply rooted in popular housing forms and building practices. Moreover, because house-building processes are predominantly incremental, the construction of this new house type is not limited to migrants and other privileged dwellers. Although at different speeds, most residents are building and transforming their houses according to spatial and constructive logics characteristic of villas. These results have implications for housing policies and programmes because they contribute to challenging assumptions about residential production, new housing typologies and the pivotal actors of these urban transformations.

Co-constructive Logics for Proofs and Refutations

This paper considers logics which are formally dual to intuitionistic logic in order to investigate a co-constructive logic for proofs and refutations. This is philosophically motivated by a set of problems regarding the nature of constructive truth, and its relation to falsity. It is well known both that intuitionism can not deal constructively with negative information, and that defining falsity by means of intuitionistic negation leads, under widely-held assumptions, to a justification of bivalence. For example, we do not want to equate falsity with the non-existence of a proof since this would render a statement such as “pi is transcendental” false prior to 1882. In addition, the intuitionist account of negation as shorthand for the derivation of absurdity is inadequate, particularly outside of purely mathematical contexts. To deal with these issues, I investigate the dual of intuitionistic logic, co-intuitionistic logic, as a logic of refutation, alongside intuitionistic logic of proofs. Direct proof and refutation are dual to each other, and are constructive, whilst there also exist syntactic, weak, negations within both logics. In this respect, the logic of refutation is weakly paraconsistent in the sense that it allows for statements for which, neither they, nor their negation, are refuted. I provide a proof theory for the co-constructive logic, a formal dualizing map between the logics, and a Kripke-style semantics. This is given an intuitive philosophical rendering in a re-interpretation of Kolmogorov's logic of problems.