8,343 research outputs found

    Indexed induction and coinduction, fibrationally.

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    This paper extends the fibrational approach to induction and coinduction pioneered by Hermida and Jacobs, and developed by the current authors, in two key directions. First, we present a sound coinduction rule for any data type arising as the final coalgebra of a functor, thus relaxing Hermida and Jacobs’ restriction to polynomial data types. For this we introduce the notion of a quotient category with equality (QCE), which both abstracts the standard notion of a fibration of relations constructed from a given fibration, and plays a role in the theory of coinduction dual to that of a comprehension category with unit (CCU) in the theory of induction. Second, we show that indexed inductive and coinductive types also admit sound induction and coinduction rules. Indexed data types often arise as initial algebras and final coalgebras of functors on slice categories, so our key technical results give sufficent conditions under which we can construct, from a CCU (QCE) U : E -> B, a fibration with base B/I that models indexing by I and is also a CCU (QCE)

    Polysemy and Co-predication

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    Many word forms in natural language are polysemous, but only some of them allow for co-predication, that is, they allow for simultaneous predications selecting for two different meanings or senses of a nominal in a sentence. In this paper, we try to explain (i) why some groups of senses allow co-predication and others do not, and (ii) how we interpret co-predicative sentences. The paper focuses on those groups of senses that allow co-predication in an especially robust and stable way. We argue, using these cases, but focusing particularly on the multiply polysemous word ‘school’, that the senses involved in co-predication form especially robust activation packages, which allow hearers and readers to access all the different senses in interpretation

    Isolating LCDs at end-of-life using active disassembly technology: A feasibility study

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    The European Union draft Waste Electrical and Electronic Equipment (WEEE) directive calls for the removal and separate treatment of liquid crystal displays (LCD). This aspect of the legislation will potentially have an important impact upon the future `End of Life' (EoL) processing of much WEEE. Active Disassembly using Smart Materials (ADSM) has been proven to have applicability in self-dismantling, nondestructive and rapid disassembly of small electronic products. This paper investigates the technical feasibility of removing LCD screens from IT communication products using ASDM technology. In this paper an option is suggested to cleanly separate LCD screens from printed circuit boards, utilizing an LCD bracket made from `shape memory polymer'. The case study products employed are Nokia Japanese J-Phones. Demonstration experiments with initial results are presented, and future developments discussed. SMB glass transformation temperatures (Tg) and time efficiency in disassembly are considered

    Kant and the Ontological Argument

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    An essay reaffirming Kant's criticism of the ontological argument for the existence of God – a conjecture conceived in the 11th century by Anselm of Canterbury and defended in the mid-20th century by Charles Hartshorne and Norman Malcolm

    Note on Governmental Product Favoritism

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    Higher Order Containers

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    Abstract. Containers are a semantic way to talk about strictly positive types. In previous work it was shown that containers are closed under various constructions including products, coproducts, initial algebras and terminal coalgebras. In the present paper we show that, surprisingly, the category of containers is cartesian closed, giving rise to a full cartesian closed subcategory of endofunctors. The result has interesting applications syntax. We also show that while the category of containers has finite limits, it is not locally cartesian closed.
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