424 research outputs found
A Convenient Category of Domains
No full texttopological spaces, generalising the usual ω-continuous dcppos of domain theory. Our category supports all the standard constructions of domain theory, including the solution of recursive domain equations. It also supports the construction of free algebras for (in)equational theories, provides a model of parametric polymorphism, and can be used as the basis for a theory of computability. This answers a question of Gordon Plotkin, who asked whether it was possible to construct a category of domains with such properties
Computational Effects in Topological Domain Theory
No full textAbstractThis paper contributes towards establishing the category QCB, of topological quotients of countably based spaces, and its subcategory TP, of topological predomains, as a flexible framework for denotational semantics of programming languages. In particular, we show that both categories have free algebras for arbitrary countable parametrised equational theories, and are thus, following ideas of Plotkin and Power, able to model a wide range of computational effects. Furthermore, we give an explicit construction of the free algebras
Compactly Generated Domain Theory
No full textWe propose compactly generated monotone convergence spaces as a well-behaved topological generalisation of directed-complete partial orders (dcpos). The category of such spaces enjoys the usual properties of categories of 'predomains' in denotational semantics. Moreover, such properties are retained if one restricts to spaces with a countable pseudobase in the sense of E. Michael, a fact that permits connections to be made with computability theory, realizability semantics and recent work on the closure properties of topological quotients of countably based spaces (qcb spaces). We compare the standard domain-theoretic constructions of products and function spaces on dcpos with their compactly generated counterparts, showing that these agree in important cases, though not in general
Ingo Plag, Word-Formation in English (2
No full text1. General observations Ingo Plag is Professor of English Linguistics at Heinrich-Heine-Universität Düsseldorf. He has published articles in specialized journals like Linguistics, Language or English Language and Linguistics and in works like the Yearbook of Morphology [2001], Word-Formation: An International Handbook of the Languages of Europe [2016] or Word Knowledge and Word Usage: A Cross-Disciplinary Guide to the Mental Lexicon [2017]. He is the author of Morphological Productivity: Stru..
Comparing free algebras in Topological and Classical Domain Theory
No full textAbstractWe compare how computational effects are modelled in Classical Domain Theory and Topological Domain Theory. Both of these theories provide powerful toolkits for denotational semantics: Classical Domain Theory having been introduced by Scott, and well established and developed since; Topological Domain Theory being a generalization in which topologies more general than the Scott-topology are admitted. Computational effects can be modelled using free algebra constructions, according to Plotkin and Power, and we show that for a wide range of computational effects, including all the classical powerdomains, this free algebra construction coincides in Classical and Topological Domain Theory, when restricted to countably-based continuous domains
Observationally-induced Algebras in Domain Theory
No full textAbstractWe investigate the observationally-induced free algebra approach for constructing computational monads in the categories of classical domain theory. Our investigation yields that the free algebra construction exists for all finitary algebraic signatures and computational prototypes. We furthermore investigate the classical powerdomain constructions in the observationally-induced approach. For the Hoare, Smyth and probabilistic powerdomain constructions we build on established results, showing that they can be recovered observationally-induced. However, the Plotkin powerdomain turns out to be more problematic. Here we show that with the obvious prototype algebra, Heckmanns algebra A, one does not get the classical Plotkin powerdomain
A domain-theoretic investigation of posets of sub-sigma-algebras (extended abstract)
No full textGiven a measurable space (X, M) there is a (Galois) connection between sub-sigma-algebras of M and equivalence relations on X. On the other hand equivalence relations on X are closely related to congruences on stochastic relations. In recent work, Doberkat has examined lattice properties of posets of congruences on a stochastic relation and motivated a domain-theoretic investigation of these ordered sets. Here we show that the posets of sub-sigma-algebras of a measurable space do not enjoy desired domain-theoretic properties and that our counterexamples can be applied to the set of smooth equivalence relations on an analytic space, thus giving a rather unsatisfactory answer to Doberkat's question
Topological Domain Theory
No full textThis thesis presents Topological Domain Theory as a powerful and flexible framework for denotational semantics. Topological Domain Theory models a wide range of type constructions and can interpret many computational features. Furthermore, it has close connections to established frameworks for denotational semantics, as well as to well-studied mathematical theories, such as topology and computable analysis.We begin by describing the categories of Topological Domain Theory, and their categorical structure. In particular, we recover the basic constructions of domain theory, such as products, function spaces, fixed points and recursive types, in the context of Topological Domain Theory.As a central contribution, we give a detailed account of how computational effects can be modelled in Topological Domain Theory. Following recent work of Plotkin and Power, who proposed to construct effect monads via free algebra functors, this is done by showing that free algebras for a large class of parametrised equational theories exist in Topological Domain Theory. These parametrised equational theories are expressive enough to generate most of the standard examples of effect monads. Moreover, the free algebras in Topological Domain Theory are obtained by an explicit inductive construction, using only basic topological and set-theoretical principles.We also give a comparison of Topological and Classical Domain Theory. The category of omega-continuous dcpos embeds into Topological Domain Theory, and we prove that this embedding preserves the basic domain-theoretic constructions in most cases. We show that the classical powerdomain constructions on omega-continuous dcpos, including the probabilistic powerdomain, can be recovered in Topological Domain Theory.Finally, we give a synthetic account of Topological Domain Theory. We show that Topological Domain Theory is a specific model of Synthetic Domain Theory in the realizability topos over Scott's graph model. We give internal characterisations of the categories of Topological Domain Theory in this realizability topos, and prove the corresponding categories to be internally complete and weakly small. This enables us to show that Topological Domain Theory can model the polymorphic lambda-calculus, and to obtain a richer collection of free algebras than those constructed earlier.In summary, this thesis shows that Topological Domain Theory supports a wide range of semantic constructions, including the standard domain-theoretic constructions, computational effects and polymorphism, all within a single setting
Observationally-induced Effects in Cartesian Closed Categories
No full textAbstractAlex Simpson has suggested an observationally-induced approach towards obtaining monads for computational effects in denotational semantics. The underlying idea of this approach is to use a single observation algebra as computational prototype and to obtain a computational monad as a free algebra construction derived from this prototype. Recently, it has been shown that free observationally-induced algebras exist in the category of continuous maps between topological spaces for arbitrary pre-chosen computational prototypes.In this work we transfer these results to cartesian closed categories. In particular, we show that, provided the category under consideration satisfies suitable completeness conditions, it supports a free observationally-induced algebra construction for arbitrary computational prototypes. We also show that the free algebras are obtained as certain subobjects of double exponentials involving the computational prototype as result type. Finally, we apply these results to show that in topological domain theory an observationally-induced lower powerspace construction over a QCB-space X is given by the space of nonempty closed subsets of X topologised suitably
Remarks on Early Medieval legal charters — The legend of “dux Ingo” and his “carta sine litteris”
No full textEnea Silvio Piccolomini in his work entitled
De Europa
written in 1458, tells an interesting story defined as a legend in terms of genre about a duke called Ingo, who lived during the reign of Charlemagne. This narrative claims that in 790
dux gentis
Ingo held a feast for the inhabitants of his province where food was served to the peasants allowed to appear before him in golden and silver bowls, while to the dignitaries standing further away from him in bowls made of clay. The researchers’ attention is deservedly raised by the query how come that this parabolical story with biblical tone was included in Enea Silvio’s work; if it had been borrowed who the
auctor
might have been he borrowed it from. The answer seems to be very simple: from the
Conversio Bagoariorum et Carantanorum
drafted regarding the lawsuit proceeded against Methodius. In the case narrated in the
Conversio
Ingo sent a charter or much rather a parchment without any writing, or letters on it
(carta sine litteris)
, which provided his legate with sufficient authenticity to demand obedience from the people.In this study-after having compared the two narratives and outlined the place of De Europa in Enea Silvio Piccolomini’s oeuvre and the circumstances of the drafting and tendencies of the Conversio Bagoariorum et Carantanorum-the author attempts to answer the following questions. To what extent can duke Ingo, mentioned by Enea Silvio and not questioned in the literature for long centuries, be considered a real historical person? Does the Conversio refer to Ingo as a duke, and if it does, what is his existence as a duke and introduction in the literature as a duke owing to? What could the meaning of carta sine litteris referred to in Conversio have been, and why did Enea Silvio not take this item over although he could have put it forward as a further proof of Ingo’s dignity? To what literary prefigurations can the description of the feast held by Ingo be traced back to, and what role did it play in the Conversio? Regarding the borrowing of the Ingo story by Enea Silvio, what possible intermediary writing and author can be reckoned with
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