1,720,973 research outputs found
Discrete decision theory: manipulations
No full textAbstractDecision trees are a frequently used form of representation especially in application areas in which efficiency is important. Despite this little is known about how they can be manipulated. This paper introduces identifies for manipulating decision trees. Decision trees are interpreted to be terms of coalgebras and for this method of interpretation it is shown that the identities are complete.When decision trees are viewed as terms of an algebraic system, it is reasonable to look for special forms into which these terms can be transformed. Not only do decision trees have a canonical form but also a number of other significant forms. These forms include the simply reduced form and the irreducible form. The former is useful in determining equality, while the latter is significant in the problem of optimizing decision trees
Categories with finite limits and stable binary coproducts can be subdirectly decomposed
No full textAbstractCategories in which the binary coproduct is preserved by pulling back are of particular relevance to computer science. An important subclass of such categories are those which are finitely complete and have disjoint coproducts, distributive categories, as they are a natural setting for the study of data structures.Unfortunately, stability of binary coproducts does not imply disjointness of coproducts. The simplest counter-example to this is provided by a nontrivial distributive lattice. However, a finitely complete category with stable coproducts may always be subdirectly decomposed into a distributive poset and a distributive category. Furthermore, the distributive component occurs as a reflexive subcategory
A Language For Multiplicative-additive Linear Logic
No full textAbstractA term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive categories with additives. It is also shown that proof equivalence is decidable by showing that the cut elimination rewrites supply a confluent rewriting system modulo equations
Linearly distributive functors
No full textAbstractThis paper introduces a notion of “linear functor” between linearly distributive categories that is general enough to account for common structure in linear logic, such as the exponentials (!, ?), and the additives (product, coproduct), and yet when interpreted in the doctrine of ∗-autonomous categories, gives the familiar notion of monoidal functor. We show that there is a bi-adjunction between the 2-categories of linearly distributive categories and linear functors, and of ∗-autonomous categories and monoidal functors, given by the construction of the “nucleus” of a linearly distributive category. We develop a calculus of proof nets for linear functors, and show how linearity accounts for the essential coherence structure of the exponentials and the additives
Categorical Models of the Differential λ-Calculus Revisited
No full textAbstractThe paper shows that the Scott-Koymans theorem for the untyped λ-calculus extends to the differential λ-calculus. The main result is that every model of the untyped differential λ-calculus may be viewed as a differential reflexive object in a Cartesian closed differential category. This extension of the Scott-Koymans theorem depends critically on unravelling the somewhat subtle issue of which idempotents can be split so that differential structure lifts to the idempotent splitting.The paper uses (total) Turing categories with “canonical codes” as the basic categorical semantics for the λ-calculus. It shows how the main result may be developed in a modular fashion by first adding left-additive structure to a Turing category, and then – on top of that – differential structure. For both levels of structure it is necessary to identify how “canonical codes” behave with respect to the added structure and, furthermore, how “universal objects” behave. The latter is closely tied to the question – which is the crux of the paper – of which idempotents can be split in these more structured settings
List-arithmetic distributive categories: Locoi
No full textAbstractA finitely complete category with stable disjoint coproducts and a parameterized list construction is called a locos. The paper proves that the property of being a locos is local in the sense of being inherited by slice categories. This is proven by establishing two important properties of the list construction in this setting.The first of these is that lists can be characterized as objects which satisfy a domain equation and have their tail maps contractions. A contraction is an endomorphism which, when it is applied frequently enough, becomes fixed. It is a central technical notion in this development. As this characterization only uses the number arithmetic of the setting, it provides a powerful tool for establishing the existence of lists.The second result is that list construction preserves and creates connected limits. Because lists satisfy a domain equation they are models of a certain type of sketch. Models of such sketches are preserved and created by connected limits. However, it is the fact that the contractions are also preserved by these limits which is crucial. This observation immediately gives the localness of list construction in a locos and is fundamental to many of the other properties of list construction
Restriction categories II: partial map classification
No full textAbstractAn algebraic characterization of monads which are abstract partial map classifiers is provided, without the assumption that the categories of total maps possess products. By an abstract partial map classifier we mean a monad whose Kleisli category is a full subcategory of a partial map category wherein the induced comonad classifies partial maps in the usual sense. A construction of the corresponding actual partial map classifier from an abstract one is described, and conditions for an abstract partial map classifier to be a real one are provided. The paper uses the notion of a restriction category developed in earlier work, and the characterization of these as full subcategories of partial map categories
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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