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    Wyświetlanie 1-6 z 6
    Tytuł:
    Category theoryand some of its logical aspects
    Teoria kategorii i niektóre jej logiczne aspekty
    Autorzy:
    Stopa, Mariusz
    Opis:
    This article is intended for philosophers as a short partial introduction to category theory (CT) and its peculiar connection with logic. First, we consider CT itself. We give a brief insight into its history, introduce some basic definitions and present examples. In the second part, we focus on categorical topos semantics for propositional logic. We give some properties of logic in toposes, which, in general, is an intuitionistic logic. We next present two families of toposes whose tautologies are identical with those of classical propositional logic. The relatively extensive bibliography is given in order to support further studies.
    Dostawca treści:
    Repozytorium Uniwersytetu Jagiellońskiego
    Artykuł
    Tytuł:
    Teoria kategorii i niektóre jej logiczne aspekty
    Category theory and some of its logical aspects
    Autorzy:
    Stopa, Mariusz
    Tematy:
    category theory
    topos theory
    categorical logic
    propositional logic
    intuitionistic logic
    non-classical logic
    Pokaż więcej
    Wydawca:
    Copernicus Center Press
    Powiązania:
    https://bibliotekanauki.pl/articles/690940.pdf  Link otwiera się w nowym oknie
    Opis:
    This article is intended for philosophers and logicians as a short partial introduction to category theory (CT) and its peculiar connection with logic. First, we consider CT itself. We give a brief insight into its history, introduce some basic definitions and present examples. In the second part, we focus on categorical topos semantics for propositional logic. We give some properties of logic in toposes, which, in general, is an intuitionistic logic. We next present two families of toposes whose tautologies are identical with those of classical propositional logic. The relatively extensive bibliography is given in order to support further studies.
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the validity of the definition of a complement-classifier
    Autorzy:
    Stopa, Mariusz
    Tematy:
    category theory
    topos theory
    categorical logic
    Heyting algebras
    co-Heyting algebras
    intuitionistic logic
    dual to intuitionistic logic
    complement-classifier
    Pokaż więcej
    Wydawca:
    Copernicus Center Press
    Powiązania:
    https://bibliotekanauki.pl/articles/1047622.pdf  Link otwiera się w nowym oknie
    Opis:
    It is well-established that topos theory is inherently connected with intuitionistic logic. In recent times several works appeared concerning so-called complement-toposes (co-toposes), which are allegedly connected to the dual to intuitionistic logic. In this paper I present this new notion, some of the motivations for it, and some of its consequences. Then, I argue that, assuming equivalence of certain two definitions of a topos, the concept of a complement-classifier (and thus of a co-topos as well) is, at least in general and within the conceptual framework of category theory, not appropriately defined. For this purpose, I first analyze the standard notion of a subobject classifier, show its connection with the representability of the functor Sub via the Yoneda lemma, recall some other properties of the internal structure of a topos and, based on these, I critically comment on the notion of a complement-classifier (and thus of a co-topos as well).
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Global versus local Casimir effect
    Autorzy:
    Herdegen, Andrzej
    Stopa, Mariusz
    Opis:
    This paper continues the investigation of the Casimir effect withthe use of the algebraic formulation of quantum field theory in the initialvalue setting. Basing on earlier papers by one of us (AH), we approximatethe Dirichlet and Neumann boundary conditions by simple interactionmodels whose nonlocality in physical space is under strict control, butwhich at the same time are admissible from the point of view of algebraicrestrictions imposed on models in the context of Casimir backreaction.The geometrical setting is that of the original parallel plates. By scalingour models and taking appropriate limit, we approach the sharp bound-ary conditions in the limit. The global force is analyzed in that limit. One finds in Neumann case that although the sharp boundary interac-tion is recovered in the norm resolvent sense for each model considered,the total force per area depends substantially on its choice and diverges inthe sharp boundary conditions limit. On the other hand thelocalenergydensity outside the interaction region, which in the limit includes anycompact setoutside the strict position of the plates, has a universal limitcorresponding to sharp conditions. This is what one should expect in gen-eral, and the lack of this discrepancy in Dirichlet case is rather accidental.Our discussion pins down its precise origin: the difference in the order inwhich scaling limit and integration over the whole space is carried out.
    Dostawca treści:
    Repozytorium Uniwersytetu Jagiellońskiego
    Artykuł
      Wyświetlanie 1-6 z 6

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