http://popups.lib.uliege.be/1373-5411/index.php?id=2391 Publications of Auteurs B. N. Rossiter fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=4546 The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the Church-Turing hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Category theory provides the necessary coordinate-free mathematical language which is both constructive and non-local to subsume the various interpretations of quantum theory in one pullback/pushout Dolittle diagram. This diagrame can be used to test and classify physical devices and proposed algorithms for weak or strong anticipation. Quantum Information Science is more than a merger of Church-Tirring and quantum theories. It has constructively to bridge the non-local chasm between the weak anticipation of mathematics and the strong anticipation of physics , Mon, 14 Oct 2024 10:51:06 +0200 Mon, 14 Oct 2024 12:59:33 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4546 http://popups.lib.uliege.be/1373-5411/index.php?id=4540 The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the Church-Turing hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Category theory provides the necessary coordinate-free mathematical language which is both constructive and non-local to subsume the various interpretations of quantum theory in one pullback/pushout Dolittle diagram. This diagrame can be used to test and classify physical devices and proposed algorithms for weak or strong anticipation. Quantum Information Science is more than a merger of Church-Tirring and quantum theories. It has constructively to bridge the non-local chasm between the weak anticipation of mathematics and the strong anticipation of physics , Mon, 14 Oct 2024 10:47:39 +0200 Mon, 14 Oct 2024 12:58:47 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4540 http://popups.lib.uliege.be/1373-5411/index.php?id=2944 Every object in existence has its type. Every subject in language has its predicate. Every intention in logic has its extension. Each therefore has two levels but with the fundamental problem of the relationship between the two. The formalism of set theory cannot guarantee the two are co-extensive. That has to be imposed by the axiom of extensibility, which is inadequate for types as shown by Bertrand Russell's ramified type theory, for language as by Henri Poincare's impredication and for intention unless satisfying Port Royal's definitive concept. An anticipatory system is usually defined to contain its own future state. What is its type? What is its predicate? What is its extension? Set theory can well represent formally the weak anticipatory system, that is in a model of itself. However we have previously shown that the metaphysics of process category theory is needed to represent strong anticipation. Time belongs to extension not intention. The apparent prediction of strong anticipation is really in the structure of its predication. The typing of anticipation arises from a combination of c5 and μ - respectively (co) multiplication of the ( co )monad induced by adjointness of the system's own process. As a property of Cartesian closed categories this predication has significance for all typing in general systems theory including even in the definition of time itself. Tue, 03 Sep 2024 15:57:17 +0200 Tue, 03 Sep 2024 15:57:28 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2944 http://popups.lib.uliege.be/1373-5411/index.php?id=2389 The possible unknown behaviour of a reactive system may not be fully understood but it may be modelled in an information system. The relationship between a system and its model can be constructed through a series of stages showing the correlation between arrows in the system and in the model. Such a diagram is formal where the system and the model are 2-cell categories and the mappings between the system and the model are adjunctions. Such mappings can be built up using basic arrow constructions or given in a more abstract form in terms of freeness and co-freeness. The adequacy of a model as a representation of a natural system is discussed in terms of mapping properties such as reflection, isomorphism and adjoint equivalence. The circumstances for the model being anticipatory are considered. Thu, 08 Aug 2024 09:27:26 +0200 Thu, 10 Oct 2024 10:34:41 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2389