http://popups.lib.uliege.be/1373-5411/index.php?id=4454 Publications of Auteurs Nick Rossiter fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=4594 Anticipation is a natural characteristic of any system. 'Natural' is difficult to define formally in a mathematical model. For a model is an artificial construct relying on reduced conditions and assumptions. A model gives rise to weak anticipation while strong anticipation requires us to raise our sights to metaphysics where naturality resides. A prime distinction is that metaphysics has a higher-order tense logic. Strong anticipation is no prisoner of time like weak anticipation. In general while adjointness has a logical ordering the operation of an environment C on a subobject A has a solution subobject B under Heyting inference A ⇒ B in the environment of C. This is represented as the expression C x A ⟶ B ┤ BA ⟵ C, the adjunction of the natural metaphysical ordering which constitutes strong anticipation. The environment C may be more particularised as an adjunction between the induced monad and comonad functors. The uniqueness of the adjunction in natural metaphysics is examined in the context of the Beck-Chevalley test for computing the multiplicity of formal models possible for weak anticipation. Mon, 14 Oct 2024 14:56:01 +0200 Mon, 14 Oct 2024 14:56:08 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4594 http://popups.lib.uliege.be/1373-5411/index.php?id=4449 Anticipation is a property of any system and resides in its semantics as a duality of the system itself. The relationship is an adjointness between levels, requiring contravariancy. The intension/extension levels are impredicative in nature but this recursive characteristic can be represented formally in category theory. This paper focuses on the vital role of contravariancy in adjointness, permitting a structured re-ordering of the categories involved. A worked example of a three-level architecture for an information system is provided, illustrating the alternation of intension/extension pairs, the adjointness of two-way functors between each level, the (bi)functors for linking intension to extension and the locally cartesian closed structure of the underlying categories. The dynamic anticipatory aspect of contravariant mapping, relative to static covariant mapping, is highlighted, reinforcing the view that contravariancy underpins anticipation. Fri, 11 Oct 2024 10:54:21 +0200 Fri, 11 Oct 2024 10:54:29 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4449