http://popups.lib.uliege.be/1373-5411/index.php?id=4315 Index terms fr 0 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 http://popups.lib.uliege.be/1373-5411/index.php?id=2678 In graph-based systems there are many methods to compose (possibly different) graphs. However, none of these usual compositions are adequate to naturally express semantics of systems with dynamic topology, i.e., systems whose topology admits successive transformations through its computation. We constructed a categorical semantic domain for graph based systems with dynamic topology using a new way to compose edges of (possible different) graphs. ln this context, sequences of different graphs represent successive transformations of system topology during its computation and the edges composition between those graphs, the semantics of the corresponding dynamic system. Then we show how the proposed approach can be used to give semantics to concurrent anticipatory systems. Fri, 30 Aug 2024 10:23:17 +0200 Thu, 10 Oct 2024 10:52:38 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2678