http://popups.lib.uliege.be/1373-5411/index.php?id=1455 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=1452 This paper describes the possibility of incursive proof in classical formal theory. Fri, 12 Jul 2024 14:22:57 +0200 Thu, 10 Oct 2024 10:33:12 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1452 http://popups.lib.uliege.be/1373-5411/index.php?id=3644 This paper outlines four major topics of tantamount importance to computing anticipatory systems. Section 1 introduces the reader to several historical facts regarding Daniel Dubois' hyperincursive modeling approach and its relationship with Gérard Langlet's work and the author's conception of parity logic systems. It provides the connection of Dubois' hyperincursivity theory and fractal machines with parity logic engines, a special class of binary integro-differential cellular automata. Section 2 on modeling anticipatory systems recalls first the essence of Dubois' anticipatory systems approach by comparing briefly recursivity, incursivity, and self-referentiality. Their impact on modeling cognitive anticipations is then discussed by rendering Piaget's recursive concept of anticipatory schemata into incursive schemata. Section 2 closes with an unresolved problem regarding anticipatory conflicts. Section 3 exhibits in a more formal way the difference between recursivity and incursivity by explicating Dubois' most important digital equations, how they apply to hyperincursive fractal machines, and how they are related to parity logic engines. This includes self-organized processing of parity intergrals and differentials, self-organized development of binary transforms, and several group theoretic implications of transforming parity matrices generated with fractal machines or parity logic engines. Finally, in section 4, further perspectives are outlined for the advancement of anticipatory systems by considering causal predictor systems in terms of fuzzy cognitive maps. This includes the law of concomitant variation, non-Aristotelian causality, the relationship between fuzzy causality, fuzzy subsethood and fuzzy causal cross-impact analysis. Thu, 26 Sep 2024 10:30:05 +0200 Thu, 26 Sep 2024 10:30:22 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3644 http://popups.lib.uliege.be/1373-5411/index.php?id=3531 This paper describes the possibility of science hyperincursive integration by construction of a formal theory which becomes a universal language for the sciences and where it is possible to build their integration process. After this integration any scientific theory assumes all the data and ideas that can be useful for it from the other scientific theories. Dubois' incursive algorithm scheme permits a good two by two integration process of all the sciences but the continous making of new scientific ideas and data in the outside environment of the integration process implies the necessity to can change it during its execution by opportune control parameters which represents the new scientific data and ideas which we can introduce. Thus we have really an hyperincursive process to integrate the sciences among them. Tue, 24 Sep 2024 10:19:55 +0200 Tue, 24 Sep 2024 10:20:05 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3531