http://popups.lib.uliege.be/1373-5411/index.php?id=155 Publications of Auteurs Paulo Fernando Blauth Menezes fr 0 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 http://popups.lib.uliege.be/1373-5411/index.php?id=2043 Aiming at developing a theoretical framework for the formal study of NP-hard optimisation problems, we have focused on structural properties of optimisation problems related to approximative issue. From the observation that, intuitively, there are many connections among categorical concepts and structural complexity notions, in this work we present a categorical approach to cope with some questions originally studied within Computational Complexity Theory. After defining the polynomial time soluble optimisation problems category OPTS and the optimisation problems category OPT, we introduce a comparison mechanism between them following the basic idea of categorical shape theory, in such way the hierarchical structure of approximation to each optimisation problem can be modelled. Fri, 26 Jul 2024 15:48:26 +0200 Thu, 10 Oct 2024 10:52:10 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2043 http://popups.lib.uliege.be/1373-5411/index.php?id=1997 Adaptive hypermedia are suitable to offer flexible Web-based courses and can be useful to solve problems associated with the use of educational hypermedia as the inability to satisfy heterogeneous needs, match a web course to students and build different courses from a set of hypermedia materials. In this context, a framework based on Automata Theory and Category Theory named Hyper-Automaton is defined in order to create a semi-automated system for developing Web Courses. Courses are (nondeterministic finite) automata with output and links between pages are automata transitions (not HTML source) and thus, reusing the instructional material is straighforward. The categorial constructions of products, coproducts, limits, colimits, restriction, relabeling and reification morphisms have meaningful interpretation as constructors to define (possible complex) hypertext documents for web courses. Then we show how adaptive web courses (i.e., courses that adapt itself according to the behavior of the student) can be defined in this framework using categorial operations for adaptive presentation (or content-level adaptation) and adaptive navigation (or link-level adaptation). Fri, 19 Jul 2024 14:04:09 +0200 Thu, 10 Oct 2024 10:51:36 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1997 http://popups.lib.uliege.be/1373-5411/index.php?id=1862 This paper describes the Geometry demonstration learning system LEEG (Learning Environment on Euclidean Geometry). This system was constructed on a learning environment composed of five agents that interact to promote the knowledge construction and evolution. The five agents are : Mestre, Oráculo, Sonda, Cliente and Aprendiz (or in English, respectively, Master, Oracle, Probe, Client, Apprentice), each one with distinctive and specific behavior. The focus of this work will be the specification of the Mestre-Oráculo and Mestre-Sonda relationships and the knowledge base specification. Wed, 17 Jul 2024 12:06:52 +0200 Wed, 17 Jul 2024 12:07:01 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1862 http://popups.lib.uliege.be/1373-5411/index.php?id=149 A categorial framework for structured graph based systems with or without distinguished nodes or labeling on both arcs and nodes is proposed. Requirements for the existence of limits and colimits in the resulting categories are set. In this context, unrestricted and bicomplete categories of graph based systems such as Petri Nets, Labeled Transition Systems, Nonsequential Automata, etc., are easily defined. Then it is shown how limits and colimits can be interpreted as structuring and anticipatory properties of systems. The proposed framework called duo-internalization generalizes the notion of intemal graphs allowing that nodes and arc may be objects from different categories. The results about limits and colimits of (reflexive) duo-intemal (labeled) graphs (with distinguished nodes) are, for our knowledge, new. Tue, 18 Jun 2024 16:30:02 +0200 Tue, 18 Jun 2024 16:30:21 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=149