TOPOS-BASED MODEL THEORY FOR HEURISTICS / TEORIA DE MODELOS PARA HEURÍSTICAS BASEADA EM TOPOI

AUTOR(ES)

FERNANDO NAUFEL DO AMARAL

DATA DE PUBLICAÇÃO

2004

RESUMO

This work employs concepts and tools from Category Theory and Topos Theory to construct a mathematical model for problems, reductions between problems, heuristic search spaces and strategies. More precisely, a search space construction strategy is represented by a functor from a certain category of problems to a certain category of forests. The collection of all such functors forms a topos, a specific model equipped with its own internal logic. This internal logic is then used to define search satrategies and heuristics in Local Set Theory. Possible applications of this work include (1) the logical specification and classification of heuristics and metaheuristics used in pratice and (2) a more abstract and general rendering of specific results relating the structure of problems to adequate problem-solving methods.

ASSUNTO(S)

logica interna teoria de categorias category theory heuristic search busca heuristica internal logic model theory teoria de modelos teoria de problemas problem theory

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