Tiziana Pacelli

Approximate distances, pointless geometry and incomplete information

In this paper an abstract notion of approximate metric space is proposed by means of an interval-valued distance between regions. Regions are interpreted as pieces of information in a space. The resulting theory supports some promising applications to some topics of fuzzy set theory, rough set theory and clustering.

Convergence and fixed points by fuzzy orders

A general approach to fixed point theory is proposed which is related to the notion of fuzzy ordering. This approach extends both the fixed point theorems in metric spaces and the ones in ordered sets.

The Development of Logical Tools Through Socially Constructed and Culturally Based Activities

In this chapter, we want to focus on the relationships between language and developmental processes of logical tools in “linguistic-manipulative” activities. A didactic path in a primary school classroom was designed based both on cooperation and meanings negotiation in interactional situations and on social-constructivist theories. The activities were deduction tasks. Our research hypothesis was that through cooperative activities related to the shared creation and the manipulation of language, socially and culturally constructed, children will be able to choose various strategies for problem solving. The children worked in cooperative groups and were interviewed using a semi-structured interview based on the explication interview method and on the biographic report. The content analysis and the observations of the activities helped us to identify topics related to the children’s processing and reprocessing of the activities.