Abstract On the basis of a labelled deduction system (LND$_{ED-}$TRS), we demonstrate how to formalize the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type. This has allowed us to carry out a formal counterpart to equality between paths which is dealt with in homotopy theory, but this time with an approach using the device of term-rewriting paths. Using such formal calculus dealing with paths, we construct the fundamental groupoid of a path-connected $ X $ type and we define the concept of isomorphism between types. Next, we show that the computational paths determine a weak category, which will be called $ \mathcal {C}_{paths} $. Finally, we show that the weak category $ \mathcal {C}_{paths} $ determines a weak groupoid.

A normalization procedure is presented for a classical natural deduction (ND) proof system. This proof system, called N-Graphs, has a multiple conclusion proof structure, where cycles are allowed. With this, we have developed a thorough treatment of

A number of studies have been developed in recent years aimed at integrating pertinent concepts and technologies for analytical multidimensional (OLAP) and geographic (GIS) processing environments. This type of integrated environment has been identified as SOLAP (Spatial OLAP). However, due to the fact that these two technologies were conceived with different purposes in mind, the interaction of the two environments is not an easy task and even with so much research being developed, there remain unresolved issues that merit exploration. One such issue refers to aggregation functions for measures. These functions are currently used in the definition of multidimensional and geographic data cubes. The aim of this paper is to present a set of aggregation functions for geographic measures. We also show these functions in practice, by taking into account their use with a SOLAP architecture prototype. This SOLAP prototype is based on a model for Geographic Data Warehouse (GDW), a data cube model and a geographic multidimensional query language.