The field of qualitative spatial reasoning is now an active research area in Geographical Information Systems (GIS) and also in Artificial Intelligence (AI). Different kinds of spatial relations play an important role in spatial reasoning, spatial analysis, and query languages for geospatial databases. GIS and image databases are often based on the description of relations between spatial regio...

Martin-Löf’s Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive recursion over higher types, induction and recursion are formally derived for a large class of well-founded relations. Included are < on natural numbers, and rela...

The multiplicate form of Gould–Hsu’s inverse series relations enables to investigate the dual relations of the Chu–Vandermonde–Gauß’s, the Pfaff–Saalschütz’s summation theorems and the binomial convolution formula due to Hagen and Rothe. Several identitity and reciprocal relations are thus established for terminating hypergeometric series. By virtue of the duplicate inversions, we establish sev...

As international relations develop into a network-like arena, new public diplomacy receives more attention, both in research and in practice. At the same time, with the increasing role of non-state actors in international relations, their significant roles and functions have come under substantial scientific analysis. While companies engage in business abroad,  unintended results may emerge, af...

We are concerned with learning relations in a reactive environment. A learning agent observes sequences of actions that may change the properties or relationships of objects in the world. The observed sequence is then used to form a theory which can be generalised and tested by imitation. That is, the learner attempts to perform its own sequence of actions. If the test completes as expected the...

Particulate air pollution has been suggested as the cause of the recently observed decreasing trends of 10 to 25% in the ratio between hilly and upwind lowland precipitation, downwind of urban and industrial areas. We quantified the dependence of this ratio of the orographic-precipitation enhancement factor on the amounts of aerosols composed mostly of pollution in the free troposphere, based o...

We extend the theory and the algorithms of Border Bases to systems of Laurent polynomial equations, defining “toric” roots. Instead of introducing new variables and new relations to saturate by the variable inverses, we propose a more efficient approach which works directly with the variables and their inverse. We show that the commutation relations and the inversion relations characterize tori...

Moore and Myhill showed that Garden-of-Eden theorem [2], [3]. A binary relation over the configurations is said to be "parallel" if it is induced by a cellular (tessellation) automaton. Richardson showed the equivalence between a parallel relation (a nondeterministic parallel map) with the quiescent state to be injective and its inverse to be parallel by the Garden-of-Eden theorem plus compactn...