This paper is a contribution to formal ontology study. We propose a new model of knowledge representation by combining ontologies and topology. In order to represent atypical entities in the ontologies, we introduce topological operators of interior, exterior, border and closure. These operators allow us to describe whether an entity, belonging to a class, is typical or not. We define a system ...

Query algorithms are used to compute mathematical functions. Classical version of this model is also known as decision trees. Quantum counterpart of decision trees – quantum query model – has been actively studied in recent years. Typically, query model is used to compute Boolean functions. In this paper, we consider computing mathematical relations instead of functions. A relation is a set of ...

In complex industrial plants, there are usually many sensors and the modeling of plants leads to lots of mathematical relations. Before using classical tools for fault detection, the first problem to solve is: what sensors and mathematical relations should be selected for the design of a detection test such as a state observer or a parity space based detection algorithms. This paper presents a ...

An artificial intelligence system that processes geo-thematic data would profit from a (semi-)formal or controlled natural language interface that incorporates concepts for nearness. Though there already exists logical-engineering approaches giving sufficient conditions for nearness relations, we show within a logical analysis that these suffer from some deficiencies. Non-engineering approaches...

An approach is described for the generation of certain mathematical objects (like sets, correspondences, mappings) in terms of relations using relation-algebraic descriptions of higher-order objects. From non-constructive characterizations executable relational speciications are obtained. We also show how to develop more eecient algorithms from the frequently ineecient speciications within the ...

In this paper we develop a formalization of semantic relations that facilitates efficient implementations of relations in lexical databases or knowledge representation systems using bases. The formalization of relations is based on a modeling of hierarchical relations in Formal Concept Analysis. Further, relations are analysed according to Relational Concept Analysis which allows a representati...

By-Domotor, Zoltan Probabilistic Relational Structures and Their Applications Stanford Univ., Calif. Inst. for Mathematical Studies in Social Science. Pub Date May 69 Note-171p; Technical Report Nc, 144 Psychology Series EDRS Price MF -10.75 HC-$8.65 Descriptors-Logic, *Mathematical Applications, *Mathematical Concepts, *Mathematics, *Probabihty, *Probability Theory The principal objects of the...

Systems are the most complicated entities and phenomena in abstract, physical, information, and social worlds across all science and engineering disciplines. System algebra is an abstract mathematical structure for the formal treatment of abstract and general systems as well as their algebraic relations, operations, and associative rules for composing and manipulating complex systems. This arti...

These are the notes for two lectures delivered at the Les Houches summer school Mathematical Statistical Mechanics, held in July 2005. I review some basic notions on sparse graph error correcting codes with emphasis on ‘modern’ aspects, such as, iterative belief propagation decoding. Relations with statistical mechanics, inference and random combinatorial optimization are stressed, as well as s...