Conceptual structures: information processing in mind and machine
Conceptual structures: information processing in mind and machine
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
ICCS '02 Proceedings of the 10th International Conference on Conceptual Structures: Integration and Interfaces
Conceptual Graphs and Formal Concept Analysis
ICCS '97 Proceedings of the Fifth International Conference on Conceptual Structures: Fulfilling Peirce's Dream
The Lattice of Concept Graphs of a Relationally Scaled Context
ICCS '99 Proceedings of the 7th International Conference on Conceptual Structures: Standards and Practices
Existential Concept Graphs of Power Context Families
ICCS '02 Proceedings of the 10th International Conference on Conceptual Structures: Integration and Interfaces
Interpretation of Automata in Temporal Concept Analysis
ICCS '02 Proceedings of the 10th International Conference on Conceptual Structures: Integration and Interfaces
Turing machine representation in temporal concept analysis
ICFCA'05 Proceedings of the Third international conference on Formal Concept Analysis
Relational Scaling in Relational Semantic Systems
ICCS '09 Proceedings of the 17th International Conference on Conceptual Structures: Conceptual Structures: Leveraging Semantic Technologies
Temporal relational semantic systems
ICCS'10 Proceedings of the 18th international conference on Conceptual structures: from information to intelligence
Applications of temporal conceptual semantic systems
KONT'07/KPP'07 Proceedings of the First international conference on Knowledge processing and data analysis
Conceptual representation of gene expression processes
KONT'07/KPP'07 Proceedings of the First international conference on Knowledge processing and data analysis
Position paper: pragmatics in fuzzy theory
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Review: Formal Concept Analysis in knowledge processing: A survey on models and techniques
Expert Systems with Applications: An International Journal
Hi-index | 0.00 |
Our classical understanding of objects in spatiotemporal systems is based on the idea that such an object is at each moment at exactly one place. As long as the notions of “moment” and “place” are not made explicit in their granularity the meaning of that idea is not clear. It became clear by the introduction of Conceptual Time Systems with Actual Objects and a Time Relation (CTSOT) using an explicit granularity description for space and time and an object representation such that each object is at each moment in exactly one state – where the states are formal concepts of the CTSOT. For the purpose of introducing also a granularity tool for the objects the author has defined Conceptual Semantic Systems where relational information is combined with the granularity tool of conceptual scales. That led to a mathematical definition of particles and waves such that the usual notions of particles and waves in physics are covered. Waves and wave packets are “distributed objects” in the sense that they may appear simultaneously at several places. Now the question arises how to introduce a mathematical notion for the “state of a distributed object”, as for example the state of an electron or the state of an institution, in the general framework of Conceptual Semantic Systems. That question is answered in this paper by the introduction of the notion of the “aspect of a concept $\textbf{c}$ with respect to some view Q”, in short “the Q-aspect of $\textbf{c}$” which is defined as a suitable set of formal concepts. For spatiotemporal Conceptual Semantic Systems the state of an object $\textbf{p}$ at a time granule $\textbf{t}$ is defined as the spatial aspect of the infimum of “realizations” of $\textbf{p}$ and $\textbf{t}$. The one-element states of “actual objects” in a CTSOT are special cases of these states which may have many elements. The information units (instances) of a Conceptual Semantic System connect the concepts of different semantical scales, for example scales for objects, space, and time. That allows for defining the information distribution of the Q-aspect of a distributed object $\textbf{c}$ which leads to a mathematical definition of the “BORN-frequency”; that is defined as a relative frequency of information units which can be understood as a very meaningful mathematical representation of the famous “probability distribution of a quantum mechanical system”.