Karl Erich Wolff

Conceptual Structures at Work

In Peirce’s account of the normative sciences, logical validity and truth ultimately rely upon – though they are not reduced to – ethical and esthetic insight. An examination of the relations among critical esthetics, ethics and logic in Peirce’s system suggests a possible account of the logic of creative discovery, which Peirce identified as abductive inference.

States, transitions, and life tracks in temporal concept analysis

Based on Formal Concept Analysis, we introduce Temporal Concept Analysis as a temporal conceptual granularity theory for movements of general objects in abstract or “real” space and time such that the notions of states, situations, transitions and life tracks of objects in conceptual time systems are defined mathematically. The life track lemma is a first approach to granularity reasoning. Applications of Temporal Concept Analysis in medicine and in chemical industry are demonstrated as well as recent developments of computer programs for graphical representations of temporal systems. Basic relations between Temporal Concept Analysis and other temporal theories, namely theoretical physics, mathematical system theory, automata theory, and temporal logic are discussed.

Interpretation of Automata in Temporal Concept Analysis

The purpose of this paper is to relate the notions of states and transitions in Automata Theory to the conceptual descriptions of states, situations, and transitions in Temporal Concept Analysis. The first key for that relation is that states and situations can be described as formal concepts of formal contexts whose objects are points of time. The second key is the introduction of certain subsystems (interpreted as persons or agents). We prove that labeled transition systems with attributes (a recently introduced generalization of automata) can be represented as state-transition-systems of conceptual time systems.

Concepts, states, and systems

Mathematical System Theory is extended to Conceptual System Theory using Formal Concept Analysis (Wille 1982). States are defined as formal concepts and ‘points of time’ are generalized to ‘time granules,’ interpreted as ‘pieces’ of time needed for the realization of measurements. As a generalization of classical time systems we define conceptual time systems, their state spaces and phase spaces. Time dependent relations among the parts of a conceptual time system are introduced in ‘relational conceptual time systems.’ Applications in psychology and industry, including ‘conceptual films’ are mentioned.

Time Dimension, Objects, and Life Tracks. A Conceptual Analysis

The purpose of this paper is to clarify in the framework of Temporal Concept Analysis the distinction between the notion of the dimension of time and the one-dimensionality of life tracks of simple objects. The reader is led to the central problems by many examples.

‘Particles’ and ‘Waves’ as Understood by Temporal Concept Analysis

A qualitative mathematical framework for a granular representation of relational information about general objects, as for examples particles, waves, persons, families, institutions or other systems in discrete or continuous “space-time” is introduced. That leads to a common description of particles and waves in physics, such that the intuitive physical notion of “wave packet” can be captured by the mathematical notion of a general object or a packet in a spatio-temporal Conceptual Semantic System. In these systems particles and waves are defined as special packets. It is proved, that “classical objects” and “classical waves” can be represented as, respectively, particles and waves in spatio-temporal Conceptual Semantic Systems.

States of distributed objects in conceptual semantic systems

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

Temporal relational semantic systems

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Relational Scaling in Relational Semantic Systems

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Turing machine representation in temporal concept analysis

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