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1

Continuous-Logical Methods in Mathematical Economics

100%
Levin V. I.
Studia Humana
|
2016
|
vol. 5
|
issue 1
31-39
EN
An application of continuous logic for the mathematical description of economical systems is given. Parallel, sequential, parallel-sequential and sequentialparallel systems are calculated using continuous logic (CL) methods.
2

Continuous Logic and Scheduling in Systems with Indeterminate Processing Times

100%
Levin V. I.
Studia Humana
|
2014
|
vol. 3
|
issue 1
38-47
EN
A general approach to the synthesis of an optimal order of executing jobs in engineering systems with indeterminate (interval) times of job processing is presented. As a mathematical model of the system, a two-stage pipeline is taken whose first and second stages are, respectively, the input of data and its processing, and the corresponding mathematical apparatus is continuous logic and logic determinants.
3

Mereological foundations of point-free geometry via multi-valued logic

75%
Coppola C., Gerla G.
Logic and Logical Philosophy
|
2015
|
vol. 24
|
issue 4 Mereology and Beyond
535-553
EN
We suggest possible approaches to point-free geometry based on multi-valued logic. The idea is to assume as primitives the notion of a region together with suitable vague predicates whose meaning is geometrical in nature, e.g. ‘close’, ‘small’, ‘contained’. Accordingly, some first-order multi-valued theories are proposed. We show that, given a multi-valued model of one of these theories, by a suitable definition of point and distance we can construct a metrical space in a natural way. Taking into account that interesting metrical approaches to geometry exist, this looks to be promising for a point-free foundation of the notion of space. We hope also that this way to face point-free geometry provides a tool to illustrate the passage from a naïve and ‘qualitative’ approach to geometry to the ‘quantitative’ approach of advanced science.
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