# Fuzzy logic of Aristotelian forms

## Abstract

Model-based approaches to pattern recognition and machine vision have been proposed to overcome the exorbitant training requirements of earlier computational paradigms. However, uncertainties in data were found to lead to a combinatorial explosion of the computational complexity. This issue is related here to the roles of a priori knowledge vs. adaptive learning. What is the a-priori knowledge representation that supports learning? I introduce Modeling Field Theory (MFT), a model-based neural network whose adaptive learning is based on a priori models. These models combine deterministic, fuzzy, and statistical aspects to account for a priori knowledge, its fuzzy nature, and data uncertainties. In the process of learning, a priori fuzzy concepts converge to crisp or probabilistic concepts. The MFT is a convergent dynamical system of only linear computational complexity. Fuzzy logic turns out to be essential for reducing the combinatorial complexity to linear one. I will discuss the relationship of the new computational paradigm to two theories due to Aristotle: theory of Forms and logic. While theory of Forms argued that the mind cannot be based on ready-made a priori concepts, Aristotelian logic operated with just such concepts. I discuss an interpretation of MFT suggesting that its fuzzy logic, combining a-priority andmore »

- Authors:

- Nichols Research Corp., Lexington, MA (United States)

- Publication Date:

- OSTI Identifier:
- 466430

- Report Number(s):
- CONF-9610138-

TRN: 97:001309-0009

- Resource Type:
- Conference

- Resource Relation:
- Conference: International multi-disciplinary conference on intelligent systems: a semiotic perspective, Gaithersburg, MD (United States), 21-23 Oct 1996; Other Information: PBD: 1996; Related Information: Is Part Of Intelligent systems: A semiotic perspective. Volume I: Theoretical semiotics; Albus, J.; Meystel, A.; Quintero, R.; PB: 303 p.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; FUZZY LOGIC; ARTIFICIAL INTELLIGENCE; MATHEMATICAL LOGIC; LEARNING; NEURAL NETWORKS; PATTERN RECOGNITION

### Citation Formats

```
Perlovsky, L.I..
```*Fuzzy logic of Aristotelian forms*. United States: N. p., 1996.
Web.

```
Perlovsky, L.I..
```*Fuzzy logic of Aristotelian forms*. United States.

```
Perlovsky, L.I.. Tue .
"Fuzzy logic of Aristotelian forms". United States.
```

```
@article{osti_466430,
```

title = {Fuzzy logic of Aristotelian forms},

author = {Perlovsky, L.I.},

abstractNote = {Model-based approaches to pattern recognition and machine vision have been proposed to overcome the exorbitant training requirements of earlier computational paradigms. However, uncertainties in data were found to lead to a combinatorial explosion of the computational complexity. This issue is related here to the roles of a priori knowledge vs. adaptive learning. What is the a-priori knowledge representation that supports learning? I introduce Modeling Field Theory (MFT), a model-based neural network whose adaptive learning is based on a priori models. These models combine deterministic, fuzzy, and statistical aspects to account for a priori knowledge, its fuzzy nature, and data uncertainties. In the process of learning, a priori fuzzy concepts converge to crisp or probabilistic concepts. The MFT is a convergent dynamical system of only linear computational complexity. Fuzzy logic turns out to be essential for reducing the combinatorial complexity to linear one. I will discuss the relationship of the new computational paradigm to two theories due to Aristotle: theory of Forms and logic. While theory of Forms argued that the mind cannot be based on ready-made a priori concepts, Aristotelian logic operated with just such concepts. I discuss an interpretation of MFT suggesting that its fuzzy logic, combining a-priority and adaptivity, implements Aristotelian theory of Forms (theory of mind). Thus, 2300 years after Aristotle, a logic is developed suitable for his theory of mind.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Dec 31 00:00:00 EST 1996},

month = {Tue Dec 31 00:00:00 EST 1996}

}