We introduce a method to estimate parameters and states from a differential equation model while enforcing interpretability constraints such as monotone or non-negative states. We motivate the methodology using a real data chemical engineering example and show that a variety of restrictive constraints from earlier analyses do not address the problem of interpretability. Our proposed method esti...

In this paper we give a characterization of all the interpretations of the varieties of bounded distributive lattices, De Morgan algebras and Lukasiewicz algebras of order m in the variety of Lukasiewicz algebras of order n. In the case of distributive lattices we give a structure theorem that is generalized to De Morgan algebras and to Lukasiewicz algebras of order m. In the last two cases we ...

The present paper studies the general implications of the principle of compo-sitionality for the organization of grammar. It will be argued that Janssen's (1986) requirement that syntax and semantics be similar algebras is too strong, and that the more liberal requirement that syntax be interpretable into semantics leads to a formalization that can be motivated and applied more easily, while it...

Many studies on modeling of fuzzy inference systems have been made. The issue of these studies is to construct automatically fuzzy inference systems with interpretability and accuracy from learning data based on metaheuristic methods. Since accuracy and interpretability are contradicting issues, there are some disadvantages for self-tuning method by metaheuristic methods. Obvious drawbacks of t...

A number of visual quality measures have been introduced in visual analytics literature in order to automatically select the best views of high dimensional data from a large number of candidate data projections. These methods generally concentrate on the interpretability of the visualization and pay little attention to the interpretability of the projection axes. In this paper, we argue that in...

Many studies on modeling of fuzzy inference systems have been made. The issue of these studies is to construct automatically fuzzy systems with interpretability and accuracy from learning data based on meta-heuristic methods. Since accuracy and interpretability are contradicting issues, there are some disadvantages for self-tuning method. Obvious drawbacks of the method are lack of interpretabi...

Edward Nelson published in 1986 a book defending an extreme formalist view of mathematics according to which there is an impassable barrier in the totality of exponentiation. On the positive side, Nelson embarks on a program of investigating how much mathematics can be interpreted in Raphael Robinson’s theory of arithmetic Q. In the shadow of this program, some very nice logical investigations ...