Let T be an arithmetical theory. We introduce a unary modal operator T to be interpreted arithmetically as the unary interpretability predicate over T. We present complete axiomatizations of the (unary) interpretability principles underlying two important classes of theories. We also prove some basic modal results about these new axiomatizations.

Œe ability to interpret machine learning models has become increasingly important now that machine learning is used to inform consequential decisions. We propose an approach called model extraction for interpreting complex, blackbox models. Our approach approximates the complex model using a much more interpretable model; as long as the approximation quality is good, then statistical properties...

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...