In this paper, a new invariant called {it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {it conditional logical entropy} is defined and then some of its properties are studied.  The invariance of the {it logic entropy} of a system  under isomorphism is proved. At the end,  the notion of an $ m $-generator of a dynamical system is introduced and a version of the Kolm...

In this paper, we focus on the combination of probabilistic logic programming with the principle of maximum entropy. We start by deening probabilistic queries to probabilistic logic programs and their answer substitutions under maximum entropy. We then present an ef-cient linear programming characterization for the problem of deciding whether a probabilistic logic program is satissable. Finally...

In this paper, we focus on the combination of probabilistic logic programming with the principle of maximum entropy. We start by deening probabilistic queries to probabilistic logic programs and their answer substitutions under maximum entropy. We then present an eecient linear programming characterization for the problem of deciding whether a probabilistic logic program is satissable. Finally,...

Explainable artificial intelligence has rapidly emerged since lawmakers have started requiring interpretable models for safety-critical domains. Concept-based neural networks arisen as explainable-by-design methods they leverage human-understandable symbols (i.e. concepts) to predict class memberships. However, most of these approaches focus on the identification relevant concepts but do not pr...

Recent research has shown there are two types of uncertainty that can be expressed in first-order logic— propositional and statistical uncertainty—and that both types can be represented in terms of probability spaces. However, these efforts have fallen short of providing a general account of how to design probability measures for these spaces; as a result, we lack a crucial component of any sys...

The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite ...

The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite ...