A probability distribution can be given to the set of isomorphism classes of models with universe {1, . . . , n} of a sentence in rst-order logic. We study the entropy of this distribution and derive a result from the 0-1 law for rst-order sentences.

True random number generators (TRNGs) are important as a basis for computer security. Though there are some TRNGs composed of analog circuit, the use of digital circuits is desired for the application of TRNGs to logic LSIs. Some of the digital TRNGs utilize jitter in freerunning ring oscillators as a source of entropy, which consume large power. Another type of TRNG exploits the metastability ...

A new family of implication operators, called probabilistic implications, is introduced. The suggested implications are based on conditional copulas and make a bridge between probability theory and fuzzy logic. It is shown that some well-known fuzzy implications appear as a particular probabilistic implications. Therefore, it seems that this new family of implication operators might be a useful...

A logic is defined that allows to express in­ formation about statistical probabilities and about degrees of belief in specific proposi­ tions. By interpreting the two types of proba­ bilities in one common probability space, the semantics given are well suited to model the influence of statistical information on the for­ mation of subjective beliefs. Cross entropy minimization is a key element...

Employing maximum entropy methods on probabilistic conditional logic has proven to be a useful approach for commonsense reasoning. Yet, the expressive power of this logic and similar formalisms is limited due to their foundations on propositional logic and in the past few years a lot of proposals have been made for probabilistic reasoning in relational settings. Most of these proposals rely on ...

In three case studies on notions of fuzzy logic and fuzzy set theory (Dubois–Prade’s gradual elements, the entropy of a fuzzy set, and aggregation operators), the paper exemplifies methodological differences between traditional and deductive fuzzy logic. While traditional fuzzy logic admits various interpretations of membership degrees, deductive fuzzy logic always interprets them as degrees of...

In this paper, we present a study on the relationship between entropy and the average power consumption of circuits generated from Boolean functions. Based on a general-delay model, an entropy-based formulation for power estimation is derived from a large set of experimental data. The study shows that the entropy measure provides an e ective power estimate for single-output and fully-correlated...

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others ar...

This paper answers a question posed by Nils Nilsson in his paper [9] on Probabilistic Logic: When is the maximum entropy solution to the entailment problem equal to the solution obtained by the projection method? Conditions are given for the relevant matrices and vectors which can be tested without actually computing the two solutions and comparing them. Examples are discussed and some comments...

Reversible computing has been studied since Rolf Landauer advanced the argument that has come to be known as Landauer's principle. This principle states that there is no minimum energy dissipation for logic operations in reversible computing, because it is not accompanied by reductions in information entropy. However, until now, no practical reversible logic gates have been demonstrated. One of...