Abstract Eroders are monotonic cellular automata with a linearly ordered state set that eventually wipe out any finite island of nonzero states. One-dimensional eroders were studied by Gal’perin in the 1970s, who presented simple combinatorial characterization class. The multi-dimensional case has been Toom and others, but no such found. We prove similar for those one-dimensional even presence ...

In this paper, some logarithmically completely monotonic, strongly completely monotonic and completely monotonic functions related to the gamma, digamma and polygamma functions are established. Several inequalities, whose bounds are best possible, are obtained.

Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we show that we can also integrate the two formalisms by studying belief change within a (preferential) non-monotonic framework. This integration relies heavily on the identification of the monotonic core of a non-...

Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. The non-monotonicity here refers to the fact that, while in usual (monotonic) reasoning adding more axioms leads to potentially more possible conclusions, in non-monotonic reasoning adding new facts to a knowledge base may prevent previously...