This paper reconsiders Bernardo’s T-lumpability on continuous-time Markov chains (CTMCs). This notion allows for a more aggressive state-level aggregation than ordinary lumpability. We provide a novel structural definition of (what we refer to as) weighted lumpability, prove some elementary properties, and investigate its compatibility with linear real-time objectives. The main result is that t...

A weighted Hamming metric is introduced in [4] and it showed that the binary generalized Goppa code is a perfect code in some weighted Hamming metric. In this paper, we study the weight structures which admit the binary Hamming code and the extended binary Hamming code to be perfect codes in the weighted Hamming metric. And, we also give some structures of a 2-perfect code and how to construct ...

Weighted metric scaling (Cuadras and Fortiana 1995b) is a natural extension of classic metric scaling which encompasses several well-known techniques of Euclidean representation of data, including correspondence analysis of bivariate contingency tables. A continuous version of this technique, following the trend initiated in (Cuadras and For-tiana 1993, 1995a) is applied to the study of several...

While logic provides an appealing formalism for knowledge representation and reasoning, it is not without drawbacks. There are many aspects of human reasoning that are not adequately handled by pure logic. (Of course there are also many aspects that we would rather avoid capturing.) For example, suppose a human is told that “all aliens are blue”. Later, however, the human also learns the fact t...