Parametric Constructive Kripke-Semantics for Standard Multi-Agent Belief and Knowledge (Knowledge As Unbiased Belief)

We propose parametric constructive Kripke-semantics for multi-agent KD45-belief and S5-knowledge in terms of elementary set-theoretic constructions of two basic functional building blocks, namely bias (or viewpoint) and visibility, functioning also as the parameters of the doxastic and epistemic accessibility relation. The doxastic accessibility relates two possible worlds whenever the application of the composition of bias with visibility to the first world is equal to the application of visibility to the second world. The epistemic accessibility is the transitive closure of the union of our doxastic accessibility and its converse. Therefrom, accessibility relations for common and distributed belief and knowledge can be constructed in a standard way. As a result, we obtain a general definition of knowledge in terms of belief that enables us to view S5-knowledge as accurate (unbiased and thus true) KD45-belief, negation-complete belief and knowledge as exact KD45-belief and S5-knowledge, respectively, and perfect S5-knowledge as precise (exact and accurate) KD45-belief, and all this generically for arbitrary functions of bias and visibility. Our results can be seen as a semantic complement to previous foundational results by Halpern et al. about the (un)definability and (non-)reducibility of knowledge in terms of and to belief, respectively

A Teacher of Great Strengths

The research on formal languages and their algebraic relationships were among the topics that brought visibility to Romania in the field of computer science in the 1970’s. Alexandru Ioan Cuza University of Iași was known by its researchers and teachers in these topics

Antenas nano-estructuradas: de su construcción como fractales

Investigación TecnológicaEste trabajo describe los conceptos básicos de antenas, y la construcción de antenas nano estructuradas, específicamente con geometrías fractales.PregradoIngeniero Electrónic

An Efficient Itemset Representation for Mining Frequent Patterns in Transactional Databases

In this paper we propose very efficient itemset representation for frequent itemset mining from transactional databases. The combinatorial number system is used to uniquely represent frequent k-itemset with just one integer value, for any k ≥ 2. Experiments show that memory requirements can be reduced up to 300 %, especially for very low minimal support thresholds. Further, we exploit combinatorial number schema for representing candidate itemsets during iterative join-based approach. The novel algorithm maintains one-dimensional array rank, starting from k = 2nd iteration. At the index r of the array, the proposed algorithm stores unique integer representation of the r-th candidate in lexicographic order. The rank array provides joining of two candidate k-itemsets to be O(1) instead of O(k) operation. Additionally, the rank array provides faster determination which candidates are contained in the given transaction during the support count and test phase. Finally, we believe that itemset ranking by combinatorial number system can be effectively integrated into pattern-growth algorithms, that are state-of-the-art in frequent itemset mining, and additionally improve their performances

On Partition Metric Space, Index Function, and Data Compression

We discuss a metric structure on the set of partitions of a finite set induced by the Gini index and two applications of this metric: the identification of determining sets for index functions using techniques that originate in machine learning, and a data compression algorithm

A New Rymon Tree Based Procedure for Mining Statistically Significant Frequent Itemsets

In this paper we suggest a new method for frequent itemsets mining, which is more efficient than well known Apriori algorithm. The method is based on special structure called Rymon tree. For its implementation, we suggest modified sort-merge-join algorithm. Finally, we explain how support measure, which is used in Apriori algorithm, gives statistically significant frequent itemsets