(1) For every relational structure L and for all elements x, y of Lop holds x ≤ y iff xx ≥xy. (2) Let L be a relational structure, x be an element of L, and y be an element of Lop. Then (i) x ≤xy iff x` ≥ y, and (ii) x ≥xy iff x` ≤ y. (3) For every relational structure L holds L is empty iff Lop is empty. (4) For every relational structure L holds L is reflexive iff Lop is reflexive. (5) For ev...

Relational learners need to be able to handle the information contained in a set of related tuples. Most current relational learners are biased either towards the use of aggregate functions that summarize that set, or towards checking the existence of specific kinds of elements in that set. Learning patterns that contain a combination of both is a challenging task. In this paper we introduce a ...

Conventional operators for data retrieval are either based on exact matching or on total order relationship among elements. Neither of them is appropriate to manage complex data, such as multimedia data, time series and genetic sequences. In fact, the most meaningful way to compare complex data is by similarity. However, the Relational Algebra, employed in the Relational Database Management Sys...

This study investigated the nature of internal representations constructed from learning concrete or generic instantiations of an abstract concept. Undergraduate students learned instantiations of a mathematical group that were generic, communicated concreteness relevant to the concept, or communicated concreteness irrelevant to the concept. Students who learned relevantly concrete instantiatio...

Sequential behavior and sequence learning is essential to intelligence. Often the elements of sequences exhibit an internal structure that can elegantly be represented using relational atoms. Applying traditional sequential learning techniques to such relational sequences requires either to ignore the internal structure or to put up with a combinatorial explosion in the model complexity. This c...

We describe a coherent view of learning and reasoning with relational representations in the context of natural language processing. In particular, we discuss the Neuroidal Architecture, Inductive Logic Programming and the SNoW system explaining the relationships among these, and thereby offer an explanation of the theoretical basis for the SNoW system. We suggest that extensions of this system...

The concept of grouping in relational algebra is well-known from its connection to aggregation. In this paper we generalize the grouping notion by defining a simultaneous grouping of more than one relation, and we discuss the application of operations on grouping elements other than just arithmetic aggregation. Finally we show that this grouping mechanism can be added to relational algebra with...

We present a general method, based on the usage of typical DBMS primitives, for maintaining authenticated relational tables. The authentication process is managed by an application external to the DBMS, that stores just one hash information of the authentication structure. The method exploits techniques to represent hierarchical data structures into relational tables and queries that allow an e...