Ordinary logical implication is not enough for answering queries in a logic database, since especially negative information is only implicitly represented in the database state. Many database completions have been proposed to remedy this problem, but a clear understanding of their properties and differences is still needed. In this paper, a general framework is proposed for studying database co...

In this paper we initiate a systematic study of the abstract commensurators of profinite groups. The abstract commensurator of a profinite group G is a group Comm(G) which depends only on the commensurability class of G. We study various properties of Comm(G); in particular, we find two natural ways to turn it into a topological group. We also use Comm(G) to study topological groups which conta...

Unitary symmetric completions of complex symmetric matrices are obtained via Autonne decomposition. The problem arises from atomic physics. Of independent interest unitary skew symmetric completions of skew symmetric matrices are also obtained by Hua decomposition.

This paper gives a further development of p-regular completion theory, including a study ofp-regular Reed completions, the role of diagonal axioms, and the relationship between p-regular and p-topological completions.

For a modal algebra (B, f), there are two natural ways to extend f to an operation on the MacNeille completion of B. The resulting structures are called the lower and upper MacNeille completions of (B, f). In this paper we consider lower and upper MacNeille completions for various varieties of modal algebras. In particular, we characterize the varieties of closure algebras and diagonalizable al...

There is a strong tendency to complete a partly occluded shape. Two types of pattern completion, global and local, are frequently reported. By means of the primed-matching paradigm, it has previously been shown that global completions are prevalent for stimuli in which regularity is abundantly present. In our study the primed-matching paradigm is applied to such stimuli in order to find out whe...

we analyze some properties of the distribution $q_{g,k}$ of the first component in a $k$-tuple chosen uniformly‎ ‎in the set of all the $k$-tuples generating a finite group $g$ (the limiting distribution of the product replacement algorithm)‎. ‎in particular‎, ‎we concentrate our attention on‎ ‎the study of the variation distance $beta_k(g)$ between $q_{g,k}$ and the uniform distribution‎. ‎we ...