This paper attempts to serve as an introduction to abstract model theory. We introduce the notion of abstract logics, explore first-order logic as an instance of and as the basis for abstract logics, and end by proving Lindström’s theorem.

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We can learn a lot about what features are important for retrieval by comparing similar cases in a case-base. We can determine which features are important in predicting outcomes and we can assign weights to features accordingly. In the same manner we can discover which features are important in specific contexts and determine localised feature weights that are specific to individual cases. In ...

Axiomatizations of the General Theory of Relativity.have occasionally been conducted to achieve precision and clarification of underlying concepts. Rigorous and inspiring work towards that aim based on first-order logic has been performed by Professor Németi and his working group (see references below). A complementary approach (Benda 2008) constructs the relativistic spacetime manifold ab init...

We consider fragments of first-order logic over finite words. In particular, we deal with first-order logic with a restricted number of variables and with the lower levels of the alternation hierarchy. We use the algebraic approach to show decidability of expressibility within these fragments. As a byproduct, we survey several characterizations of the respective fragments. We give complete proo...

Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially generalize known interpolation results; all the others are new. We also discuss some applications of our results to the theory of institutio...

The CMBR spectral-spatial fluctuations (SSF) formed in early Universe during the Dark Ages are considered. Main attention is focused on the narrow-band spectral properties of the SSF. Based on these properties we propose to use a differential method in order to search for these fluctuations. Description of the method is given.

Misconceptions about the nature of the computing disciplines pose a serious problem to university faculties that offer computing degrees, as students enrolling on their programmes may come to realise that their expectations are not met by reality. This frequently results in the students’ early disengagement from the subject of their degrees which in turn can lead to excessive ‘wastage’, i.e. re...