There is a growing need for abstractions in logic specification languages such as FO(·) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always described through a syntactical rewriting scheme, we present an alternative view on templates as second order definitions. To extend the existing definition cons...

We construct a minimal rK-degree, continuum many, in fact. We also show that every minimal sequence, that is, a sequence with minimal rK-degree, must have very low descriptional complexity, that every minimal sequence is rK-reducible to a random sequence, and that there is a random sequence with no minimal sequence rK-reducible to it.

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In this paper we develop a computational framework for the measurement of different factors or abilities which are usually found in intelligent behaviours. For this, we first develop a scale for measuring the complexity of an instance of a problem, depending on the descriptional complexity (Levin LT variant) of the ‘explanation’ of the answer to the problem. We centre on the establishment of ei...