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A polynomial translation of logic programs with nested expressions into disjunctive logic programs
(2002)
A common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular operator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then prove that it can be captured by an extension of Equilibrium Logic with this second negation. We study some properties of this variant and compare to the already known combination of Equilibrium Logic with Nelson's strong negation.
Proglacial environments are ideal for studying the development of soils through the changes of rocks exposed by glacier retreat to weathering and microbial processes. Carbon (C) and nitrogen (N) contents as well as soil pH and soil elemental compositions are thought to be dominant factors structuring the bacterial, archaeal and fungal communities in the early stages of soil ecosystem formation. However, the functional linkages between C and N contents, soil composition and microbial community structures remain poorly understood. Here, we describe a multivariate analysis of geochemical properties and associated microbial community structures between a moraine and a glaciofluvial outwash in the proglacial area of a High Arctic glacier (Longyearbreen, Svalbard). Our results reveal distinct differences in developmental stages and heterogeneity between the moraine and the glaciofluvial outwash. We observed significant relationships between C and N contents, delta C-13(org) and delta N-15 isotopic ratios, weathering and microbial abundance and community structures. We suggest that the observed differences in microbial and geochemical parameters between the moraine and the glaciofluvial outwash are primarily a result of geomorphological variations of the proglacial terrain.
In this work we tackle the problem of checking strong equivalence of logic programs that may contain local auxiliary atoms, to be removed from their stable models and to be forbidden in any external context. We call this property projective strong equivalence (PSE). It has been recently proved that not any logic program containing auxiliary atoms can be reformulated, under PSE, as another logic program or formula without them – this is known as strongly persistent forgetting. In this paper, we introduce a conservative extension of Equilibrium Logic and its monotonic basis, the logic of Here-and-There, in which we deal with a new connective ‘|’ we call fork. We provide a semantic characterisation of PSE for forks and use it to show that, in this extension, it is always possible to forget auxiliary atoms under strong persistence. We further define when the obtained fork is representable as a regular formula.