Rational descriptive classification of duricrusts

The term duricrust appears to be extending itself to include calcareous, gypseous, and saline crusts, in addition to crusts composed dominantly of silica and/or of sesquioxides of iron and aluminium, with or without significant contents of dioxides of manganese or titanium. This latter group can be distinguished as duricrusts proper. Its nomenclature is highly confused, and its classification, in writings in the English language, defective. The relevant problems can be resolved, at least in considerable part, by the introduction, adaptation, and extension of modern terms current in tropical pedology, to give a descriptive classification free of genetic implications. When content of SiO₂, Al₂O₃, and Fe₂O₃ is used as a primary basis for the classification of duricrusts proper, plots on a ternary diagram justify the recognition of seven named types in the fersiallitic range

A new problem of descriptive power

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The descriptive complexity approach to LOGCFL

Building upon the known generalized-quantifier-based first-order characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory relating monoidal quantifiers to NC1 and its subclasses. In the absence of the BIT predicate, we resolve the main issues: we show in particular that no single outermost unary groupoidal quantifier with FO can capture all the context-free languages, and we obtain the surprising result that a variant of Greibach's ``hardest context-free language'' is LOGCFL-complete under quantifier-free BIT-free projections. We then prove that FO with unary groupoidal quantifiers is strictly more expressive with the BIT predicate than without. Considering a particular groupoidal quantifier, we prove that first-order logic with majority of pairs is strictly more expressive than first-order with majority of individuals. As a technical tool of independent interest, we define the notion of an aperiodic nondeterministic finite automaton and prove that FO translations are precisely the mappings computed by single-valued aperiodic nondeterministic finite transducers.Comment: 10 pages, 1 figur

The Descriptive Challenges of Fiber Art

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