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This paper provides a fully word-based, abstractive analysis of predictability in Latin verb paradigms. After reviewing previous traditional and theoretically grounded accounts of Latin verb inflection, a procedure is outlined where the uncertainty in guessing the content of paradigm cells given knowledge of one or more inflected wordforms is measured by means of the information-theoretic notions of unary and n-ary implicative entropy, respectively, in a quantitative approach that uses the type frequency of alternation patterns between wordforms as an estimate of their probability of application. Entropy computations are performed by using the Qumin toolkit on data taken from the inflected lexicon LatInfLexi. Unary entropy values are used to draw a mapping of the verbal paradigm in zones of full interpredictability, composed of cells that can be inferred from one another with no uncertainty. N-ary entropy values are used to extract categorical and near principal part sets, that allow to fill the rest of the paradigm with little or no uncertainty. Lastly, the issue of the impact of information on the derivational relatedness of lexemes on uncertainty in inflectional predictions is tackled, showing that adding a classification of verbs in derivational families allows for a relevant reduction of entropy, not only for derived verbs, but also for simple ones. [ABSTRACT FROM AUTHOR]

This article deals with verbal inflection based on concepts introduced in the word-based morphological model; in particular, the Word and Paradigm model. We propose a methodology for the analysis of verbal inflection of Spanish. For this, we take only the first conjugation of Spanish. The analysis here is based on determining the main parts that allow prediction of verbal paradigms of first conjugation. We show that from a few main parts it is possible to obtain the complete paradigm of a verbal form. We also discuss the phenomena of competition between schemas where there is a change of accent ("hablemos" and "háblemos" case) as well as the diphthongizations /o/ → /ue/ and /e/ → /ie/. This phenomenon responds to the modification of the principal part. Finally, the advantages that the word-based model presents in the inflection analysis are shown. [ABSTRACT FROM AUTHOR]

We study the principal parts bundles $\mathcal {P}^{k}\mathcal {O}_{\mathbb {P}^{n}}(d)$ as homogeneous bundles and we describe their associated quiver representations. With this technique we show that if n≥2 and 0≤ d< k then there exists an invariant decomposition $\mathcal {P}^{k}\mathcal {O}_{\mathbb {P}^{n}}(d)=Q_{k,d}\oplus(S^{d}V\otimes \mathcal {O}_{\mathbb {P}^{n}})$ with Q a stable homogeneous vector bundle. The decomposition properties of such bundles were previously known only for n=1 or k≤ d or d<0. Moreover we show that the Taylor truncation maps $H^{0}\mathcal {P}^{k}\mathcal {O}_{\mathbb {P}^{n}}(d)\to H^{0}\mathcal {P}^{h}\mathcal {O}_{\mathbb {P}^{n}}(d)$, defined for any h≤ k and any d, have maximal rank. [ABSTRACT FROM AUTHOR]

Like the numbers in a sudoku puzzle, a lexeme’s principal parts provide enough information–but only enough–to deduce all of the remaining forms in its paradigm. Because principal parts are a distillation of the implicative relations that exist among the members of a lexeme’s paradigm, they afford an important (but heretofore neglected) basis for typological classification. We recognize three logically distinct sorts of principal-part systems that might be postulated for a given language: static, adaptive, and dynamic. Focussing for present purposes on dynamic systems, we propose five crosscutting criteria for the typological classification of principal-part systems. These criteria relate to (i) how many principal parts are needed to determine a lexeme’s paradigm; (ii) whether distinct lexemes possess parallel sets of principal parts; (iii) how many principal parts are needed to determine a given word in a lexeme’s paradigm; (iv) what sort of morphological relation exists between a principal part and the forms that it is used to deduce; and (v) whether lexemes’ nonprincipal parts are inferred from their principal parts in the same way from one inflection class to another. Drawing on these criteria, we propose a novel classification of a range of typologically diverse languages. [ABSTRACT FROM AUTHOR]

We construct a substitute for principal parts for systems of algebras with a natural local presentation by free modules. The main application of the theory is to families of locally complete intersection curves. In that case we obtain the sheaves of Esteves. The advantage of the greater generality is that it makes the theory much more transparent. It also makes it possible to avoid many technical di3culties. [ABSTRACT FROM AUTHOR]