612 research outputs found
Universals in ontological investigations
No full textUniversals appear to be as central in today's computational-based ontology as they were in medieval ontological investigations. As the author of a recent work on the history of universals (Pinzani, 2018), I was asked for a commentary on Augusto’s article “Bridging Mainstream and Formal Ontology” (Augusto, 2021), which aims at showing that medieval ontological investigations can be relevant for contemporary ontology engineering. In this commentary, I begin by saying something about my way of reading 12th-century logical literature and then offer some modest considerations on the general theme addressed in Augusto's article
Il De Generibus et Speciebus e la teoria della collectio
No full textThe De Generibus (attributed to Gauslenus ) can be divided into three
parts: the first is about the notion of whole, the second deals with
contemporary theories on universals, the third contains the presentation
of the collectio theory and the solution of the problem of universals. The
author considers universals like ‘humanity’ as collections composed of
single essences built from particular generic essences and particular
differential properties (rationality, mortality, being two-footed). One can
say that Gauslenus is a philosopher who does not believe in abstract and
universal entities, and imagines that these entities be multiplicities of
individual essences
Alberto non è diverso da Søren. Una teoria dell'identità parziale nel BN 17813
No full textIl manoscritto 17.813 della Biblioteca Nazionale di Parigi contiene alcuni trattati dell’inizio del XII
che presentano un certo interesse nella ricostruzione del dibattito sul problema degli universali. Il testo (ff. 16va-19ra) di cui ci occupiamo in questo lavoro, sviluppa una teoria piuttosto sofisticata dell’identità parziale in modo del tutto autonomo rispetto ai commenti boeziani. Il trattato viene attribuito dagli editori, pur con qualche incertezza, a Gualtiero di Mortagne
Prove e sillogismi topici in Boezio
No full textGli argomenti topici e quelli sillogistici si possano chiamare entrambi « sillogismi » in un qualche senso. Per stabilire come possiamo impiegare il termine « sillogismo » quello che cercherò di fare è da un lato confrontare la forma degli argomenti topici con quella dei sillogismi, da un altro cercare di ricostruire il contesto teorico delle rispettive teorie, topica e sillogistica, della prova
Polyominoes determined by permutations: enumeration via bijections
No full textA permutominide is a set of cells in the plane satisfying special connectivity constraints and uniquely defined by a pair of permutations. It naturally generalizes the concept of permutomino, recently investigated by several authors and from different points of view [1, 2, 4, 6, 7]. In this paper, using bijective methods, we determine the enumeration of various classes of convex permutominides, including, parallelogram, directed convex, convex, and row convex permutominides. As a corollary we have a bijective proof for the number of convex permutominoes, which was still an open problem
Generation and enumeration of some classes of interval orders
No full textIn this paper we consider the class of interval orders, recently considered by several authors from both an algebraic and an enumerative point of view. According to Fishburn's Theorem (Fishburn J Math Psychol 7:144-149, 1970), these objects can be characterized as posets avoiding the poset 2 + 2. We provide a recursive method for the unique generation of interval orders of size n + 1 from those of size n, extending the technique presented by El-Zahar (1989) and then re-obtain the enumeration of this class, as done in Bousquet-Melou et al. (2010). As a consequence we provide a method for the enumeration of several subclasses of interval orders, namely AV(2 + 2, N), AV(2 + 2, 3 + 1), AV(2 + 2, N, 3 + 1). In particular, we prove that the first two classes are enumerated by the sequence of Catalan numbers, and we establish a bijection between the two classes, based on the cardinalities of the principal ideals of the posets
Somes notes on the sources and content of De generibus
No full textIn the first part of De Generibus the focus is on the distinction between different ways of understanding essential and non-essential parts. The removal of non-essential parts does not involve the destruction of the whole. According to the author’s master, in order to determine whether a part is essential or not, one must see if its removal involves an alteration of the whole essence. In the treatise on universals, species and genera are considered collections of essences whose parts/ elements are not sensitive to accidental changes in their bearer. Both in the case of quantities and in the case of universals, a totality turns out to be the sum of essential parts assembled according to a certain project of constructio
Catalan relations: a relational-theoretic approach to Catalan numbers
No full textWe define the notion of a Catalan pair (which is a pair of binary
relations (S, R) satisfying certain axioms) with the aim of
giving a common language to several combinatorial interpretations
of Catalan numbers. We show, in particular, that the second
component R uniquely determines the pair, and we give a characterization of R in terms of forbidden configurations. We also
propose some generalizations of Catalan pairs arising from some
slight modifications of (some of the) axioms
THE COMBINATORICS OF CONVEX PERMUTOMINOES
No full textA permutomino of size n is a polyomino determined by particular pairs (1, 2) of permutations of n. Here we study
various classes of convex permutominoes. We determine some combinatorial properties and, in particular, the characterization for the permutations defining convex, directed-convex, and parallelogram permutominoes.
Using standard combinatorial techniques we provide a recursive decomposition for permutations associated with convex permutominoes, and we derive a closed formula
for the number of these permutations of size n
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