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Learning discrete categorial grammars from structures

Jérôme Besombes, Jean-Yves Marion (2008)

RAIRO - Theoretical Informatics and Applications

We define the class of discrete classical categorial grammars, similar in the spirit to the notion of reversible class of languages introduced by Angluin and Sakakibara. We show that the class of discrete classical categorial grammars is identifiable from positive structured examples. For this, we provide an original algorithm, which runs in quadratic time in the size of the examples. This work extends the previous results of Kanazawa. Indeed, in our work, several types can be associated to a word...

Lebesgue's Convergence Theorem of Complex-Valued Function

Keiko Narita, Noboru Endou, Yasunari Shidama (2009)

Formalized Mathematics

In this article, we formalized Lebesgue's Convergence theorem of complex-valued function. We proved Lebesgue's Convergence Theorem of realvalued function using the theorem of extensional real-valued function. Then applying the former theorem to real part and imaginary part of complex-valued functional sequences, we proved Lebesgue's Convergence Theorem of complex-valued function. We also defined partial sums of real-valued functional sequences and complex-valued functional sequences and showed their...

Left and right semi-uninorms on a complete lattice

Yong Su, Zhudeng Wang, Keming Tang (2013)

Kybernetika

Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary...

Leibniz Series forπ

Karol Pąk (2016)

Formalized Mathematics

In this article we prove the Leibniz series for π which states that π4=∑n=0∞(−1)n2⋅n+1. π 4 = ∑ n = 0 ∞ - 1 n 2 · n + 1 . The formalization follows K. Knopp [8], [1] and [6]. Leibniz’s Series for Pi is item 26 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.

Les I -types du système ℱ

K. Nour (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Nous démontrons dans ce papier que les types du système ℱ habités uniquement par des λ I -termes (les I -types) sont à quantificateur positif. Nous présentons ensuite des conséquenses de ce résultat et quelques exemples.

Les I-types du système ℱ

K. Nour (2010)

RAIRO - Theoretical Informatics and Applications

We prove in this paper that the types of system ℱ inhabited uniquely by λI-terms (the I-types) have a positive quantifier. We give also consequences of this result and some examples.

Les types de données syntaxiques du système ℱ

Samir Farkh, Karim Nour (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Nous présentons dans ce papier une définition purement syntaxique des types entrées et des types sorties du système ℱ . Nous définissons les types de données syntaxiques comme étant des types entrées et sorties. Nous démontrons que les types à quantificateurs positifs sont des types de données syntaxiques et qu’un type entrée est un type sortie. Nous imposons des restrictions sur la règle d’élimination des quantificateurs pour démontrer qu’un type sortie est un type entrée.

Les types de données syntaxiques du système ℱ

Samir Farkh, Karim Nour (2010)

RAIRO - Theoretical Informatics and Applications

We give in this paper a purely syntactical definition of input and output types of system ℱ . We define the syntactical data types as input and output types. We show that any type with positive quantifiers is a syntactical data type and that an input type is an output type. We give some restrictions on the ∀-elimination rule in order to prove that an output type is an input type.

Letter to the editor: Consistency of LPC+Ch

Jorma K. Mattila (1998)

Kybernetika

In his paper [Kybernetika 31, No. 1, 99–106 (1995; Zbl 0857.03042)], E. Turunen says in the corollary on p. 106: “Notice that the third last line on page 195 in [J. K. Mattila, “Modifier logic”, in: J. Kacprzyk (ed.) et al., Fuzzy logic for the management of uncertainty. New York: Wiley. 191–209 (1992)] stating that LPC+Ch calculus is consistent is not correct.” The system LPC+Ch is consistent, which can be seen quite trivially.

Logiche modali con la proprietà del punto fisso

L. Sacchetti (1999)

Bollettino dell'Unione Matematica Italiana

We introduce various kinds of fixed-point properties for modal logics, and we classify the most prominent systems according to these. Our goal is to do a first step towards a complete characterization of provability logics of (possibly non standard) derivability predicates for Peano Arithmetic.

Logics for stable and unstable mereological relations

Vladislav Nenchev (2011)

Open Mathematics

In this paper we present logics about stable and unstable versions of several well-known relations from mereology: part-of, overlap and underlap. An intuitive semantics is given for the stable and unstable relations, describing them as dynamic counterparts of the base mereological relations. Stable relations are described as ones that always hold, while unstable relations hold sometimes. A set of first-order sentences is provided to serve as axioms for the stable and unstable relations, and representation...

Logics that are both paraconsistent and paracomplete

Newton C.A. da Costa (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The Author describes new systems of logic (called "nonalethic") which are both paraconsistent and paracomplete. These systems are connected with the logic of vagueness and with certain philosophical problems (e.g. with some aspects of Hegel's logic).

Currently displaying 501 – 520 of 1313