Data and Knowledge management

This paper explains new results relating modal propositional logic and rewrite rule systems. More precisely, we give complete term rewriting systems for the modal propositional systems known as K, Q, T, and S5. These systems are presented as extensions of Hsiang's system for classical propositional calculus. We have checked local confluence with the rewrite rule system K.B. (cf. the Knuth-Bendix algorithm) developed by the Formel project at INRIA. We prove that these systems are noetherian, and then infer their confluence from Newman's lemma. Therefore each term rewriting system provides a new automated decision procedure and defines a canonical form for the corresponding logic. We also show how to characterize the canonical forms thus obtained. normal modal systems; the system K is in a precise sense the weakest normal modal system. These systems are based on classical propositional calculus (CPC). We briefly recall their definitions as Hilbert systems.

This paper is concerned with learning in the model of Gold the Categorial Dependency Grammars (CDG), which express discontinuous (non-projective) dependencies. We show that rigid and k-valued CDG (without optional and iterative types) are learnable from strings. In fact, we prove that the languages of dependency nets coding rigid CDGs have finite elasticity, and we show a learning algorithm. As a standard corollary, this result leads to the learnability of rigid or kvalued CDGs (without optional and iterative types) from strings.

In this paper, we define Dependency Structure Grammars (DSG), which are rewriting rule grammars generating sentences together with their dependency structures, are more expressive than CF-grammars and non-equivalent to mildly context-sensitive grammars. We show that DSG are weakly equivalent to Categorial Dependency Grammars (CDG) recently introduced in [6, 3]. In particular, these dependency grammars naturally express long distance dependencies and enjoy good mathematical properties.

We study the learnability problem in the family of Categorial Dependency Grammars (CDG), a class of categorial grammars defining unlimited dependency structures. CDG isatisfying a reasonable condition on the iterant dependencies are shown to be incrementally learnable in the limit.

This paper investigates the learnability of Pregroup Grammars, a context-free grammar formalism recently defined in the field of computational linguistics. In a first theoretical approach, we provide learnability and non-learnability results in the sense of Gold for subclasses of Pregroup Grammars. In a second more practical approach, we propose an acquisition algorithm from a special kind of input called Feature-tagged Examples, that is based on sets of constraints.

This paper is concerned with learning categorial grammars in Gold's model. In contrast to k-valued classical categorial grammars, k-valued Lambek grammars are not learnable from strings. This result was shown for several variants but the question was left open for the weakest one, the non-associative variant NL.

This paper is concerned with learning categorial grammars in the model of Gold. We show that rigid and k-valued non-associative Lambek grammars are learnable from function-argument structured sentences. In fact, function-argument structures are natural syntactical decompositions of sentences in sub-components with the indication of the head of each sub-component.

Welcome to the proceedings of the 14th WoLLIC meeting, which was held in Rio de Janeiro, Brazil, July 2 -5, 2007. The Workshop on Logic, Language, Information and Computation (WoLLIC) is an annual international forum on inter-disciplinary research involving formal logic, computing and programming theory, and natural language and reasoning. The WoLLIC meetings alternate between Brazil (and Latin America) and other countries, with the aim of fostering interest in applied logic among Latin American scientists and students, and facilitating their interaction with the international applied logic community.

Formal approaches in semantics have long been restricted to small or mediumsized fragments of natural language grammars. We argue that categorial grammars are very suitable for reaching wide-coverage grammars for semantic interpretation because they are lexicalised and have a transparant mapping between syntactic categories and semantic types. We substantiate this claim by taking Clark & Curran's statistical CCG parser (trained on Hockenmaier's CCGbank for English) and show how to build a principled syntax-semantic interface situated in Discourse Representation Theory. Despite the theoretical beauty of categorial grammars, not all is hunky-dory, and we will illustrate both the attractive and the less attractive aspects that arise in developing practical grammar formalisms. We will illustrate the resulting system for robust text interpretation in applications such as question answering and textual inference.

Welcome to the proceedings of the 14th WoLLIC meeting, which was held in Rio de Janeiro, Brazil, July 2 -5, 2007. The Workshop on Logic, Language, Information and Computation (WoLLIC) is an annual international forum on inter-disciplinary research involving formal logic, computing and programming theory, and natural language and reasoning. The WoLLIC meetings alternate between Brazil (and Latin America) and other countries, with the aim of fostering interest in applied logic among Latin American scientists and students, and facilitating their interaction with the international applied logic community.

We study learnability of Categorial Dependency Grammars (CDG), a family of categorial grammars expressing all kinds of projective, discontinuous and repeatable dependencies. For these grammars, it is known that they are not learnable from dependency structures. We propose two different ways of modelling the repeatable dependencies through iterated types and the two corresponding families of CDG which cannot distinguish between the dependencies repeatable at least K times and those repeatable any number of times. For both we show that they are incrementally learnable in the limit from dependency structures.

Pregroup grammars are a context-free grammar formalism which may be used to describe the syntax of natural languages. However, this formalism is not able to naturally define types corresponding to optional and iterated arguments such as optional complements of verbs or verbs' adverbial modifiers. This paper introduces two constructions that make up for this deficiency. We briefly recall that a monoid is a structure < M, ·, 1 >, such that · is associative and has a neutral element 1 (∀x ∈ M : 1 · x = x · 1 = x). A partially ordered monoid is a monoid < M, ·, 1 > with a partial order ≤ that satisfies ∀a, b, c: a ≤ b ⇒ c · a ≤ c · b and a · c ≤ b · c. 4 Left and right adjoints are defined by (p (n) ) l = p (n−1) , (p (n) ) r = p (n+1) , (XY ) l = Y l X l and (XY ) r = Y r X r . We write p for p (0) . We also iterate left and right adjoints for every X ∈ T (P,≤) : X (0) = X, X (n+1) = (X r ) (n) and X (n−1) = (X l ) (n) 5 ≤ is only a preorder. Thus, in fact, the pregroup is the quotient of T (P,≤) by the equivalence relation X ≤ Y & Y ≤ X.

Nous nous intéressons au problème de l'apprentissage des grammaires catégorielles utilisées pour la modélisation syntaxique des langues. Récemment, des algorithmes ontété proposés dans le modèle d'apprentissage de Gold, pour certaines classes de grammaires catégorielles. En revanche, les grammaires de Lambek rigides ou ¤ -valuées ne sont pas apprenablesà partir des chaînes. Nous nous intéressons icià une autre classification de ces grammaires selon l'arité des types. Nous montrons ainsi qu'une borne sur l'arité des types permet d'identifierà la limite les grammaires de Lambek rigides ou ¤

Cet article traite de l'acquisition automatique des grammaires de Lambek, utilisées pour la modélisation syntaxique des langues. Récemment, des algorithmes ont été proposés dans le modèle d'apprentissage de Gold, pour certaines classes de grammaires catégorielles. En revenche, les grammaires de Lambek rigides ou k-valuées ne sont pas apprenables à partir des chaînes. Nous nous intéressons ici au cas des grammaires de prégroupe. Nous montrons que la classe des grammaires de prégroupe n'est pas apprenable à partir des chaînes, même si on limite fortement l'ordre des types (ordre 1/2) ; notre preuve revient à construire un point limite pour cette classe.

The notion of k-valued categorial grammars where a word is associated to at most k types is often used in the field of lexicalized grammars as a fruitful constraint for obtaining several properties like the existence of learning algorithms. This principle is relevant only when the classes of k-valued grammars correspond to a real hierarchy of languages. Such a property had been shown earlier for classical categorial grammars. This paper establishes the relevance of this notion when categorial grammars are enriched with iterated types. 3 no product connective is used in the paper 4 the order o is null on primitive types s.t. o(X / Y ) = o(Y \ X) = max(o(X), 1 + o(Y ))

This paper is concerned with the inference of categorial grammars, a context-free grammar formalism in the field of computational linguistics. A recent result has shown that whereas they are not learnable from strings in the model of Gold, rigid and k-valued non-associative Lambek grammars are still learnable from generalized functor-argument structured sentences. We focus here on the algorithmic part of this result and provide an algorithm that can be seen as an extension of Buszkowski, Penn and Kanazawa's contributions for classical categorial grammars.