Building and Combining Matching Algorithms

International audienceThe concept of matching is ubiquitous in declarative programming and in automated reasoning. For instance, it is a key mechanism to run rule-based programs and to simplify clauses generated by theorem provers. A matching problem can be seen as a particular conjunction of equations where each equation has a ground side. We give an overview of techniques that can be applied to build and combine matching algorithms. First, we survey mutation-based techniques as a way to build a generic matching algorithm for a large class of equational theories. Second, combination techniques are introduced to get combined matching algorithms for disjoint unions of theories. Then we show how these combination algorithms can be extended to handle non-disjoint unions of theories sharing only constructors. These extensions are possible if an appropriate notion of normal form is computable

Prolegomena to a neurocomputational architecture for human grammatical encoding and decoding

The study develops a neurocomputational architecture for grammatical processing in language production and language comprehension (grammatical encoding and decoding, respectively). It seeks to answer two questions. First, how is online syntactic structure formation of the complexity required by natural-language grammars possible in a fixed, preexisting neural network without the need for online creation of new connections or associations? Second, is it realistic to assume that the seemingly disparate instantiations of syntactic structure formation in grammatical encoding and grammatical decoding can run on the same neural infrastructure? This issue is prompted by accumulating experimental evidence for the hypothesis that the mechanisms for grammatical decoding overlap with those for grammatical encoding to a considerable extent, thus inviting the hypothesis of a single “grammatical coder.” The paper answers both questions by providing the blueprint for a syntactic structure formation mechanism that is entirely based on prewired circuitry (except for referential processing, which relies on the rapid learning capacity of the hippocampal complex), and can subserve decoding as well as encoding tasks. The model builds on the “Unification Space” model of syntactic parsing developed by Vosse & Kempen (2000, 2008, 2009). The design includes a neurocomputational mechanism for the treatment of an important class of grammatical movement phenomena

Termination of Narrowing: Automated Proofs and Modularity Properties

En 1936 Alan Turing demostro que el halting problem, esto es, el problema de decidir si un programa termina o no, es un problema indecidible para la inmensa mayoria de los lenguajes de programacion. A pesar de ello, la terminacion es un problema tan relevante que en las ultimas decadas un gran numero de tecnicas han sido desarrolladas para demostrar la terminacion de forma automatica de la maxima cantidad posible de programas. Los sistemas de reescritura de terminos proporcionan un marco teorico abstracto perfecto para el estudio de la terminacion de programas. En este marco, la evaluaci on de un t ermino consiste en la aplicacion no determinista de un conjunto de reglas de reescritura. El estrechamiento (narrowing) de terminos es una generalizacion de la reescritura que proporciona un mecanismo de razonamiento automatico. Por ejemplo, dado un conjunto de reglas que denan la suma y la multiplicacion, la reescritura permite calcular expresiones aritmeticas, mientras que el estrechamiento permite resolver ecuaciones con variables. Esta tesis constituye el primer estudio en profundidad de las propiedades de terminacion del estrechamiento. Las contribuciones son las siguientes. En primer lugar, se identican clases de sistemas en las que el estrechamiento tiene un comportamiento bueno, en el sentido de que siempre termina. Muchos metodos de razonamiento automatico, como el analisis de la semantica de lenguajes de programaci on mediante operadores de punto jo, se benefician de esta caracterizacion. En segundo lugar, se introduce un metodo automatico, basado en el marco teorico de pares de dependencia, para demostrar la terminacion del estrechamiento en un sistema particular. Nuestro metodo es, por primera vez, aplicable a cualquier clase de sistemas. En tercer lugar, se propone un nuevo metodo para estudiar la terminacion del estrechamiento desde un termino particular, permitiendo el analisis de la terminacion de lenguajes de programacion. El nuevo metodo generaliza losIborra López, J. (2010). Termination of Narrowing: Automated Proofs and Modularity Properties [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/19251Palanci

Rule-Based Unification in Combined Theories and the Finite Variant Property

International audienceWe investigate the unification problemin theories defined by rewrite systems which are both convergent andforward-closed. These theories are also known in the context ofprotocol analysis as theories with the finite variant property andadmit a variant-based unification algorithm. In this paper, wepresent a new rule-based unification algorithm which can be seen as analternative to the variant-based approach. In addition, we defineforward-closed combination to capture the union of a forward-closedconvergent rewrite system with another theory, such as theAssociativity-Commutativity, whose function symbols may occur inright-hand sides of the rewrite system. Finally, we present acombination algorithm for this particular class of non-disjoint unionsof theories

Approximate text generation from non-hierarchical representations in a declarative framework

This thesis is on Natural Language Generation. It describes a linguistic realisation system that translates the semantic information encoded in a conceptual graph into an English language sentence. The use of a non-hierarchically structured semantic representation (conceptual graphs) and an approximate matching between semantic structures allows us to investigate a more general version of the sentence generation problem where one is not pre-committed to a choice of the syntactically prominent elements in the initial semantics. We show clearly how the semantic structure is declaratively related to linguistically motivated syntactic representation — we use D-Tree Grammars which stem from work on Tree-Adjoining Grammars. The declarative specification of the mapping between semantics and syntax allows for different processing strategies to be exploited. A number of generation strategies have been considered: a pure topdown strategy and a chart-based generation technique which allows partially successful computations to be reused in other branches of the search space. Having a generator with increased paraphrasing power as a consequence of using non-hierarchical input and approximate matching raises the issue whether certain 'better' paraphrases can be generated before others. We investigate preference-based processing in the context of generation

Unification dans des mélanges non-disjoints avec des théories fermées en avant

We investigate the unification problemin theories defined by rewrite systems which are both convergent andforward-closed. These theories are also known in the context ofprotocol analysis as theories with the finite variant property andadmit a variant-based unification algorithm. In this paper, wepresent a new rule-based unification algorithm which can be seen as analternative to the variant-based approach. In addition, we defineforward-closed combination to capture the union of a forward-closedconvergent rewrite system with another theory, such as theAssociativity-Commutativity, whose function symbols may occur inright-hand sides of the rewrite system. Finally, we present acombination algorithm for this particular class of non-disjoint unionsof theories.On étudie le problème d’unification dans les théories définies par des systèmes deréécriture qui sont à la fois convergents et fermés en avant. Ces théories sont connues dans lecontexte de l’analyse de protocoles de sécurité comme les théories ayant la propriété des variantsfinis et admettant de ce fait un algorithme d’unification à base de variants. Dans ce papier,on présente un nouvel algorithme d’unification à base de règles qui peut être vu comme unealternative à l’approche basée sur le calcul de variants. On étudie l’union d’un système deréécriture convergent et fermé en avant avec une autre théorie dont les symboles de fonctionpeuvent apparaître dans les membres droits du système de réécriture. Finalement, on présenteun algorithme de combinaison pour cette classe particulière d’unions non-disjointes de théories