Semantic interpolation

We treat interpolation for various logics

Methods to integrate a language model with semantic information for a word prediction component

Most current word prediction systems make use of n-gram language models (LM) to estimate the probability of the following word in a phrase. In the past years there have been many attempts to enrich such language models with further syntactic or semantic information. We want to explore the predictive powers of Latent Semantic Analysis (LSA), a method that has been shown to provide reliable information on long-distance semantic dependencies between words in a context. We present and evaluate here several methods that integrate LSA-based information with a standard language model: a semantic cache, partial reranking, and different forms of interpolation. We found that all methods show significant improvements, compared to the 4-gram baseline, and most of them to a simple cache model as well.Comment: 10 pages ; EMNLP'2007 Conference (Prague

Syntactic Interpolation for Tense Logics and Bi-Intuitionistic Logic via Nested Sequents

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting to embeddings, semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants

Deep Semantic Image Interpolation

Image datasets often live on a continuum: Images from an outdoor scene vary from day to night, across different weather conditions, and over the course of seasons. Faces age and exhibit different expressions. We consider the problem of taking individual images from these datasets and explicitly manipulating those images to change where they lie on the continuum. We focus on a version of this problem that requires as little input as possible, and we build off of previous work using CNN features to construct an intermediate image manifold on which to manipulate the images. We also investigate a novel way of reconstructing images from their CNN features using alpha compositions of the input images. These technique produce convincing semantic interpolations of images and timelapse video from a variety of sources

A semantic approach to interpolation

Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially generalize known interpolation results; all the others are new. We also discuss someapplications of our results to the theory of institutions and of algebraic specifications,and a Craig-Robinson version of these results

A semantic approach to interpolation

Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially generalize known interpolation results; all the others are new. We also discuss someapplications of our results to the theory of institutions and of algebraic specifications,and a Craig-Robinson version of these results

Uniform interpolation via nested sequents

A modular proof-theoretic framework was recently developed to prove Craig interpolation for normal modal logics based on generalizations of sequent calculi (e.g., nested sequents, hypersequents, and labelled sequents). In this paper, we turn to uniform interpolation, which is stronger than Craig interpolation. We develop a constructive method for proving uniform interpolation via nested sequents and apply it to reprove the uniform interpolation property for normal modal logics K, D, and T. While our method is proof-theoretic, the definition of uniform interpolation for nested sequents also uses semantic notions, including bisimulation modulo an atomic proposition

Clustering of syntactic and discursive information for the dynamic adaptation of Language Models

Presentamos una estrategia de agrupamiento de elementos de diálogo, de tipo semántico y discursivo. Empleando Latent Semantic Analysis (LSA) agru- pamos los diferentes elementos de acuerdo a un criterio de distancia basado en correlación. Tras seleccionar un conjunto de grupos que forman una partición del espacio semántico o discursivo considerado, entrenamos unos modelos de lenguaje estocásticos (LM) asociados a cada modelo. Dichos modelos se emplearán en la adaptación dinámica del modelo de lenguaje empleado por el reconocedor de habla incluido en un sistema de diálogo. Mediante el empleo de información de diálogo (las probabilidades a posteriori que el gestor de diálogo asigna a cada elemento de diálogo en cada turno), estimamos los pesos de interpolación correspondientes a cada LM. Los experimentos iniciales muestran una reducción de la tasa de error de palabra al emplear la información obtenida a partir de una frase para reestimar la misma frase