Efficient learning of context-free grammars from positive structural examples

AbstractIn this paper, we introduce a new normal form for context-free grammars, called reversible context-free grammars, for the problem of learning context-free grammars from positive-only examples. A context-free grammar G = (N, Σ, P, S) is said to be reversible if (1) A → α and B → α in P implies A = B and (2) A → αBβ and A → αCβ in P implies B = C. We show that the class of reversible context-free grammars can be identified in the limit from positive samples of structural descriptions and there exists an efficient algorithm to identify them from positive samples of structural descriptions, where a structural description of a context-free grammar is an unlabelled derivation tree of the grammar. This implies that if positive structural examples of a reversible context-free grammar for the target language are available to the learning algorithm, the full class of context-free languages can be learned efficiently from positive samples

RevBayes: Bayesian Phylogenetic Inference Using Graphical Models and an Interactive Model-Specification Language.

Programs for Bayesian inference of phylogeny currently implement a unique and fixed suite of models. Consequently, users of these software packages are simultaneously forced to use a number of programs for a given study, while also lacking the freedom to explore models that have not been implemented by the developers of those programs. We developed a new open-source software package, RevBayes, to address these problems. RevBayes is entirely based on probabilistic graphical models, a powerful generic framework for specifying and analyzing statistical models. Phylogenetic-graphical models can be specified interactively in RevBayes, piece by piece, using a new succinct and intuitive language called Rev. Rev is similar to the R language and the BUGS model-specification language, and should be easy to learn for most users. The strength of RevBayes is the simplicity with which one can design, specify, and implement new and complex models. Fortunately, this tremendous flexibility does not come at the cost of slower computation; as we demonstrate, RevBayes outperforms competing software for several standard analyses. Compared with other programs, RevBayes has fewer black-box elements. Users need to explicitly specify each part of the model and analysis. Although this explicitness may initially be unfamiliar, we are convinced that this transparency will improve understanding of phylogenetic models in our field. Moreover, it will motivate the search for improvements to existing methods by brazenly exposing the model choices that we make to critical scrutiny. RevBayes is freely available at http://www.RevBayes.com [Bayesian inference; Graphical models; MCMC; statistical phylogenetics.]

Phrase structure grammars as indicative of uniquely human thoughts

I argue that the ability to compute phrase structure grammars is indicative of a particular kind of thought. This type of thought that is only available to cognitive systems that have access to the computations that allow the generation and interpretation of the structural descriptions of phrase structure grammars. The study of phrase structure grammars, and formal language theory in general, is thus indispensable to studies of human cognition, for it makes explicit both the unique type of human thought and the underlying mechanisms in virtue of which this thought is made possible