Pragmatic Languages with Universal Grammars

This paper shows the existence of an equilibrium pragmatic Language with a universal grammar as a coordination device under communication misunderstandings. Such a language plays a key role in achieving efficient outcomes in those Sender-Receiver games where there may exist noisy information transmission. The Language is pragmatic in the sense that the Receiver’ best response depends on the context, i.e, on the payoffs and on the initial probability distribution of the states of nature of the underlying game. The Language has a universal grammar because the coding rule does not depend on such specific parameters and can then be applied to any Sender-Receiver game with noisy communication.grammar, pragmatic language, prototypes, separating equilibria

Assumptions behind grammatical approaches to code-switching: when the blueprint is a red herring

Many of the so-called ‘grammars’ of code-switching are based on various underlying assumptions, e.g. that informal speech can be adequately or appropriately described in terms of ‘‘grammar’’; that deep, rather than surface, structures are involved in code-switching; that one ‘language’ is the ‘base’ or ‘matrix’; and that constraints derived from existing data are universal and predictive. We question these assumptions on several grounds. First, ‘grammar’ is arguably distinct from the processes driving speech production. Second, the role of grammar is mediated by the variable, poly-idiolectal repertoires of bilingual speakers. Third, in many instances of CS the notion of a ‘base’ system is either irrelevant, or fails to explain the facts. Fourth, sociolinguistic factors frequently override ‘grammatical’ factors, as evidence from the same language pairs in different settings has shown. No principles proposed to date account for all the facts, and it seems unlikely that ‘grammar’, as conventionally conceived, can provide definitive answers. We conclude that rather than seeking universal, predictive grammatical rules, research on CS should focus on the variability of bilingual grammars

Unification and Matching on Compressed Terms

Term unification plays an important role in many areas of computer science, especially in those related to logic. The universal mechanism of grammar-based compression for terms, in particular the so-called Singleton Tree Grammars (STG), have recently drawn considerable attention. Using STGs, terms of exponential size and height can be represented in linear space. Furthermore, the term representation by directed acyclic graphs (dags) can be efficiently simulated. The present paper is the result of an investigation on term unification and matching when the terms given as input are represented using different compression mechanisms for terms such as dags and Singleton Tree Grammars. We describe a polynomial time algorithm for context matching with dags, when the number of different context variables is fixed for the problem. For the same problem, NP-completeness is obtained when the terms are represented using the more general formalism of Singleton Tree Grammars. For first-order unification and matching polynomial time algorithms are presented, each of them improving previous results for those problems.Comment: This paper is posted at the Computing Research Repository (CoRR) as part of the process of submission to the journal ACM Transactions on Computational Logic (TOCL)

Language Sampling for Universal Grammars

In this paper we present a sampling algorithm for constrained strings representing the state of parameters of a universal grammar. This sampling algorithm has been used to assess statistical significance of the parametric comparison method, a new syntax-based approach to reconstruct linguistic phylogeny

Shapes: Seeing and doing with shape grammars

This paper describes the visual interface of a configurable and extensible system to support generic work with shape grammars. Shape grammars allow the implementation of computational mechanisms to analyze and synthesize designs of visual languages and have been used to represent the knowledge behind the creative work of architects, designers and artists. This kind of grammars is inherently visual. The system described, a kind of universal machine for shape grammars, allows users to build their own shape grammars and experiment with them. It has been the focus of our past work, it mixes technological and artistic aspects and it has a specific computational architecture which includes a symbolic and a visual interface. The latter one is the subject of this paper.info:eu-repo/semantics/acceptedVersio

Small Universal Antiport P Systems and Universal Multiset Grammars

Based on the construction of a universal register machine we construct a universal antiport P system working with 31 rules in the maximally parallel mode in one membrane, and a universal antiport P system with forbidden context working with 16 rules in the sequential derivation mode in one membrane for computing any partial recursive function on the set of natural numbers. For accepting/generating any arbitrary recursively enumerable set of natural numbers we need 31/33 and 16/18 rules, respectively. As a consequence of the result for antiport P systems with forbidden context we immediately infer similar results for forbidden random context multiset grammars with arbitrary rules

Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability

Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and the associated Universal Distribution are (or should be) of the greatest importance in science. Here we investigate the emergence, the rates of emergence and convergence, and the Coding-theorem like behaviour of AP in Turing-subuniversal models of computation. We investigate empirical distributions of computing models in the Chomsky hierarchy. We introduce measures of algorithmic probability and algorithmic complexity based upon resource-bounded computation, in contrast to previously thoroughly investigated distributions produced from the output distribution of Turing machines. This approach allows for numerical approximations to algorithmic (Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a computational hierarchy. We demonstrate that all these estimations are correlated in rank and that they converge both in rank and values as a function of computational power, despite fundamental differences between computational models. In the context of natural processes that operate below the Turing universal level because of finite resources and physical degradation, the investigation of natural biases stemming from algorithmic rules may shed light on the distribution of outcomes. We show that up to 60\% of the simplicity/complexity bias in distributions produced even by the weakest of the computational models can be accounted for by Algorithmic Probability in its approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity calculator: http://complexitycalculator.com

On vocabulary size of grammar-based codes

We discuss inequalities holding between the vocabulary size, i.e., the number of distinct nonterminal symbols in a grammar-based compression for a string, and the excess length of the respective universal code, i.e., the code-based analog of algorithmic mutual information. The aim is to strengthen inequalities which were discussed in a weaker form in linguistics but shed some light on redundancy of efficiently computable codes. The main contribution of the paper is a construction of universal grammar-based codes for which the excess lengths can be bounded easily.Comment: 5 pages, accepted to ISIT 2007 and correcte