The first part of this article gives a brief overview of the four levels of the Chomsky hierarchy, with a special emphasis on context-free and regular languages. It then recapitulates the arguments why neither regular nor context-free grammar is sufficiently expressive to capture all phenomena in the natural language syntax. In the second part, two refinements of the Chomsky hierarchy are reviewed, which are both relevant to the extant research in cognitive science: the mildly context-sensitive languages (which are located between context-free and context-sensitive languages), and the sub-regular hierarchy (which distinguishes several levels of complexity within the class of regular languages).

Probabilistic pragmatics aspires to explain certain regularities of language use and interpretation as behavior of speakers and listeners who want to satisfy their conversational interests in a context that may contain a substantial amount of uncertainty. This approach differs substantially from more familiar approaches in theoretical pragmatics. To set it apart, we here work out some of its key distinguishing features and show, by way of some simple examples, how probabilistic pragmatics instantiates these.

This article deals with the typology of the case marking of semantic core roles. The competing economy considerations of hearer (disambiguation) and speaker (minimal effort) are formalized in terms of EVOLUTIONARY GAME THEORY. It is shown that the case-marking patterns that are attested in the languages of the world are those that are evolutionarily stable for different relative weightings of speaker economy and hearer economy, given the statistical patterns of language use that were extracted from corpora of naturally occurring conversations.

Automatic phylogenetic inference plays an increasingly important role in computational historical linguistics. Most pertinent work is currently based on expert cognate judgments. This limits the scope of this approach to a small number of well-studied language families. We used machine learning techniques to compile data suitable for phylogenetic inference from the ASJP database, a collection of almost 7,000 phonetically transcribed word lists over 40 concepts, covering two thirds of the extant world-wide linguistic diversity. First, we estimated Pointwise Mutual Information scores between sound classes using weighted sequence alignment and general-purpose optimization. From this we computed a dissimilarity matrix over all ASJP word lists. This matrix is suitable for distance-based phylogenetic inference. Second, we applied cognate clustering to the ASJP data, using supervised training of an SVM classifier on expert cognacy judgments. Third, we defined two types of binary characters, based on automatically inferred cognate classes and on sound-class occurrences. Several tests are reported demonstrating the suitability of these characters for character-based phylogenetic inference.

Abstract. This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories ID a and ID< a ; the exact proof-theoretic ordinals of these systems are presented. §1. Introduction. The transfinitely iterated fixed point theories ID« are relatives of the better known theories ID Q for iterated inductive definitions. These latter theories have been extensively studied during the last years (cf., e.g., Buchholz et al.[1]) and their proof-theoretic analysis has been carried through in all detail.The basic axioms of ID a provide hierarchies of least (definable) fixed points of a times iterated positive inductive definitions given by arithmetic operator forms. In the case of the fixed point theories ID Q , on the other hand, one confines oneself to hierarchies of arbitrary fixed points of the corresponding inductive definitions and drops the requirement for minimality.The finitely iterated fixed point theories ID" were first introduced in Feferman [5] in connection with his proof of Hancock's conjecture. Among other things, it is shown in this article that the proof-theoretic ordinal of ID" is a" for ao := e 0 and a n+ \ := ipa"0. Hence, the union of all ID" for n < co, i.e., the system ID co. It is a technical paper, which establishes the proof-theoretic ordinals of these systems. The relationship between transfinitely iterated fixed point theories and subsystems of second order arithmetic and the role of transfinitely iterated fixed point theories for metapredicativity in general are only briefly addressed in the conclusion.The plan of this paper is as follows. In Section 2 we discuss some ordinal-theoretic preliminaries; namely, we sketch an ordinal notation system which is based on nary