The Logical Problem of Language Change

This paper considers the problem of language change. Linguists must explain not only how languages are learned but also how and why they have evolved along certain trajectories and not others. While the language learning problem has focused on the behavior of individuals and how they acquire a particular grammar from a class of grammars ${cal G}$, here we consider a population of such learners and investigate the emergent, global population characteristics of linguistic communities over several generations. We argue that language change follows logically from specific assumptions about grammatical theories and learning paradigms. In particular, we are able to transform parameterized theories and memoryless acquisition algorithms into grammatical dynamical systems, whose evolution depicts a population's evolving linguistic composition. We investigate the linguistic and computational consequences of this model, showing that the formalization allows one to ask questions about diachronic that one otherwise could not ask, such as the effect of varying initial conditions on the resulting diachronic trajectories. From a more programmatic perspective, we give an example of how the dynamical system model for language change can serve as a way to distinguish among alternative grammatical theories, introducing a formal diachronic adequacy criterion for linguistic theories.

Natural Language Syntax and First Order Preference

We have argued elsewhere that first order inference can be made more efficient by using non-standard syntax for first order logic. In this paper we show how a fragment of English syntax under Montague semantics provides the foundation of a new inference procedure. This procedure seems more effective than corresponding procedures based on either classical syntax of our previously proposed taxonomic syntax. This observation may provide a functional explanation for some of the syntactic structure of English.

Computational Consequences of Agreement and Ambiguity in Natural Language

The computer science technique of computational complexity analysis can provide powerful insights into the algorithm-neutral analysis of information processing tasks. Here we show that a simple, theory-neutral linguistic model of syntactic agreement and ambiguity demonstrates that natural language parsing may be computationally intractable. Significantly, we show that it may be syntactic features rather than rules that can cause this difficulty. Informally, human languages and the computationally intractable Satisfiability (SAT) problem share two costly computional mechanisms: both enforce agreement among symbols across unbounded distances (Subject-Verb agreement) and both allow ambiguity (is a word a Noun or a Verb?).

The Behavior Language; User's Guide

The Behavior Language is a rule-based real-time parallel robot programming language originally based on ideas from [Brooks 86], [Connell 89], and [Maes 89]. It compiles into a modified and extended version of the subsumption architecture [Brooks 86] and thus has backends for a number of processors including the Motorola 68000 and 68HCll, the Hitachi 6301, and Common Lisp. Behaviors are groups of rules which are activatable by a number of different schemes. There are no shared data structures across behaviors, but instead all communication is by explicit message passing. All rules are assumed to run in parallel and asynchronously. It includes the earlier notions of inhibition and suppression, along with a number of mechanisms for spreading of activation.

Motivated Action Theory: A Formal Theory of Causal Reasoning

When we reason about change over time, causation provides an implicit preference: we prefer sequences of situations in which one situation leads causally to the next, rather than sequences in which one situation follows another at random and without causal connections. In this paper, we explore the problem of temporal reasoning --- reasoning about change over time --- and the crucial role that causation plays in our intuitions. We examine previous approaches to temporal reasoning, and their shortcomings, in light of this analysis. We propose a new system for causal reasoning, motivated action theory, which builds upon causation as a crucial preference creterion. Motivated action theory solves the traditional problems of both forward and backward reasoning, and additionally provides a basis for a new theory of explanation.

Type-omega DPLs

Type-omega DPLs (Denotational Proof Languages) are languages for proof presentation and search that offer strong soundness guarantees. LCF-type systems such as HOL offer similar guarantees, but their soundness relies heavily on static type systems. By contrast, DPLs ensure soundness dynamically, through their evaluation semantics; no type system is necessary. This is possible owing to a novel two-tier syntax that separates deductions from computations, and to the abstraction of assumption bases, which is factored into the semantics of the language and allows for sound evaluation. Every type-omega DPL properly contains a type-alpha DPL, which can be used to present proofs in a lucid and detailed form, exclusively in terms of primitive inference rules. Derived inference rules are expressed as user-defined methods, which are "proof recipes" that take arguments and dynamically perform appropriate deductions. Methods arise naturally via parametric abstraction over type-alpha proofs. In that light, the evaluation of a method call can be viewed as a computation that carries out a type-alpha deduction. The type-alpha proof "unwound" by such a method call is called the "certificate" of the call. Certificates can be checked by exceptionally simple type-alpha interpreters, and thus they are useful whenever we wish to minimize our trusted base. Methods are statically closed over lexical environments, but dynamically scoped over assumption bases. They can take other methods as arguments, they can iterate, and they can branch conditionally. These capabilities, in tandem with the bifurcated syntax of type-omega DPLs and their dynamic assumption-base semantics, allow the user to define methods in a style that is disciplined enough to ensure soundness yet fluid enough to permit succinct and perspicuous expression of arbitrarily sophisticated derived inference rules. We demonstrate every major feature of type-omega DPLs by defining and studying NDL-omega, a higher-order, lexically scoped, call-by-value type-omega DPL for classical zero-order natural deduction---a simple choice that allows us to focus on type-omega syntax and semantics rather than on the subtleties of the underlying logic. We start by illustrating how type-alpha DPLs naturally lead to type-omega DPLs by way of abstraction; present the formal syntax and semantics of NDL-omega; prove several results about it, including soundness; give numerous examples of methods; point out connections to the lambda-phi calculus, a very general framework for type-omega DPLs; introduce a notion of computational and deductive cost; define several instrumented interpreters for computing such costs and for generating certificates; explore the use of type-omega DPLs as general programming languages; show that DPLs do not have to be type-less by formulating a static Hindley-Milner polymorphic type system for NDL-omega; discuss some idiosyncrasies of type-omega DPLs such as the potential divergence of proof checking; and compare type-omega DPLs to other approaches to proof presentation and discovery. Finally, a complete implementation of NDL-omega in SML-NJ is given for users who want to run the examples and experiment with the language.

Simplifying transformations for type-alpha certificates

This paper presents an algorithm for simplifying NDL deductions. An array of simplifying transformations are rigorously defined. They are shown to be terminating, and to respect the formal semantis of the language. We also show that the transformations never increase the size or complexity of a deduction---in the worst case, they produce deductions of the same size and complexity as the original. We present several examples of proofs containing various types of "detours", and explain how our procedure eliminates them, resulting in smaller and cleaner deductions. All of the given transformations are fully implemented in SML-NJ. The complete code listing is presented, along with explanatory comments. Finally, although the transformations given here are defined for NDL, we point out that they can be applied to any type-alpha DPL that satisfies a few simple conditions.

Advanced Programming Language Features for Executable Design Patterns "Better Patterns Through Reflection

The Design Patterns book [GOF95] presents 24 time-tested patterns that consistently appear in well-designed software systems. Each pattern is presented with a description of the design problem the pattern addresses, as well as sample implementation code and design considerations. This paper explores how the patterns from the "Gang of Four'', or "GOF'' book, as it is often called, appear when similar problems are addressed using a dynamic, higher-order, object-oriented programming language. Some of the patterns disappear -- that is, they are supported directly by language features, some patterns are simpler or have a different focus, and some are essentially unchanged.

Tense, Aspect and the Cognitive Representation of Time

This paper explores the relationships between a computation theory of temporal representation (as developed by James Allen) and a formal linguistic theory of tense (as developed by Norbert Hornstein) and aspect. It aims to provide explicit answers to four fundamental questions: (1) what is the computational justification for the primitive of a linguistic theory; (2) what is the computational explanation of the formal grammatical constraints; (3) what are the processing constraints imposed on the learnability and markedness of these theoretical constructs; and (4) what are the constraints that a linguistic theory imposes on representations. We show that one can effectively exploit the interface between the language faculty and the cognitive faculties by using linguistic constraints to determine restrictions on the cognitive representation and vice versa. Three main results are obtained: (1) We derive an explanation of an observed grammatical constraint on tense?? Linear Order Constraint??m the information monotonicity property of the constraint propagation algorithm of Allen's temporal system: (2) We formulate a principle of markedness for the basic tense structures based on the computational efficiency of the temporal representations; and (3) We show Allen's interval-based temporal system is not arbitrary, but it can be used to explain independently motivated linguistic constraints on tense and aspect interpretations. We also claim that the methodology of research developed in this study??oss-level" investigation of independently motivated formal grammatical theory and computational models??a powerful paradigm with which to attack representational problems in basic cognitive domains, e.g., space, time, causality, etc.

Revised Report on the Algorithmic Language Scheme

Data and procedures and the values they amass, Higher-order functions to combine and mix and match, Objects with their local state, the message they pass, A property, a package, the control of point for a catch- In the Lambda Order they are all first-class. One thing to name them all, one things to define them, one thing to place them in environments and bind them, in the Lambda Order they are all first-class. Keywords: Scheme, Lisp, functional programming, computer languages.

Leveraging Learning and Language Via Communication Bootstrapping

In a Communication Bootstrapping system, peer components with different perceptual worlds invent symbols and syntax based on correlations between their percepts. I propose that Communication Bootstrapping can also be used to acquire functional definitions of words and causal reasoning knowledge. I illustrate this point with several examples, then sketch the architecture of a system in progress which attempts to execute this task.

Naive Physics, Event Perception, Lexical Semantics, and Language Acquisition

This thesis proposes a computational model of how children may come to learn the meanings of words in their native language. The proposed model is divided into two separate components. One component produces semantic descriptions of visually observed events while the other correlates those descriptions with co-occurring descriptions of those events in natural language. The first part of this thesis describes three implementations of the correlation process whereby representations of the meanings of whole utterances can be decomposed into fragments assigned as representations of the meanings of individual words. The second part of this thesis describes an implemented computer program that recognizes the occurrence of simple spatial motion events in simulated video input.

Automated Acquisition of Evolving Informal Descriptions

The Listener is an automated system that unintrusively performs knowledge acquisition from informal input. The Listener develops a coherent internal representation of a description from an initial set of disorganized, imprecise, incomplete, ambiguous, and possibly inconsistent statements. The Listener can produce a summary document from its internal representation to facilitate communication, review, and validation. A special purpose Listener, called the Requirements Apprentice (RA), has been implemented in the software requirements acquisition domain. Unlike most other requirements analysis tools, which start from a formal description language, the focus of the RA is on the transition between informal and formal specifications.

Computational Structure of GPSG Models: Revised Generalized Phrase Structure Grammar

The primary goal of this report is to demonstrate how considerations from computational complexity theory can inform grammatical theorizing. To this end, generalized phrase structure grammar (GPSG) linguistic theory is revised so that its power more closely matches the limited ability of an ideal speaker--hearer: GPSG Recognition is EXP-POLY time hard, while Revised GPSG Recognition is NP-complete. A second goal is to provide a theoretical framework within which to better understand the wide range of existing GPSG models, embodied in formal definitions as well as in implemented computer programs. A grammar for English and an informal explanation of the GPSG/RGPSG syntactic features are included in appendices.

ARLO: Another Representation Language Offer

This paper describes ARLO, a representation language loosely modelled after Greiner and Lenant's RLL-1. ARLO is a structure-based representation language for describing structure-based representation languages, including itself. A given representation language is specified in ARLO by a collection of structures describing how its descriptions are interpreted, defaulted, and verified. This high level description is compiles into lisp code and ARLO structures whose interpretation fulfills the specified semantics of the representation. In addition, ARLO itself- as a representation language for expressing and compiling partial and complete language specifications- is described and interpreted in the same manner as the language it describes and implements. This self-description can be extended of modified to expand or alter the expressive power of ARLO's initial configuration. Languages which describe themselves like ARLO- provide powerful mediums for systems which perform automatic self-modification, optimization, debugging, or documentation. AI systems implemented in such a self-descriptive language can reflect on their own capabilities and limitations, applying general learning and problem solving strategies to enlarge or alleviate them.