CS 466/666: Introduction to Formal Languages

CS 466/666 is an introduction to formal language and automata theory. In this course we will examine methods for defining syntax of languages and recognizing patterns: the syntax of languages can be defined using grammars and patterns accepted by finite state machines. Along with presenting the fundamentals of these two topics, the course will develop and investigate the relationships between language definition and pattern recognition. The text will be the third edition of Languages and Machines: An Introduction to the Theory of Computer Science

A Note on Derived Geometric Interpretation of Classical Field Theories

In this note, we would like to provide a conceptional introduction to the interaction between derived geometry and physics based on the formalism that has been heavily studied by Kevin Costello. Main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, which can be, roughly speaking, thought of as a higher categorical refinement of an ordinary algebraic geometry, (ii) to understand how certain derived objects naturally appear in a theory describing a particular physical phenomenon and give rise to a formal mathematical treatment, such as redefining a perturbative classical field theory (or its quantum counterpart) by using the language of derived algebraic geometry, and (iii) how the notion of factorization algebra together with certain higher categorical structures come into play to encode the structure of so-called observables in those theories by employing certain cohomological/homotopical methods. Adopting such a heavy and relatively enriched language allows us to formalize the notion of quantization and observables in quantum field theory as well.Comment: 14 pages. This note serves as an introductory survey on certain mathematical structures encoding the essence of Costello's approach to derived-geometric formulation of field theories and the structure of observables in an expository manne

CS 3200/5200: Theoretical Foundations of Computing

CS 3200/5200 is an introduction to (a) formal language and automata theory and (b) computability. For (a), we will examine mechanisms for defining syntax of languages and devices for recognizing languages. Along with the fundamentals of these two topics, the course will investigate the relationships between language definition mechanisms and language recognition devices. For (b), we will study decision problems, the Church-Turing thesis, the undecidability of the Halting Problem, and problem reduction and undecidability. The text will be the third edition of Languages and Machines: An Introduction to the Theory of Computer Science, by Thomas Sudkamp

An Introduction to String Diagrams for Computer Scientists

This document is an elementary introduction to string diagrams. It takes a computer science perspective: rather than using category theory as a starting point, we build on intuitions from formal language theory, treating string diagrams as a syntax with its semantics. After the basic theory, pointers are provided to contemporary applications of string diagrams in various fields of science

Handbook of Lexical Functional Grammar

Lexical Functional Grammar (LFG) is a nontransformational theory of linguistic structure, first developed in the 1970s by Joan Bresnan and Ronald M. Kaplan, which assumes that language is best described and modeled by parallel structures representing different facets of linguistic organization and information, related by means of functional correspondences. This volume has five parts. Part I, Overview and Introduction, provides an introduction to core syntactic concepts and representations. Part II, Grammatical Phenomena, reviews LFG work on a range of grammatical phenomena or constructions. Part III, Grammatical modules and interfaces, provides an overview of LFG work on semantics, argument structure, prosody, information structure, and morphology. Part IV, Linguistic disciplines, reviews LFG work in the disciplines of historical linguistics, learnability, psycholinguistics, and second language learning. Part V, Formal and computational issues and applications, provides an overview of computational and formal properties of the theory, implementations, and computational work on parsing, translation, grammar induction, and treebanks. Part VI, Language families and regions, reviews LFG work on languages spoken in particular geographical areas or in particular language families. The final section, Comparing LFG with other linguistic theories, discusses LFG work in relation to other theoretical approaches

Frame-Based Knowledge Representation

This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. The author was sponsored by the Institute of International Education on an ITT-fellowship.The paper introduces a language for representing knowledge in a declarative form. With this language it is possible to define knowledge about a certain domain by introducing a number of concepts and by specifying their interrelations. The paper is meant to be an informal introduction to the language. We present the available constructs, describe their meaning and present a number of examples. In other papers (currently in preparation) we will give a formal semantics of the language, introduce the interference theory and discuss a possible procedural embedding.MIT Artificial Intelligence Laboratory Institute of International Educatio

Formal Methods in the Foundations of Science

The intent of this study is to provide formal apparatus which facilitates the investigation of problems in the methodology of science. The introduction contains several examples of such problems and motivates the subsequent formalism. A general definition of a formal language is presented, and this definition is used to characterize an individual's view of the world around him. A notion of empirical observation is developed which is independent of language. The interplay of formal language and observation is taken as the central theme. The process of science is conceived as the finding of that formal language that best expresses the available experimental evidence. To characterize the manner in which a formal language imposes structure on its universe of discourse, the fundamental concepts of elements and states of a formal language are introduced. Using these, the notion of a basis for a formal language is developed as a collection of minimal states distinguishable within the language. The relation of these concepts to those of model theory is discussed. An a priori probability defined on sets of observations is postulated as a reflection of an individual's ontology. This probability, in conjunction with a formal language and a basis for that language, induces a subjective probability describing and individual's conceptual view of admissible configurations of the universe. As a function of this subjective probability, and consequently of language, a measure of the informativeness of empirical observations is introduced and is shown to be intuitively plausible- particularly in the case of scientific experimentation. The developed formalism is then systematically applied to the general problems presented in the introduction. The relationship of scientific theories to empirical observations is discussed and the need for certain tacit, unstatable knowledge is shown to be necessary to fully comprehend the meaning of realistic theories. The idea that many common concepts can be specified only by drawing on knowledge obtained from an infinite number of observations is presented and the problems of reductionism are examined in this context. A definition of when one formal language can be considered to be more expressive than another is presented, and the change in the informativeness of an observation as language changes is investigated. In this regard it is shown that the information inherent in an observation may decrease for a more expressive language. The general problem of induction and its relation to the scientific method are discussed. Two hypotheses concerning an individual's selection of an optimal language for a particular domain of discourse are presented and specific examples from the introduction are examined

EMIL: Extracting Meaning from Inconsistent Language

Developments in formal and computational theories of argumentation reason with inconsistency. Developments in Computational Linguistics extract arguments from large textual corpora. Both developments head in the direction of automated processing and reasoning with inconsistent, linguistic knowledge so as to explain and justify arguments in a humanly accessible form. Yet, there is a gap between the coarse-grained, semi-structured knowledge-bases of computational theories of argumentation and fine-grained, highly-structured inferences from knowledge-bases derived from natural language. We identify several subproblems which must be addressed in order to bridge the gap. We provide a direct semantics for argumentation. It has attractive properties in terms of expressivity and complexity, enables reasoning by cases, and can be more highly structured. For language processing, we work with an existing controlled natural language (CNL), which interfaces with our computational theory of argumentation; the tool processes natural language input, translates them into a form for automated inference engines, outputs argument extensions, then generates natural language statements. The key novel adaptation incorporates the defeasible expression ‘it is usual that’. This is an important, albeit incremental, step to incorporate linguistic expressions of defeasibility. Overall, the novel contribution of the paper is an integrated, end-to-end argumentation system which bridges between automated defeasible reasoning and a natural language interface. Specific novel contributions are the theory of ‘direct semantics’, motivations for our theory, results with respect to the direct semantics, an implementation, experimental results, the tie between the formalisation and the CNL, the introduction into a CNL of a natural language expression of defeasibility, and an ‘engineering’ approach to fine-grained argument analysis