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Language at Work
Analyzing Communication Breakdown in the Workplace to Inform Systems Design
Keith Devlin and Duska Rosenberg
CSLI, 1996
People are very creative in their use of language. This observation was made convincingly by Chomsky in the 1950s and is generally accepted in the scientific communities concerned with the study of language. Computers, on the other hand, are neither creative, flexible, nor adaptable. This is in spite of the fact that their ability to process language is based largely on the grammars developed by linguists and computer scientists. Thus, there is a mismatch between the observed human creativity and our ability as theorists to explain it. Language at Work examines grammars and other descriptions of language by combining the scientific and the practical. The scientific motivation is to unite distinct intellectual traditions, mathematics and descriptive social science, which have tried to provide an adequate explanation of language and its use on their own to no avail. This volume argues that Situation Theory, a theory of information couched in mathematics, has provided a uniform framework for the investigation of the creative aspects of language use. The application of Situation Theory in the study of language use in everyday communication to improve human/computer interaction is explored and espoused.
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Language, Proof, and Logic
Second Edition
Dave Barker-Plummer, Jon Barwise, and John Etchemendy
CSLI, 2011

Language Proof and Logic is available as a physical book with the software included and as a downloadable package of software plus the book in PDF format. The all-electronic version is available from Openproof at gradegrinder.net.

The textbook/software package covers first-order language in a method appropriate for first and second courses in logic. An on-line grading services instantly grades solutions to hundred of computer exercises. It is designed to be used by philosophy instructors teaching a logic course to undergraduates in philosophy, computer science, mathematics, and linguistics.

Introductory material is presented in a systematic and accessible fashion. Advanced chapters include proofs of soundness and completeness for propositional and predicate logic, as well as an accessible sketch of Godel's first incompleteness theorem. The book is appropriate for a wide range of courses, from first logic courses for undergraduates (philosophy, mathematics, and computer science) to a first graduate logic course.

The software package includes four programs:

Tarski's World, a new version of the popular program that teaches the basic first-order language and its semantics;

Fitch, a natural deduction proof environment for giving and checking first-order proofs;

Boole, a program that facilitates the construction and checking of truth tables and related notions (tautology, tautological consequence, etc.);

Submit, a program that allows students to submit exercises done with the above programs to the Grade Grinder, the automatic grading service.

Grade reports are returned to the student and, if requested, to the student's instructor, eliminating the need for tedious checking of homework. All programs are available for Windows and Macintosh systems. Instructors do not need to use the programs themselves in order to be able to take advantage of their pedagogical value. More about the software can be found at gradegrinder.net.

The price of a new text/software package includes one Registration ID, which must be used each time work is submitted to the grading service. Once activated, the Registration ID is not transferable.

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Lectures on Buildings
Updated and Revised
Mark Ronan
University of Chicago Press, 2009

In mathematics, “buildings” are geometric structures that represent groups of Lie type over an arbitrary field. This concept is critical to physicists and mathematicians working in discrete mathematics, simple groups, and algebraic group theory, to name just a few areas.

            Almost twenty years after its original publication, Mark Ronan’s Lectures on Buildings remains one of the best introductory texts on the subject. A thorough, concise introduction to mathematical buildings, it contains problem sets and an excellent bibliography that will prove invaluable to students new to the field. Lectures on Buildings will find a grateful audience among those doing research or teaching courses on Lie-type groups, on finite groups, or on discrete groups.

            “Ronan’s account of the classification of affine buildings [is] both interesting and stimulating, and his book is highly recommended to those who already have some knowledge and enthusiasm for the theory of buildings.”—Bulletin of the London Mathematical Society

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Lectures on Exceptional Lie Groups
J. F. Adams
University of Chicago Press, 1996
J. Frank Adams was internationally known and respected as one of the great algebraic topologists. Adams had long been fascinated with exceptional Lie groups, about which he published several papers, and he gave a series of lectures on the topic. The author's detailed lecture notes have enabled volume editors Zafer Mahmud and Mamoru Mimura to preserve the substance and character of Adams's work.

Because Lie groups form a staple of most mathematics graduate students' diets, this work on exceptional Lie groups should appeal to many of them, as well as to researchers of algebraic geometry and topology.

J. Frank Adams was Lowndean professor of astronomy and geometry at the University of Cambridge. The University of Chicago Press published his Lectures on Lie Groups and has reprinted his Stable Homotopy and Generalized Homology.

Chicago Lectures in Mathematics Series
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Lectures on Lie Groups
J. F. Adams
University of Chicago Press, 1983
"[Lectures in Lie Groups] fulfills its aim admirably and should be a useful reference for any mathematician who would like to learn the basic results for compact Lie groups. . . . The book is a well written basic text [and Adams] has done a service to the mathematical community."—Irving Kaplansky
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Lectures on Linear Logic
A. S. Troelstra
CSLI, 1992
Linear logic is an example of a "resource-sensitive" logic, keeping track of the number of times data of given types are used. Formulas in linear logic represent either the data themselves or data types, whereas in ordinary logic a formula is a proposition. If ordinary logic is a logic of truth, linear logic is a logic of actions. Linear logic and its implications are explored in depth in this volume. Particular attention has been given to the various formalisms for linear logic, embeddings of classical and intuitionistic logic into linear logic, the connection with certain types of categories, the "formulas-as-types" paradigm for linear logic and associated computational interpretations, and Girard's proof nets for classical linear logic as an analogue of natural deduction. It is also shown that linear logic is undecidable. A final section, contributed by D. Roorda, presents a proof of strong normalization for cut elimination in linear logic. Linear logic is of interest to logicians and computer scientists, and shows links with many other topics, such as coherence theorems in category theory, the theory of Petri nets, and abstract computing machines without garbage collection
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Legendre Polynomials
George C. Clark and Stuart W. Churchill
University of Michigan Press, 1957
A research program on the engineering applications of light-scattering has been in progress in the Department of Chemical and Metallurgical Engineering of the University of Michigan. As part of this program it has been found necessary to compute various mathematical functions that occur in the Mie solution for the scattering of electromagnetic radiation by single spheres. The Legendre polynomials arise from many problems in mathematical physics, particularly from those involving the Laplace equation in spherical coordinates.
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Liberty's Grid
A Founding Father, a Mathematical Dreamland, and the Shaping of America
Amir Alexander
University of Chicago Press, 2024
The surprising history behind a ubiquitous facet of the United States: the gridded landscape.
 
Seen from an airplane, much of the United States appears to be a gridded land of startling uniformity. Perpendicular streets and rectangular fields, all precisely measured and perfectly aligned, turn both urban and rural America into a checkerboard landscape that stretches from horizon to horizon. In evidence throughout the country, but especially the West, the pattern is a hallmark of American life. One might consider it an administrative convenience—an easy way to divide land and lay down streets—but it is not. The colossal grid carved into the North American continent, argues historian and writer Amir Alexander, is a plan redolent with philosophical and political meaning.
 
In 1784 Thomas Jefferson presented Congress with an audacious scheme to reshape the territory of the young United States. All western lands, he proposed, would be inscribed with a single rectilinear grid, transforming the natural landscape into a mathematical one. Following Isaac Newton and John Locke, he viewed mathematical space as a blank slate on which anything is possible and where new Americans, acting freely, could find liberty. And if the real America, with its diverse landscapes and rich human history, did not match his vision, then it must be made to match it.
 
From the halls of Congress to the open prairies, and from the fight against George III to the Trail of Tears, Liberty’s Grid tells the story of the battle between grid makers and their opponents. When Congress endorsed Jefferson’s plan, it set off a struggle over American space that has not subsided. Transcendentalists, urban reformers, and conservationists saw the grid not as a place of possibility but as an artificial imposition that crushed the human spirit. Today, the ideas Jefferson associated with the grid still echo through political rhetoric about the country’s founding, and competing visions for the nation are visible from Manhattan avenues and Kansan pastures to Yosemite’s cliffs and suburbia’s cul-de-sacs. An engrossing read, Liberty’s Grid offers a powerful look at the ideological conflict written on the landscape.
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Lie Algebras and Locally Compact Groups
Irving Kaplansky
University of Chicago Press, 1971
This volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, "Lie Algebras," the structure theory of semi-simple Lie algebras in characteristic zero is presented, following the ideas of Killing and Cartan. Chapter 2, "The Structure of Locally Compact Groups," deals with the solution of Hilbert's fifth problem given by Gleason, Montgomery, and Zipplin in 1952.
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Living by Numbers
In Defence of Quantity
Steven Connor
Reaktion Books, 2016
How do we really think about the world? We may use words to tell stories about it or draw pictures to represent it, but one thing we do far more than either of those is make calculations of the things that are in it—and to do that we use numbers. Numbers give shape and texture to almost everything we feel, say, dream, and do, a fact that Steven Connor explores in this qualitative assessment of the quantifiable. Looking at how numbers play a part in nearly every aspect of our lives, he offers a fascinating portrait of the world as a world of numbers.
            Connor explores a host of thought-provoking aspects of our numerical existence. He looks at the unexpected oddities that shape the loneliest number—the number one. He looks at counting as a human phenomenon and the ways we negotiate crowds, swarms, and multitudes. He demonstrates the work of calculation as it lies at the heart of poetry, jokes, painting, and music. He shows how we use numbers to adjust to uncertainty and chance and how they help us visualize the world in diagrammatic ways, and he unveils how numbers even help us think about death. Altogether, Connor brings into relief an aspect of our lives so ubiquitous that we often can’t see it, unveiling a rich new way of thinking about our existence.
 
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Logic and Automata
History and Perspectives
Edited by Jörg Flum, Erich Grädel, and Thomas Wilke
Amsterdam University Press, 2008
Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d’horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field.
 
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Logic and Representation
Robert C. Moore
CSLI, 1993
Logic and Representation brings together a collection of essays, written over a period of ten years, that apply formal logic and the notion of explicit representation of knowledge to a variety of problems in artificial intelligence, natural language semantics, and the philosophy of mind and language. Particular attention is paid to modeling and reasoning about knowledge and belief, including reasoning about one's own beliefs, and the semantics of sentences about knowledge and belief. Robert C. Moore begins by exploring the role of logic in artificial intelligence, considering logic as an analytical tool., as a basis for reasoning systems, and as a programming language. He then looks at various logical analyses of propositional attitudes, including possible-world models, syntactic models, and models based on Russellian propositions. Next Moore examines autoepistemic logic, a logic for modeling reasoning about one's own beliefs. Rounding out the volume is a section on the semantics of natural language, including a survey of problems in semantic representation; a detailed study of the relations among events, situations, and adverbs; and a presentation of a unification-based approach to semantic interpretation. Robert C. Moore is principal scientist of the Artificial Intelligence Center of SRI International.
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Logic and Visual Information
Eric M. Hammer
CSLI, 1995

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Logic Colloquium '92
Edited by Lázló Csirmaz, Dov M. Gabbay, and Maarten de Rijke
CSLI, 1995
Logic Colloquium '92, the European Summer Meeting of the Association for Symbolic Logic, was held in Veszpre;m, Hungary, in August 1992. Two of the main themes of the event were algebraic logic, and axiomatisability and decidability of logical systems. The present volume contains a selection of papers that grew out of invited and contributed talks on these themes. Most of the papers have a strong interdisciplinary flavour as they investigate logical properties of formal systems by studying algebraic properties of corresponding classes of algebras, or vice versa. The remaining papers focus on connected areas from model theory and the combination of logics. This is a useful and timely volume on algebraic logic and related areas, with contributions by leading people in the field.
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Logic, Logic, and Logic
George Boolos
Harvard University Press, 1998
George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.
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The Logic of Decision
Richard C. Jeffrey
University of Chicago Press, 1983
"[This book] proposes new foundations for the Bayesian principle of rational action, and goes on to develop a new logic of desirability and probabtility."—Frederic Schick, Journal of Philosophy
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Logics of Time and Computation
Robert Goldblatt
CSLI, 1992
"This is a short but excellent introduction to modal, temporal, and dynamic logic....It manages to cover, in highly readable style, the basic completeness, decidability, and expressability results in a variety of logics of the three kinds considered." -Rohit Parikh, reviewing the first edition in the Journal of Symbolic Logic. Now revised and significantly expanded, this textbook introduces modal logic and examines the relevance of modal systems for theoretical computer science. Golblatt sets out a basic theory of normal modal and temporal propositional logics, including issues such as completeness proofs, decidability, first-order defiability, and canonicity. The basic theory is then applied to logics of discrete, dense, and continuous time; to the temporal logic of concurrent programs involving the connectives henceforth, next , anduntil; and to the dynamic logic of regular programs. New material for the second edition extends the temporal logic of concurrency to branching time, studying a system of Computational Tree Logic that formalizes reasoning about behavior. Dynamic logic is also extended to the case of concurrency, intorducing a connective for the parallel execution of commands. A seperate section is devoted to the quantificational dynamic logic. Numerous excercises are included for use in the classroom. Robert Goldblatt is a professor of pure mathematics at the Victoria University of Wellington, New Zealand. Center for the Study of Language and Information- Lecture Notes, Number 7
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