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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.

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

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.

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.

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.

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.

"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