The use of diagrams in logic and geometry has encountered resistance in recent years. For a proof to be valid in geometry, it must not rely on the graphical properties of a diagram. In logic, the teaching of proofs depends on sentenial representations, ideas formed as natural language sentences such as "If A is true and B is true...." No serious formal proof system is based on diagrams.
This book explores the reasons why structured graphics have been largely ignored in contemporary formal theories of axiomatic systems. In particular, it elucidates the systematic forces in the intellectual...

The papers collected here focus on probabilistic causality, addressing topics such as the search for causal mechanisms, epistemic and metaphysical views of causality, Bayesian nets and causal dependence, and causation in the special sciences. Some papers stress the statistical analysis of probabilistic data; others address causal issues in physics, with an emphasis on physical processes that are also probabilistic i.e., stochastic processes.
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Mathematicians at every level use diagrams to prove theorems. "Mathematical Reasoning with Diagrams" investigates the possibilities of mechanizing this sort of diagrammatic reasoning in a formal computer proof system, even offering a semi-automatic formal proof system called Diamond which allows users to prove arithmetical theorems using diagrams."

In our multimedia age, text description presents many conceptual problems: texts, as cultural objects, cannot be interpreted without descriptions of genre, communicative conditions, and language, which positivist approaches have proved unable to provide. "Semantics for Descriptions" addresses itself as much to linguists as to computer scientists, arguing that rational hermeneutics can offer better descriptive methods by allowing the theoretical and practical conditions of text interpretation to be defined.

This volume, sixth in a series of collected works by world-renowned computer scientist Donald E. Knuth, assembles approximately two dozen of his pioneering contributions to the field of computer languages, including papers on ALGOL, SOL, Runcible, and FORTRAN. Papers on the early development of programming languages, the history of writing compilers, the characterization of parenthesis languages, and the semantics of context-free languages are also included.

With unusual structural characteristics, Finnish and Saami offer interesting challenges to linguistic theories formulated around more popular languages. Grammatically, for instance, languages in the Finnic and Saami group utilize extensive systems of case inflection on nouns to signal a broad variety of relations that in almost all other languages require additional words. Phonologically, as another example, the phenomenon of "consonant gradation" is of particular interest to linguists.
This volume is the first to examine the phonology, morphology, syntax, and semantics of Finnic and...

This book focuses on the semantic particularities of the French language, covering five empirical themes: determiners, adverbs, tense and aspect, negation, and information structure. The specialists contributing here including general linguists in France and French linguists in the Netherlands take formal approaches to semantics and its interface with syntax and pragmatics, highlighting meaning in its relation to both structure and use. Their results should be of particular interest to French and Romance linguists who want to study French from a formal semantic perspective and to general...

What does it mean to have visual intuition? Can we gain geometrical knowledge by using visual reasoning? And if we can, is it because we have a faculty of intuition? In" After Euclid," Jesse Norman reexamines the ancient and long-disregarded concept of visual reasoning and reasserts its potential as a formidable tool in our ability to grasp various kinds of geometrical knowledge. The first detailed philosophical case study of its kind, this text is essential reading for scholars in the fields of mathematics and philosophy.

This volume explores how the effectiveness of communication is shaped by aspects of semantics and pragmatics such as compositionality, the role of the speaker and hearer, and the acquisition of meaning. "Optimal Communication "surveys recent research in the fields of syntax, semantics, and pragmatics, and draws from optimality theory to argue that optimal meanings result from a compromise between competing constraints. "Optimal Communication" will be an invaluable resource for students in cognitive science, linguistics, and natural language semantics.

This anthology of essays from the inventor of literate programming is a survey of Donald Knuth's papers on computer science. Donald Knuth's influence in computer science ranges from the invention of literate programming to the development of the TeX programming language. One of the foremost figures in the field of mathematical sciences, his papers are widely referenced and stand as milestones of development over a wide range of topics. This collection focuses on Professor Knuth's published science papers that serve as accessible surveys of their subject matter. It includes articles on the...