front cover of Algebras, Diagrams and Decisions in Language, Logic and Computation
Algebras, Diagrams and Decisions in Language, Logic and Computation
Edited by Kees Vermeulen and Ann Copestake
CSLI, 2002
This exemplary volume shows how the shared interests of three different research areas can lead to significant and fruitful exchanges: six papers each very accessibly present an exciting contribution to the study and uses of algebras, diagrams, and decisions, ranging from indispensable overview papers about shared formal members to inspirational applications of formal tools to specific problems. Contributors include Pieter Adriaans, Sergei Artemov, Steven Givant, Edward Keenan, Almerindo Ojeda, Patrick Scotto di Luzio, and Edward Stabler.
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front cover of Euclid and His Twentieth Century Rivals
Euclid and His Twentieth Century Rivals
Diagrams in the Logic of Euclidean Geometry
Nathaniel Miller
CSLI, 2007
Twentieth-century developments in logic and mathematics have led many people to view Euclid’s proofs as inherently informal, especially due to the use of diagrams in proofs. In Euclid and His Twentieth-Century Rivals, Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, computer scientists, and anyone interested in the use of diagrams in geometry.
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front cover of Logical Reasoning with Diagrams and Sentences
Logical Reasoning with Diagrams and Sentences
Using Hyperproof
Dave Barker-Plummer, Jon Barwise, and John Etchemendy
CSLI, 2016
The Logical Reasoning with Diagrams and Sentences courseware package teaches the principles of analytical reasoning and proof construction using a carefully crafted combination of textbook, desktop, and online materials. This package is sure to be an essential resource in a range of courses incorporating logical reasoning, including formal linguistics, philosophy, mathematics, and computer science.

Unlike traditional formal treatments of reasoning, this package uses both graphical and sentential representations to reflect common situations in everyday reasoning where information is expressed in many forms, such as finding your way to a location using a map and an address. It also teaches students how to construct and check the logical validity of a variety of proofs—of consequence and non-consequence, consistency and inconsistency, and independence—using an intuitive proof system which extends standard proof treatments with sentential, graphical, and heterogeneous inference rules, allowing students to focus on proof content rather than syntactic structure. Building upon the widely used Tarski’s World and Language, Proof and Logic courseware packages, Logical Reasoning with Diagrams and Sentences contains more than three hundred exercises, most of which can be assessed by the Grade Grinder online assessment service; is supported by an extensive website through which students and instructors can access online video lectures by the authors; and allows instructors to create their own exercises and assess their students’ work.

Logical Reasoning with Diagrams and Sentences is an expanded revision of the Hyperproof courseware package.
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front cover of Mathematical Reasoning with Diagrams
Mathematical Reasoning with Diagrams
Mateja Jamnik
CSLI, 2001
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.
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front cover of The Philosophical Status of Diagrams
The Philosophical Status of Diagrams
Mark Greaves
CSLI, 2001
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 history of mathematics which have driven the adoption of sentential representational styles over diagrammatic ones. In this book, the effects of historical forces on the evolution of diagrammatically-based systems of inference in logic and geometry are traced from antiquity to the early twentieth-century work of David Hilbert. From this exploration emerges an understanding that the present negative attitudes towards the use of diagrams in logic and geometry owe more to implicit appeals to their history and philosophical background than to any technical incompatibility with modern theories of logical systems.
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front cover of Semantic Properties of Diagrams and Their Cognitive Potentials
Semantic Properties of Diagrams and Their Cognitive Potentials
Atsushi Shimojima
CSLI, 2015
Why are diagrams sometimes so useful, facilitating our understanding and thinking, while at other times they can be unhelpful and even misleading? Drawing on a comprehensive survey of modern research in philosophy, logic, artificial intelligence, cognitive psychology, and graphic design, Semantic Properties of Diagrams and Their Cognitive Potentials reveals the systematic reasons for this dichotomy, showing that the cognitive functions of diagrams are rooted in the characteristic ways they carry information. In analyzing the logical mechanisms behind the relative efficacy of diagrammatic representation, Atsushi Shimojima provides deep insight into the crucial question: What makes a diagram a diagram?
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