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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.

Modal logic is the study of modalities—expressions that qualify assertions about the truth of statements—like some ordinary language phrases and mathematically motivated expressions. The study of modalities dates from antiquity, but has been most actively pursued in the last three decades. This volume collects together a number of Golblatt's papers on modal logic, beginning with his work on the duality between algebraic and set-theoretic models, and including two new articles, one on infinitary rules of inference, and the other about recent results on the relationship between modal logic and first-order logic.

After the Vietnam War, the U.S. Army considered counterinsurgency (COIN) a mistake to be avoided. Many found it surprising, then, when setbacks in recent conflicts led the same army to adopt a COIN doctrine. Scholarly debates have primarily employed existing theories of military bureaucracy or culture to explain the army’s re-embrace of COIN, but Peter Campbell advances a unique argument centering on military realism to explain the complex evolution of army doctrinal thinking from 1960 to 2008.

In five case studies of U.S. Army doctrine, Campbell pits military realism against bureaucratic and cultural perspectives in three key areas—nuclear versus conventional warfare, preferences for offense versus defense, and COIN missions—and finds that the army has been more doctrinally flexible than those perspectives would predict. He demonstrates that decision makers, while vowing in the wake of Vietnam to avoid (COIN) missions, nonetheless found themselves adapting to the geopolitical realities of fighting “low intensity” conflicts. In essence, he demonstrates that pragmatism has won out over dogmatism. At a time when American policymakers remain similarly conflicted about future defense strategies, Campbell’s work will undoubtedly shape and guide the debate.
 

In Modal Logic for Open Minds, Johan van Benthem provides an up-to-date introduction to the field of modal logic, outlining its major ideas and exploring the numerous ways in which various academic fields have adopted it. Van Benthem begins with the basic theories of modal logic, semantics, bisimulation, and axiomatics, and also covers more advanced topics, such as expressive power and computational complexity. The book then moves to a wide range of applications, including new developments in information flow, intelligent agency, and games. Taken together, the chapters show modal logic at the crossroads of philosophy, mathematics, linguistics, computer science, and economics. Most of the chapters are followed by exercises, making this volume ideal for undergraduate and graduate students in philosophy, computer science, symbolic systems, cognitive science, and linguistics.