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Logic is the study of truth and falsity, of theorem and proof, of validreasoning in any context. It’s also the foundation of all of computerscience, the very reasoning that you use when you write the condition of anif statement in a Java program, or when you design an algorithm to beat agrandmaster at chess. More concretely, logic is also the foundation of allcomputers. At its heart, a computer is a collection ofcarefully arranged wires that transport electrons (which serve as a physicalmanifestation of information) and “gates” (which serve asphysical manifestations of logical operations to manipulate thoseelectrons).
This book has introduced the mathematical foundations of computerscience—the conceptual building blocks of, among other things, thelarge, complex computational systems that have become central aspects of ourdaily lives, some of which have already genuinely and meaningfully improvedthe world in their own unique ways, profound and small. Understanding andreasoning about these fundamental building blocks is necessary for you tounderstand, develop, and evaluate the key ideas of these many newapplications of computer science, and introducing these foundations has beenthe underlying goal of this book.
Several kinds of relations between events often have distinct complex sentence constructions, in particular those involving degree, causation, factivity (epistemic stance), or a combination of these. Comparative and equative constructions compare degrees of a property predicated of two different referents. The strategy chosen depends on the strategy used for temporal complex sentences, at least for comparative constructions. Conditional constructions express a causal relation (content, epistemic, or speech act), but, unlike causal relations, also express a nonfactive (neutral or negative) epistemic stance toward the events. Past tense constructions are often recruited to express nonfactivity. Concessive constructions presuppose a causal relation that is unexpectedly violated; concessive conditional constructions are the nonfactive counterparts. Strategies use conjunctions recruited from conditionals or expressions of obstinacy, focus marking, and remarkable co-occurrence. Concessive conditionals use a scalar, alternative, or universal strategy to conceptualize the concessive conditional relation. Other relations, such as the comparative conditional, may also be conventionalized.