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.

Relative clause constructions express an event that functions as a modifier of a referent. As such, relative clause constructions share a participant with the matrix clause -- namely, the referent that they modify. Like other complex sentence constructions, relative clause constructions may be balanced or deranked. The primary differences in strategy involve the expression of the shared participant. The most common strategy is the externally headed strategy: the referent is expressed as a common noun phrase in the matrix clause, and in reduced or zero form in the relative clause. A small minority of languages use strategies that appear to form a continuum from internally headed to correlative to adjoined constructions. Events that function to modify a referent that is a very peripheral participant in the relative clause events form noun-modifying clause constructions; these constructions sometimes use a relative clause strategy. Relative clause construction strategies also systematically vary with respect to the semantic role of the referents in the relative clause event, which are ranked by the Accessibility Hierarchy. Relative clauses may have an anaphoric or indefinite head.

A predication prototypically predicates an event. Events have multiple participants in their semantic frame. Some participants are more central than others. The information packaging of event participants construes certain participants as core arguments and others as oblique arguments. Transitivity constructions are defined in terms of the prototypical expression of central participants as core argument phrases. ‘Subject’ and ‘object’ are defined crosslinguistically in terms of degree of topicality (salience) and force dynamics (subject acting on object). Basic argument encoding strategies are flagging, indexation, and word order. An exemplar approach to defining transitive constructions is taken, using the agentive change of state event of breaking as the exemplar event, following Haspelmath. Subject generally precedes verb and object in word order. Variation in alignment is based on the system of transitive and intransitive constructions, in terms of which core argument of the transitive construction the intransitive argument aligns with, including the rare case where the core arguments of intransitive constructions are split between transitive subject and object.

Speech act constructions bear a close functional relationship to modality and polarity, and also to the information packaging of clauses (Chapters 10–11). Declaratives are associated with the modal category of polarity: declaratives assert or deny the truth of a proposition. Interrogatives (questions, and also responses) are associated with identificational packaging: the information asked about is the focus. They are also associated with epistemic modality: they involve degrees of (un)certainty about an event. Imperative--hortative speech acts are associated with deontic modality: both express a future event that is being at least considered by an agent. Exclamations are associated with the mirative (expression of surprise), which in turn is associated with thetic information packaging. These functional relations between speech act, modality, and clausal information packaging are manifested in the sharing of morphosyntactic strategies between the related categories.