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Description: Language employs various coordinators to connect propositions, a subset of which are "logical" in nature and thus analogous to the truth operators of formal logic. We here focus on two linguistic connectives and their negations: conjunction "and" and (inclusive) disjunction "or". Linguistic connectives exhibit a truth-conditional component as part of their meaning (their semantics), but their use in context can give rise to various implicatures and presuppositions (the domain of pragmatics) as well as to inferences that go beyond semantic/pragmatic properties (as in reasoning processes). We provide a comprehensive review of the role of the logical connectives in language and argue that three sets of factors --semantic, pragmatic, and those related to reasoning-- are separate and separable, though some details may differ cross-linguistically. As a way to showcase the argument, we present two experiments in language comprehension in Spanish wherein pragmatic content was minimised and reasoning processes neutered, thus potentially highlighting what might be the default meanings of the connectives under study. In Experiment 1 we show that the conjunctive (true-true) reading of inclusive disjunction is available in positive contexts other than in exceptional cases such as downward entailing and free choice contexts, contrary to what has been claimed in the literature. In Experiment 2 we show that negated conjunctions and disjunctions in Spanish can easily receive the same interpretation when contrasted against the same context and, moreover, that these interpretations match those obtained in English, despite claims from the literature that linguistic connectives and a negative operator interact differently in English and Romance languages.