Logic has been intertwined with the study of language and meaning since antiquity, and such connections persist in present day research in linguistic theory (formal semantics) and cognitive psychology (e.g., studies of human reasoning). However, few studies in cognitive neuroscience have addressed logical dimensions of sentence-level language processing, and none have directly compared these aspects of processing with syntax and lexical/conceptual-semantics. We used ERPs to examine a violation paradigm involving "Negative Polarity Items" or NPIs (e.g., ever/any), which are sensitive to logical/truth-conditional properties of the environments in which they occur (e.g., presence/absence of negation in: John hasn't ever been to Paris, versus: John has *ever been to Paris). Previous studies examining similar types of contrasts found a mix of effects on familiar ERP components (e.g., LAN, N400, P600). We argue that their experimental designs and/or analyses were incapable of separating which effects are connected to NPI-licensing violations proper. Our design enabled statistical analyses teasing apart genuine violation effects from independent effects tied solely to lexical/contextual factors. Here unlicensed NPIs elicited a late P600 followed in onset by a late left anterior negativity (or "L-LAN"), an ERP profile which has also appeared elsewhere in studies targeting logical semantics. Crucially, qualitatively distinct ERP-profiles emerged for syntactic and conceptual semantic violations which we also tested here. We discuss how these findings may be linked to previous findings in the ERP literature. Apart from methodological recommendations, we suggest that the study of logical semantics may aid advancing our understanding of the underlying neurocognitive etiology of ERP components.