A core activity in information systems development involves building a conceptual model of the domain that an information system is intended to support. Such models are created using a conceptual-modeling (CM) grammar. Just as high-quality conceptual models facilitate high-quality systems development, high-quality CM grammars facilitate high-quality CM. This paper provides a new perspective on ways to improve the quality of the semantics of CM grammars. For many years, the leading approach to this topic has relied on ontological theory. We show, however, that the ontological approach captures only half the story; it needs to be coupled with a logical approach. We explain how the ontological and logical qualities of CM grammars interrelate. Furthermore, we outline three contributions of a logical approach to evaluating the quality of CM grammars: a means of seeing some familiar CM problems in simpler ways, illumination of new problems, and proving the benefit of modifying existing CM grammars in particular ways. We demonstrate these benefits in the context of the Entity-Relationship grammar. More generally, our paper opens a new area of research with many opportunities for future research and practice.