Logicality in natural language

Is there a relation of logical consequence in natural language? Logicality, in the philosophical literature, has been conceived of as a restrictive phenomenon that is at odds with the unbridled richness and complexity of natural language. This article claims that there is a relation of logical consequence in natural language, and moreover, that it is the subject matter of the bulk of current theories of formal semantics. I employ the framework of semantic constraints (Sagi in Log Anal 57(227):259–276, 2014), which generalizes the Tarskian definition of logical consequence. I apply the widely accepted criterion of invariance under isomorphisms (Sher in J. Symb Log 61(2):653–686, 1996) generalized to the framework of semantic constraints (Sagi in Bull Symb Log 28(1):104–132, 2022b), combined with a theory of Glanzberg (in Metasemantics: new essays on the foundations of meaning, 2014) to delineate the relation of logical consequence in natural language.