Other answers refer to the classical paradigms. My answer will refer to a more recent, computation-centric paradigm. Distributional semantics may be taken as the observables sampled from a mixing process. The inferential semantics of such a scheme derive from the latent model structure, which is accessible by Monte Carlo , spectral, or constraint-satisfying inference, but in any case should be expressible as operator algebras over the space of factors underlying the conditional distributions of utterances.
In some application domains, e.g. machine translation, text generation, the Neural model has recently taken the stage by storm, demonstrating overwhelming out-performance on a preponderance of important benchmarks. Responsible professionals, therefore, are in process of reorienting themselves to align to the "deep learning" paradigm, which is consonant with an essentially distributional+spectral representation and inference schema. Rather than "standardizing" to an (imposed) crisp logical representation, such schemata let the data derive a representation - one more generally adequate to the capture of inherent ambiguities and other semantic phenomena which are particularly intractable in FoL decorated with simply typed lambda calculus, for example.
Which paradigm is most productive? Surely this will depend on application. If early disambiguation contributes strongly to mitigating loses, a combinatorial logical semantics (q.v. the Groningen Meaning Bank) is a good bet. If carrying ambiguities along through the chain of inference is helpful (even if only as a form of regularization), then a highly parametric vector space representation is likely to capture more of the underlying logical dynamics of agent linguistic processes.
