Logical inference in English: A preliminary analysis

The perfect fit of syntactic derivability and logical consequence in first-order logic is one of the most celebrated facts of modern logic. In the present flurry of attention given to the semantics of natural language, surprisingly little effort has been focused on the problem of logical inference in natural language and the possibility of its completeness. Even the traditional theory of the syllogism does not give a thorough analysis of the restricted syntax it uses.My objective is to show how a theory of inference may be formulated for a fragment of English that includes a good deal more than the classical syllogism. The syntax and semantics are made as formal and as explicit as is customary for artificial formal languages. The fragment chosen is not maximal but is restricted severely in order to provide a clear overview of the method without the cluttering details that seem to be an inevitable part of any grammar covering a substantial fragment of a natural language. (Some readers may feel the details given here are too onerous.).