Tags:conditional logic, epistemic modality, Import-Export, modus ponens and validity
Abstract:
Slightly altering and extending McGee's semantics for conditionals, we define a ternary notion of validity for natural language arguments, which can be regarded as a unification of two kinds of validity in the literature. By the new notion of validity, an inference is not just valid or invalid, but valid or invalid under a set of assumptions. Based on this notion, we formulate the validity and invalidity of modus ponens.