A Nonmonotonic Sequent Calculus for Inferentialist Expressivists

I am presenting a sequent calculus that extends a nonmonotonic consequence relation over an atomic language to a logically complex language. The system is in line with two guiding philosophical ideas: (i) logical inferentialism and (ii) logical expressivism. The extension defined by the sequent rules is conservative. The conditional tracks the consequence relation and negation tracks incoherence. Besides the ordinary propositional connectives, the sequent calculus introduces a new kind of modal operator that marks implications that hold monotonically. Transitivity fails, but for good reasons. Intuitionism and classical logic can easily be recovered from the system

Are "Modal Adverbs" automatically Modal Markers? The Case of French "Certainement" with its Epistemico-Modal and its Evidential Use

The French adverb certainement (‘certainly’) is labelled a “modal adverb”. It has two (sentence adverb) uses according to the literature, called “strong modal use” and “weak modal use”. The strong modal use is indeed strong (epistemico-)modal in that it indicates total certainty, whether subjective or intersubjective. What is called its “weak modal use” is shown to be an evidential use. It indicates primarily that the content qualified by the adverb results from a non-monotonic inference, performed by the speaker, whose conclusions are plausible, defeasible, and thus never totally certain. This is due to the presence of an evidential-inferential component in its meaning. As for the so-called weak modal element of “probability” in its meaning, we reanalyse it as “non- certainty” and argue it is an element of utterance meaning, a property of quasi-assertions to which non-monotonically inferred content gives rise. Finally, we claim that the adverb also has a meaning component that we call “epistemic posture of certainty”, shown to be different from epistemic modality. On the basis of three parameters and their values, we show how certainementcan be interpreted, in a series of contextual configurations, either as an instance of its epistemico- modal use or of its evidential use