A Compositional Generalisation of Adams Logic of Conditionals

The paper shows that Adams Logic of Conditional may be so generalised that it allows for considering the conditional connective as a compositional connective ina a Partial Modal Logic. A general Semantics for that Logic is provided. It is shown that every sentence may be represnted as a simple conditional of the form (A -> C), where both A and C belong to the modal system S5. Lewis Triviality Results do not apply in this context due to the fact that sentences may lack a truth-value.