A Partial Modal Semantics for the Adams Logic of Indicative Conditionals

Adams p-entailment provides a probabilistic extension of sentential logical consequence to simple indicative conditionals. Adams approach, taken together with David Lewis’ Triviality Results, supports the view that indicative conditionals of the form p ⇒ q lack any truth-value (NTV thesis). In this paper, by providing a new partial modal semantics for sentential logic that encompasses Adams Logic, both the NTV thesis and the opposite view (according to which indicative conditionals always bear a truth-value) are questioned. Moreover, since every probability function P defined on the underlying algebraic structure satisfies the equation P(p ⇒ q) = P(q |p) whenever P(p) > 0, Lewis’ Triviality Results are also challenged.