A modal logic for non-deterministic discourse processing (Q1961953)

Inspired by context-dependence of interpreting an arbitrary English sentence, the author develops a Kripkean modal logic \({\mathcal L}_0\) that makes it possible to treat statements of the form \[ \text{` ``}e\text{ may'' translate to a logical form entailing }\varphi \text{'} \] as modal formulas. The most important basic notion is Stage, which is a subset of the Cartesian product of \(E^n\) (sequences \(s_e\) of English expressions) and \(\Phi^n\) (sequences \(s_\varphi\) of `logical forms'), where the intended interpretation is that the membership of \(\langle s_e,s_\varphi\rangle\) in Stage means: a processor \(\alpha\) accepting \(s_e\) may guess \(s_\varphi\). The system is nondeterministic. The problems solved in the article concern dynamic semantics, presuppositions, ambiguity and persistence. Decidability is proved, an axiomatization is presented. Further problems to be solved are suggested in the conclusion.