Extending possibility semantics with new operators

Identify, formalize, and axiomatize new logical operators that can be integrated with possibility semantics by exploiting refinement structure in posets (beyond flat sets of worlds), such as epistemic modals, indicative conditionals, counterfactuals, determinacy operators, and awareness operators; develop corresponding semantics, completeness results, and categorical bridges.

Background

Possibility semantics naturally supports operators that leverage partial information and refinement. While inquisitive disjunction is one such example, a broader suite of operators remains to be systematically incorporated.

The authors call for a program to expand the expressive power of possibility semantics with operators whose meaning depends on partiality and refinement, potentially connecting to established areas like epistemic logic, conditionals, and counterfactuals.