Axiomatization and complexity of modal logic with knowing-what operator on model class K

TL;DR

This paper develops an axiomatization and analyzes the complexity of a modal logic that includes a 'knowing-what' operator, extending standard epistemic logic to arbitrary models and establishing PSPACE-completeness for its satisfiability problem.

Contribution

It provides an axiomatization and tableau method for the modal logic with 'knowing-what' on arbitrary models, and determines the PSPACE-completeness of its satisfiability problem.

Findings

Axiomatization of the logic on arbitrary models

Tableau method for the logic

Satisfiability problem is PSPACE-complete

Abstract

Standard epistemic logic studies propositional knowledge, yet many other types of knowledge such as "knowing whether", "knowing what", "knowing how" are frequently and widely used in everyday life as well as academic fields. In "Conditionally Knowing What" by Wang and Fan, an axiomatization of the epistemic logic with both regular "knowing that" operator and "conditionally knowing what" operator is given. Then the decidability and complexity of this logic command our study. In this paper, we direct our attention to the arbitrary models instead of epistemic models, thus making things clearer, and then give a axiomatization and a tableau for the modal logic with same operators on arbitrary Kripke models. Given the tableau of this logic, the complexity of the satisfiability problem of this logic is PSPACE-complete.