Tableaux for the Logic of Strategically Knowing How
Yanjun Li
TL;DR
This paper introduces a tableau method for multi-agent logic of strategically knowing-how, proving its soundness, completeness, and PSPACE decidability, advancing formal reasoning about strategic knowledge.
Contribution
It develops a tableau procedure for multi-agent strategically knowing-how logic, establishing its theoretical properties and decision complexity.
Findings
Tableau procedure is sound and complete.
Satisfiability can be decided in PSPACE.
Advances formal reasoning in multi-agent strategic knowledge.
Abstract
The logic of goal-directed knowing-how extends the standard epistemic logic with an operator of knowing-how. The knowing-how operator is interpreted as that there exists a strategy such that the agent knows that the strategy can make sure that p. This paper presents a tableau procedure for the multi-agent version of the logic of strategically knowing-how and shows the soundness and completeness of this tableau procedure. This paper also shows that the satisfiability problem of the logic can be decided in PSPACE.
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