An approach to logical omniscience which explicitly takes computational complexity into account is proposed by Artemov and Kuznets (2014). They suggest that a logic of knowledge should formalize not just statements of the form ‘\(\phi\) is knowable by agent \(i\)’ but also ones of the form ‘\(\phi\) is known by agent \(i\) on the basis of evidence \(t\)’. They then exhibit a family of Justification Logics for reasoning about statements of the latter form which satisfy the so-called Strong Logical Omniscience Test – i.e. if a statement of the form ‘\(\phi\) is known by agent \(i\) on the basis of evidence \(t\)’ is derivable, then a proof of \(\phi\) can be found in time polynomial in the size of \(t\) and \(\phi\).