 The propositional part of \(\mathbf{EIFL}\) involves the four operators \(\neg , {\sim}, \wedge\), and \(\vee\). Hintikka (2004b) raises the question of the algebraic structure induced by these operators, when any two truth equivalent sentences are identified. The operators \(\neg , \wedge\), and \(\vee\) give rise to a Boolean algebra – but what does the strong negation \({\sim}\) add to this structure? 