Propositional Epistemic Logics with Quantification Over Agents of Knowledge (An Alternative Approach)

In the previous paper with a similar title (see Shtakser in Stud Log 106(2):311-344, 2018), we presented a family of propositional epistemic logics whose languages are extended by two ingredients: (a) by quantification over modal (epistemic) operators or over agents of knowledge and (b) by predicate symbols that take modal (epistemic) operators (or agents) as arguments. We denoted this family by PEL(QK). The family PEL(QK) is defined on the basis of a decidable higher-order generalization of the loosely guarded fragment (HO-LGF) of first-order logic. And since HO-LGF is decidable, we obtain the decidability of logics of PEL(QK). In this paper we construct an alternative family of decidable propositional epistemic logics whose languages include ingredients (a) and (b). Denote this family by PEL(QK)alt</mml:msubsup>. Now we will use another decidable fragment of first-order logic: the two variable fragment of first-order logic with two equivalence relations (FO2+2E) [the decidability of FO2+2E was proved in Kieroski and Otto (J Symb Log 77(3):729-765, 2012)]. The families PEL(QK)alt and <mml:msub>PEL(QK) differ in the expressive power. In particular, we exhibit classes of epistemic sentences considered in works on first-order modal logic demonstrating this difference.