A Loop-Free Decision Procedure for Modal Propositional Logics K4, S4 and S5

An Axiomatic Account of Question Evocation: The Propositional Case

“…Although IEL gave rise to the so-called method of Socratic proofs and some logical calculi (for Classical Logic as well as non-classical logics) which are useful in proof-search (see e.g., [22][23][24][25]), the system PMC E , pertaining to one of the central notions of IEL, is barely useful in this respect. This is due to the presence of rule R 2 .…”

The Method of Socratic Proofs for Modal Propositional Logics: K5, S4.2, S4.3, S4F, S4R, S4M and G

“…It is characterized by the class of frames which are reflexive, transitive and satisfy the following condition (cf. [4]) 11 :…”

“…See also[11] where the author analyses the problem of loops, which is characteristic to transitive modal logics, within the framework of erotetic calculi 3. The notation we have used here for the names of the logics comes from[4].…”

Loop-free sequent calculus for modal logic K4

“…This method was first introduced in [3] for modal logic S4 and our aim is to extend it to the logic K4. For other methods of effective decision procedures the reader could refer to [1] or [2].…”