Inessential Features, Ineliminable Features, and Modal Logics for Model Theoretic Syntax

While monadic second-order logic (MSO) has played a prominent role in model theoretic syntax, modal logics have been used in this context since its inception. When comparing propositional dynamic logic (PDL) to MSO over trees, Kracht (1997) noted that there are tree languages that can be defined in MSO that can only be defined in PDL by adding new features whose distribution is predictable. He named such features "inessential features". We show that Kracht's observation can be extended to other modal logics of trees in two ways. First, we demonstrate that for each stronger modal logic, there exists a tree language that can only be defined in a weaker modal logic with inessential features. Second, we show that any tree language that can be defined in a stronger modal logic, but not in some weaker modal logic, can be defined with inessential features. Additionally, we consider Kracht's definition of inessential features more closely. It turns out that there are featur...

• Type: Journal
• Year: 2008
• Where: JOLLI
• Authors: Hans-Jörg Tiede
• Keywords: JOLLI 2008, Logic, Modal Logic, Monadic Second-order Logic