Frame Based Formulas for Intermediate Logics

In this paper we define a new notion of frame based formulas. We show that the well-known examples of formulas arising from a finite frame, such as the Jankov-de Jongh formulas, subframe formulas and cofinal subframe formulas, are all particular cases of the frame based formulas. We give a criterion for an intermediate logic to be axiomatizable by the frame based formulas and use this criterion to obtain a simple proof that every locally tabular intermediate logic is axiomatizable by the Jankov-de Jongh formulas. We also show that not every intermediate logic is axiomatizable by the frame based formulas.

• Type: Journal
• Year: 2008
• Where: SLOGICA
• Authors: Nick Bezhanishvili
• Keywords: Formulas, Intermediate Logic, Jankov-de Jongh Formulas, SLOGICA 2008