On axiomatising products of Kripke frames, part II

We generalise some results of [7, 5] and show that if L is an -modal logic (for some ordinal 3) such that (i) L contains the product logic K and (ii) the product of -many trees of depth one and with arbitrary large finite branching is a frame for L, then any axiomatisation of L must contain infinitely many propositional variables. As a consequence we obtain that product logics like K, K4 , S4 , GL , and Grz cannot be axiomatised using finitely many propositional variables, whenever 3.

• Type: Conference
• Year: 2008
• Where: AIML
• Authors: Agi Kurucz
• Keywords: AIML 2008, Large Finite Branching, Logical Reasoning, Product Logics, Propositional Variables