S5 x S5 x S5 lacks the finite model property
Agi Kurucz · 2000
It follows from algebraic results of Maddux that every multi-modal logic L such that [S5, S5,..., S5] ⊆ L ⊆ S5 n is undecidable, whenever n ≥ 3. This implies that the product logic S5×S5×S5 does not have the product finite model property. Here we answer a question of Gabbay and Shehtman by showing that S5 × S5 × S5 also lacks the ‘real ’ finite model property (fmp). We prove that every logic L from the above interval lacks the fmp. (In algebraic setting: If V is a variety of n-dimensional diagonalfree cylindric algebras which contains all the representables then V does not have the finite algebra property.) 1 Introduction and the result Multi-modal logics are of growing importance in many areas of computer science, artificial intelligence, knowledge representation and reasoning, and linguistics. In this paper we discuss the finite model property of n-modal logics: