The article investigates the local tabularity of products of modal logics. It makes the following key observations:
Local tabularity of the factors L1 and L2 is necessary but not sufficient for local tabularity of the product L1 × L2. The simplest counterexample is the logic S5 × S5, which is not locally tabular despite both factors being locally tabular.
The authors provide extra semantic and axiomatic conditions that give criteria for local tabularity of the product of two locally tabular logics:
They apply these criteria to identify new families of locally tabular products, including:
The article also gives a semantic argument for the known result that all proper extensions of S5 × S5 are locally tabular.
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