Modal logic
On compositionality and its limitations
ACM Transactions on Computational Logic (TOCL)
Model theory makes formulas large
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
LTL-Model-Checking via model composition
RP'12 Proceedings of the 6th international conference on Reachability Problems
An Optimal Gaifman Normal Form Construction for Structures of Bounded Degree
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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We show that the satisfiability problem for the two-dimensional extension KxK of unimodal K is nonelementary, hereby confirming a conjecture of Marx and Mikulas from 2001. Our lower bound technique allows us to derive further lower bounds for many-dimensional modal logics for which only elementary lower bounds were previously known. We also derive nonelementary lower bounds on the sizes of Feferman-Vaught decompositions w.r.t. product for any decomposable logic that is at least as expressive as unimodal K. Finally, we study the sizes of Feferman-Vaught decompositions and formulas in Gaifman normal form for fixed-variable fragments of first-order logic.