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arXiv · 1104.3148

Complexity of two-variable Dependence Logic and IF-Logic

Juha Kontinen·Antti Kuusisto·Peter Lohmann·Jonni Virtema
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Abstract

We study the two-variable fragments D^2 and IF^2 of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D^2, both problems are NEXPTIME-complete, whereas for IF^2, the problems are undecidable. We also show that D^2 is strictly less expressive than IF^2 and that already in D^2, equicardinality of two unary predicates and infinity can be expressed (the latter in the presence of a constant symbol). This is an extended version of a publication in the proceedings of the 26th Annual IEEE Symposium on Logic in Computer Science (LICS 2011).

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Juha Kontinen, Antti Kuusisto, Peter Lohmann, Jonni Virtema. 2011-04-15. Complexity of two-variable Dependence Logic and IF-Logic. https://arxiv.org/abs/1104.3148

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