Complexity of Two-Variable Dependence Logic and IF-Logic

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 Π 0 1 and Σ 0 1-complete, respectively. 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

Hierarchies in independence and inclusion logic with strict semantics

“…• The Satisfiability problem for the two variable fragment of dependence logic was shown to be NEXPTIME-complete in [15].…”

Dependence Logic: A survey of some recent work

“…For example, if then the satisfiability problem is complete for non‐deterministic exponential time (NEXPTIME) (Sevenster, ). In (Kontinen et al, ), the two‐variable fragment of dependence logic was studied. The two‐variable fragment FO 2 of first‐order logic, and its many extensions, have been widely studied due to their connections to modal logic and to many practical applications.…”

Decidability of predicate logics with team semantics

“…While the descriptive complexity of most known logics based on team semantics is understood reasonably well, the complexity of related satisfiability problems has received somewhat less attention. The satisfiability problem of the two-variable fragment of dependence logic and IF-logic have been studied in [18]. It is shown that while the two-variable IF-logic is undecidable, the corresponding fragment of dependence logic is NEXPTIME-complete.…”

“…Furthermore, we prove that the validity problem of two-variable dependence logic is undecidable; this result is the main result of the paper. The problem has been open for some time in the team semantics literature and has been explicitly posed in, e.g., [5], [18], [25], and elsewhere.…”