One-Dimensional Fragment over Words and Trees

Abstract

One-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential (universal) quantifiers that leave at most one variable free. We investigate this fragment over words and trees, presenting a complete classification of the complexity of its satisfiability problem for various navigational signatures, and comparing its expressive power with other important formalisms. These include the two-variable fragment with counting and the unary negation fragment.

Full version of [1] Emanuel Kieronski: One-Dimensional Logic over Words. CSL 2016: 38:1-38:15 [2] Emanuel Kieronski, Antti Kuusisto: One-Dimensional Logic over Trees. MFCS 2017: 64:1-64:13

References in corpus (3)

• Two-variable Logic with Counting and a Linear Order
• Unary negation
• Satisfiability of the Two-Variable Fragment of First-Order Logic over Trees