Two Variable First-Order Logic over Ordered Domains

One-Dimensional Logic over Trees

A one-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential quantifiers that leave at most one variable free. This fragment contains two-variable logic, and it is known that over words both formalisms have the same complexity and expressive power. Here we investigate the one-dimensional fragment over trees. We consider unranked unordered tr...

Two Variable First-Order Logi over Ordered Domains

Optimal Tableau Systems for Propositional Neighborhood Logic over All, Dense, and Discrete Linear Orders

In this paper, we focus our attention on tableau systems for the propositional interval logic of temporal neighborhood (Propositional Neighborhood Logic, PNL for short). PNL is the proper subset of Halpern and Shoham’s modal logic of intervals whose modalities correspond to Allen’s relations meets and met by. We first prove by a modeltheoretic argument that the satisfiability problem for PNL ov...

Two-Variable Logic on 2-Dimensional Structures

This paper continues the study of the two-variable fragment of first-order logic (FO2) over twodimensional structures, more precisely structures with two orders, their induced successor relations and arbitrarily many unary relations. Our main focus is on ordered data words which are finite sequences from the set Σ×D where Σ is a finite alphabet and D is an ordered domain. These are naturally re...

Two-variable Logic with Counting and a Linear Order

We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of two linear orders (in the presence of two other binary symbols). In the case of one linear order it is NExpTime-complete, even in the presence of the successor...