The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese [24]. We prove that the following problem is decidable: Input: (i) A monadic second order logic sentence α, and (ii) a sentence β in the two-variable fragment of first order logic extended with counting quantifiers. The vocabularies of α...

We introduce a modal language L which is obtained from standard modal logic by adding the Boolean operators on accessibility relations, the identity relation, and the converse of relations. It is proved that L has the same expressive power as the two-variable fragment FO of first-order logic, but speaks less succinctly about relational structures: if the number of relations is bounded, then L-s...

The double-cued task switching procedure has recently been introduced as a new way to measure externally cued switch costs. In the present individual differences study, two hundred fifty young adults completed measures of task switching, inhibition, and long-term memory. A latent variable approach was taken to examine the relationships among these cognitive measures. Decomposing the externally ...

Communicating finite-state machines are a fundamental, well-studied model of finite-state processes that communicate via unbounded first-in first-out channels. We show that they are expressively equivalent to existential MSO logic with two first-order variables and the order relation.

We prove that the positive fragment of first-order intuitionistic logic in the language with two variables and a single monadic predicate letter, without constants and equality, is undecidable. This holds true regardless of whether we consider semantics with expanding or constant domains. We then generalise this result to intervals [QBL,QKC] and [QBL,QFL], where QKC is the logic of the weak law...

The two-variable-fragment L≈ of first order logic is the set of formulas that do not contain function symbols, that possibly contain equality, and that contain at most two variables. This paper shows how resolution theorem-proving techniques can be used to provide an algorithm for deciding whether any given formula in L≈ is satisfiable. Previous resolution-based techniques could deal only with ...

We prove that the two-variable fragment of first-order intuitionistic logic is undecidable, even without constants and equality. We also show that the twovariable fragment of a quantified modal logic L with expanding first-order domains is undecidable whenever there is a Kripke frame for L with a point having infinitely many successors (such are, in particular, the first-order extensions of pra...

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...

Data trees are trees in which each node, besides carrying a label from a finite alphabet, also carries a data value from an infinite domain. They have been used as an abstraction model for reasoning tasks on XML and verification. However, most existing approaches consider the case where only equality test can be performed on the data values. In this paper we study data trees in which the data v...

We consider the satisfiability problem for the two-variable fragment of first-order logic over finite unranked trees. We work with signatures consisting of some unary predicates and the binary navigational predicates ↓ (child), → (right sibling), and their respective transitive closures ↓+, → . We prove that the satisfiability problem for the logic containing all these predicates, FO[↓, ↓+,→,→ ...