Related papers: On the Mints Hierarchy in First-Order Intuitionist…
We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…
We study first-order logic (FO) over the structure consisting of finite words over some alphabet $A$, together with the (non-contiguous) subword ordering. In terms of decidability of quantifier alternation fragments, this logic is…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain which can be compared wrt. equality. As the satisfiability problem for this logic is undecidable in general, in…
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,…
During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of…
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in…
We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply…
While modal extensions of decidable fragments of first-order logic are usually undecidable, their monodic counterparts, in which formulas in the scope of modal operators have at most one free variable, are typically decidable. This only…
The study of various decision problems for logic fragments has a long history in computer science. This paper is on the membership problem for a fragment of first-order logic over infinite words; the membership problem asks for a given…
We introduce a new decidable fragment of first-order logic with equality, which strictly generalizes two already well-known ones -- the Bernays-Sch\"onfinkel-Ramsey (BSR) Fragment and the Monadic Fragment. The defining principle is the…
We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction…
We consider the class of languages defined in the 2-variable fragment of the first-order logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier…
We introduce a novel decidable fragment of first-order logic. The fragment is one-dimensional in the sense that quantification is limited to applications of blocks of existential (universal) quantifiers such that at most one variable…
We consider first-order logics of sequences ordered by the subsequence ordering, aka sequence embedding. We show that the \Sigma_2 theory is undecidable, answering a question left open by Kuske. Regarding fragments with a bounded number of…
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…
Temporal logics for the specification of information-flow properties are able to express relations between multiple executions of a system. The two most important such logics are HyperLTL and HyperCTL*, which generalise LTL and CTL* by…
We give a new proof of a theorem of Mints that the positive fragment of minimal predicate logic is decidable. The idea of the proof is to replace the eigenvariable condition of sequent calculus by an appropriate scoping mechanism. The…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
We characterize the languages in the individual levels of the quantifier alternation hierarchy of first-order logic with two variables by identities. This implies decidability of the individual levels. More generally we show that the…