Related papers: Existential Second-Order Logic Over Graphs: A Comp…
Algorithmic meta-theorems explain the tractability of large classes of computational problems by linking logical expressibility with structural graph properties. While extensions of first-order logic such as FO+dp admit efficient model…
We characterise the sentences in Monadic Second-order Logic (MSO) that are over finite structures equivalent to a Datalog program, in terms of an existential pebble game. We also show that for every class C of finite structures that can be…
Monadic stability generalizes many tameness notions from structural graph theory such as planarity, bounded degree, bounded tree-width, and nowhere density. The sparsification conjecture predicts that the (possibly dense) monadically stable…
Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in…
We present new preservation theorems that semantically characterize the $\exists^k \forall^*$ and $\forall^k \exists^*$ prefix classes of first order logic, for each natural number $k$. Unlike preservation theorems in the literature that…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
A class of graph languages is definable in Monadic Second-Order logic (MSO) if and only if it consists of sets of models of MSO formul{\ae}. If, moreover, there is a computable bound on the tree-widths of the graphs in each such set, the…
We discuss the definability of finite graphs in first-order logic with two relation symbols for adjacency and equality of vertices. The logical depth $D(G)$ of a graph $G$ is equal to the minimum quantifier depth of a sentence defining $G$…
We survey the complexity class $\exists \mathbb{R}$, which captures the complexity of deciding the existential theory of the reals. The class $\exists \mathbb{R}$ has roots in two different traditions, one based on the Blum-Shub-Smale model…
Algorithmic meta-theorems provide an important tool for showing tractability of graph problems on graph classes defined by structural restrictions. While such results are well established for static graphs, corresponding frameworks for…
Many classical planning frameworks are built on first-order languages. The first-order expressive power is desirable for compactly representing actions via schemas, and for specifying quantified conditions such as $\neg\exists…
The celebrated Trakhtenbrot's theorem states that the set of finitely valid sentences of first-order logic is not computably enumerable. In this note we will extend this theorem by proving that the finite satisfiability problem of any…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
Lindstr\"om's Theorem characterizes first order logic as the maximal logic satisfying the Compactness Theorem and the Downward L\"owenheim-Skolem Theorem. If we do not assume that logics are closed under negation, there is an obvious…
How to efficiently represent a graph in computer memory is a fundamental data structuring question. In the present paper, we address this question from a combinatorial point of view. A representation of an $n$-vertex graph $G$ is called…
Solution discovery asks whether a given (infeasible) starting configuration to a problem can be transformed into a feasible solution using a limited number of transformation steps. This paper investigates meta-theorems for solution…
In the nineties Immerman and Medina initiated the search for syn- tactic tools to prove NP-completeness. In their work, amongst several results, they conjecture that the NP-completeness of a problem defined by the conjunction of a sentence…
Dynamic Complexity (as introduced by Patnaik and Immerman) tries to express how hard it is to update the solution to a problem when the input is changed slightly. It considers the changes required to some stored data structure (possibly a…
This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…