Related papers: Expressivity within second-order transitive-closur…
Descriptive complexity theory aims at inferring a problem's computational complexity from the syntactic complexity of its description. A cornerstone of this theory is Fagin's Theorem, by which a graph property is expressible in existential…
We combine integer linear programming and recent advances in Monadic Second-Order model checking to obtain two new algorithmic meta-theorems for graphs of bounded vertex-cover. The first shows that cardMSO1, an extension of the well-known…
In this paper we study the expressive power of k-ary exclusion logic, EXC[k], that is obtained by extending first order logic with k-ary exclusion atoms. It is known that without arity bounds exclusion logic is equivalent with dependence…
Extensional ESO is a fragment of existential second-order logic (ESO) that captures the following family of problems. Given a fixed ESO sentence $\Psi$ and an input structure $\mathbb A$ the task if to decide whether there is an extension…
In this paper we study a Separation Logic of Relations (SLR) and compare its expressiveness to (Monadic)Second Order Logic (M)SO. SLR is based on the well-known Symbolic Heap fragment of Separation Logic, whose formulae are composed of…
We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present…
One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic (MSO_2) is fixed-parameter tractable (fpt) on C by linear time parameterized algorithms,…
We give $\operatorname{CMSO}$-transductions that, given a graph $G$, output its modular decomposition, its split decomposition and its bi-join decomposition. This improves results by Courcelle [Logical Methods in Computer Science, 2006] who…
Monadic Second-Order Logic (MSO) extends First-Order Logic (FO) with variables ranging over sets and quantifications over those variables. We introduce and study Monadic Tree Logic (MTL), a fragment of MSO interpreted on infinite-tree…
We introduce a restricted second-order logic $\mathrm{SO}^{\mathit{plog}}$ for finite structures where second-order quantification ranges over relations of size at most poly-logarithmic in the size of the structure. We demonstrate the…
Spatial conjunction is a powerful construct for reasoning about dynamically allocated data structures, as well as concurrent, distributed and mobile computation. While researchers have identified many uses of spatial conjunction, its…
Order-invariant first-order logic is an extension of first-order logic FO where formulae can make use of a linear order on the structures, under the proviso that they are order-invariant, i.e. that their truth value is the same for all…
One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic is fixed-parameter tractable on C by linear time parameterised algorithms. An immediate…
Our main result is a succinct counterpoint to Courcelle's meta-theorem as follows: every cw-nontrivial monadic second-order (MSO) property is either NP-hard or coNP-hard over graphs given by succinct representations. Succint representations…
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…
In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8,…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
Research on information extraction from Web pages (wrapping) has seen much activity recently (particularly systems implementations), but little work has been done on formally studying the expressiveness of the formalisms proposed or on the…
We consider bisimulation-invariant monadic second-order logic over various classes of finite transition systems. We present several combinatorial characterisations of when the expressive power of this fragment coincides with that of the…
We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…