Related papers: One-Dimensional Fragment over Words and Trees

Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…

We prove that the two-variable fragment of first-order logic has the weak Beth definability property. This makes the two-variable fragment a natural logic separating the weak and the strong Beth properties since it does not have the strong…

In this work, we consider the satisfiability problem in a logic that combines word equations over string variables denoting words of unbounded lengths, regular languages to which words belong and Presburger constraints on the length of…

An important class of decidable first-order logic fragments are those satisfying a guardedness condition, such as the guarded fragment (GF). Usually, decidability for these logics is closely linked to the tree-like model property - the fact…

We consider the extension of the two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as "the number of incoming blue edges plus twice the number of outgoing red edges…

We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an $\exists^*\forall^*$ quantifier prefix (over variables, functions…

This paper enriches preexisting satisfiability tests for unquantified languages, which in turn augment a fragment of Tarski's elementary algebra with unary real functions possessing a continuous first derivative. Two sorts of individual…

We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This…

Ontologies often require knowledge representation on multiple levels of abstraction, but description logics (DLs) are not well-equipped for supporting this. We propose an extension of DLs in which abstraction levels are first-class citizens…

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…

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 (1991). We prove the following problem is decidable: Input: (i) A monadic second…

The notion of a two-dimensional word arises naturally in the study of combinatorics on words, while the iterative construction of pedal triangles results in a rich dynamical system in the study of geometry. At first, these two classes of…

In this note, we give a linear-size translation from formulas of first-order logic into equations of the calculus of relations preserving validity and finite validity. Our translation also gives a linear-size conservative reduction from…

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 investigate the satisfiability and finite satisfiability problem for probabilistic computation-tree logic (PCTL) where operators are not restricted by any step bounds. We establish decidability for several fragments containing…

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…

We study the reactive synthesis problem for distributed systems with an unbounded number of participants interacting with an uncontrollable environment. Executions of those systems are modeled by data words, and specifications are given as…

We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…

Lattices are a commonly used structure for the representation and analysis of relational and ontological knowledge. In particular, the analysis of these requires a decomposition of a large and high-dimensional lattice into a set of…

Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…