Related papers: Conservative Extensions in Guarded and Two-Variabl…
Preservation theorems provide a direct correspondence between the syntactic structure of first-order sentences and the closure properties of their respective classes of models. A line of work has explored preservation theorems relativised…
Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…
We establish decidability for the infinitely many axiomatic extensions of the commutative Full Lambek logic with weakening FLew (i.e. IMALLW) that have a cut-free hypersequent proof calculus (specifically: every analytic structural rule…
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…
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…
Open-world query answering is the problem of deciding, given a set of facts, conjunction of constraints, and query, whether the facts and constraints imply the query. This amounts to reasoning over all instances that include the facts and…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
We extend the two-variable logic on data words with guarded regular binary predicates of the form $\widetilde{L}(x,y)$ that is true if positions $x$ and $y$ are in the same class and the factor strictly between $x$ and $y$ is in the regular…
We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. We show that this extension has the finite model property.…
Logical formalisms such as first-order logic (FO) and fixpoint logic (FP) are well suited to express in a declarative manner fundamental graph functionalities required in distributed systems. We show that these logics constitute good…
Extensive research in the field of ontology-based query answering has led to the identification of numerous fragments of existential rules (also known as tuple-generating dependencies) that exhibit decidable answering of atomic and…
In this paper we prove that the uniform one-dimensional guarded fragment, which is a natural polyadic generalization of the guarded two-variable logic, has the Craig interpolation property. We will also prove that the satisfiability problem…
We study the positive logic FO+ on finite words, and its fragments, pursuing and refining the work initiated in [Kuperberg 2023]. First, we transpose notorious logic equivalences into positive first-order logic: FO+ is equivalent to LTL+ ,…
We study the decidability and expressiveness issues of $\mu$-calculus on data words and data $\omega$-words. It is shown that the full logic as well as the fragment which uses only the least fixpoints are undecidable, while the fragment…
Query evaluation on probabilistic databases is generally intractable (#P-hard). Existing dichotomy results have identified which queries are tractable (or safe), and connected them to tractable lineages. In our previous work, using…
This note contains some material promised in our earlier papers on submodel preservation and the guarded fragment, along with some information on the current status of the problems mentioned in these papers. Section 1 contains an early…
We investigate a number of semantically defined fragments of Tarski's algebra of binary relations, including the function-preserving fragment. We address the question whether they are generated by a finite set of operations. We obtain…
Constraint propagation is one of the basic forms of inference in many logic-based reasoning systems. In this paper, we investigate constraint propagation for first-order logic (FO), a suitable language to express a wide variety of…