Related papers: Query Answering with Transitive and Linear-Ordered…
The finite satisfiability problem of two-variable logic extended by a linear order successor and a preorder successor is shown to be undecidable.
HyperLTL, the extension of Linear Temporal Logic by trace quantifiers, is a uniform framework for expressing information flow policies by relating multiple traces of a security-critical system. HyperLTL has been successfully applied to…
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…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
The chase algorithm is a fundamental tool for query evaluation and query containment under constraints, where the constraints are (sub-classes of) tuple-generating dependencies (TGDs) and equality generating depencies (EGDs). So far, most…
Consider a linear ordering equipped with a finite sequence of monadic predicates. If the ordering contains an interval of order type \omega or -\omega, and the monadic second-order theory of the combined structure is decidable, there exists…
Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology- Based Data Access. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure the…
The query containment problem is a fundamental algorithmic problem in data management. While this problem is well understood under set semantics, it is by far less understood under bag semantics. In particular, it is a long-standing open…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…
Existential rules are a prominent formalism to enrich a database with knowledge from the domain of interest, but make even basic reasoning tasks on the resulting knowledge base undecidable. To circumvent this, several classes of rules…
Algorithms of inference in a computer system oriented to input and semantic processing of text information are presented. Such inference is necessary for logical questions when the direct comparison of objects from a question and database…
There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Go\"edel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things…
Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations…
We lay the foundations for a database-inspired approach to interpreting and understanding neural network models by querying them using declarative languages. Towards this end we study different query languages, based on first-order logic,…
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…
Ontology-based query answering (OBQA) asks whether a Boolean conjunctive query is satisfied by all models of a logical theory consisting of a relational database paired with an ontology. The introduction of existential rules (i.e., Datalog…
Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…
The chase procedure is a fundamental algorithmic tool in databases that allows us to reason with constraints, such as existential rules, with a plethora of applications. It takes as input a database and a set of constraints, and iteratively…
We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded…