Related papers: A Decidable Case of Query Determinacy: Project-Sel…
We consider the decidability of the verification problem of programs \emph{modulo axioms} --- that is, verifying whether programs satisfy their assertions, when the functions and relations it uses are assumed to interpreted by arbitrary…
Definite descriptions, such as 'the General Chair of KR 2024', are a semantically transparent device for object identification in knowledge representation. In first-order modal logic, definite descriptions have been widely investigated for…
We study the finitary satisfiability problem for first order logic with two variables and two binary relations, corresponding to the induced successor relations of two finite linear orders. We show that the problem is decidable in NEXPTIME.
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain which can be compared wrt. equality. As the satisfiability problem for this logic is undecidable in general, in…
Even though query evaluation is a fundamental task in databases, known classifications of conjunctive queries by their fine-grained complexity only apply to queries without self-joins. We study how self-joins affect enumeration complexity,…
Join query evaluation with ordering is a fundamental data processing task in relational database management systems. SQL and custom graph query languages such as Cypher offer this functionality by allowing users to specify the order via the…
This paper explores goal-directed proof search in first-order multi-modal logic. The key issue is to design a proof system that respects the modularity and locality of assumptions of many modal logics. By forcing ambiguities to be…
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…
We study the problem of completely automatically verifying uninterpreted programs---programs that work over arbitrary data models that provide an interpretation for the constants, functions and relations the program uses. The verification…
One of the most interesting questions concerning hierarchical control of discrete-event systems with partial observations is a condition under which the language observability is preserved between the original and the abstracted plant.…
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…
There are many different semantics for general logic programs (i.e. programs that use negation in the bodies of clauses). Most of these semantics are Turing complete (in a sense that can be made precise), implying that they are undecidable.…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
To answer database queries over incomplete data the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their…
A special case of the satisfiability problem, in which the clauses have a hierarchical structure, is shown to be solvable in linear time, assuming that the clauses have been represented in a convenient way.
We introduce a model of one-way language acceptors (a variant of a checking stack automaton) and show the following decidability properties: (1) The deterministic version has a decidable membership problem but has an undecidable emptiness…
Argumentation is a promising model for reasoning with uncertain knowledge. The key concept of acceptability enables to differentiate arguments and counterarguments: The certainty of a proposition can then be evaluated through the most…
A group is called square-like if it is universally equivalent to its direct square. It is known that the class of all square-like groups admits an explicit first order axiomatization but its theory is undecidable. We prove that the theory…
Let $K$ be a subfield of $\mathbb{R}$. The theory of $\mathbb{R}$ viewed as an ordered $K$-vector space and expanded by a predicate for $\mathbb{Z}$ is decidable if and only if $K$ is a real quadratic field.
The ordered structures of natural, integer, rational and real numbers are studied in this thesis. The theories of these numbers in the language of order are decidable and finitely axiomatizable. Also, their theories in the language of order…