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Tomasz Gogacz

Publications and source records attributed to Tomasz Gogacz.

12 recordsLinked to original sources
arXiv2026

Partially Finite Model Reasoning in Description Logics Extended Version

Aiming to harmonise finite and infinite model reasoning, we initiate the study of partially finite models, where the reasoning task comes with a formula that specifies a part of the model that must be finite. We focus on the problem of partially finite query entailment in description logics (DLs): given a knowledge base (KB), a query, and a distinguished concept, decide whether the query holds in all models of the KB that interpret the distinguished concept as a finite set. To break the ground, we work with the DL S, an extension of the basic DL ALC with transitive roles, which is one of the simplest cases where finite and infinite query entailment diverge. Generalising previous results on the finite and infinite cases, we show that also partially finite entailment of conjunctive queries is in 2-exptime for S. The solution involves sophisticated infinite model surgery and goes far beyond combining the arguments for the two special cases. As a direct application, we show how the problem of query containment in the presence of closed predicates can be solved by reduction to partially finite query entailment.

cs.LO↗
arXiv2020

On Finite Entailment of Non-Local Queries in Description Logics

We study the problem of finite entailment of ontology-mediated queries. Going beyond local queries, we allow transitive closure over roles. We focus on ontologies formulated in the description logics ALCOI and ALCOQ, extended with transitive closure. For both logics, we show 2EXPTIME upper bounds for finite entailment of unions of conjunctive queries with transitive closure. We also provide a matching lower bound by showing that finite entailment of conjunctive queries with transitive closure in ALC is 2EXPTIME-hard.

cs.AI↗
arXiv2019

All-Instances Restricted Chase Termination

The chase procedure is a fundamental algorithmic tool in database theory with a variety of applications. A key problem concerning the chase procedure is all-instances termination: for a given set of tuple-generating dependencies (TGDs), is it the case that the chase terminates for every input database? In view of the fact that this problem is undecidable, it is natural to ask whether known well-behaved classes of TGDs ensure decidability. We consider here the main paradigms that led to robust TGD-based formalisms, that is, guardedness and stickiness. Although all-instances termination is well-understood for the oblivious version of the chase, the more subtle case of the restricted (a.k.a. the standard) chase is rather unexplored. We show that all-instances restricted chase termination for guarded and sticky single-head TGDs is decidable.

cs.DB↗
arXiv2019

Ontology Focusing: Knowledge-enriched Databases on Demand

We propose a novel framework to facilitate the on-demand design of data-centric systems by exploiting domain knowledge from an existing ontology. Its key ingredient is a process that we call focusing, which allows to obtain a schema for a (possibly knowledge-enriched) database semi-automatically, given an ontology and a specification of the scope of the desired system. We formalize the inputs and outputs of focusing, and identify relevant computational problems: finding a schema via focusing, testing its consistency, and answering queries in the knowledge-enriched databases it produces. These definitions are fully independent of the ontology language. We then instantiate the framework using selected description logics as ontology languages, and popular classes of queries for specifying the scope of the system. For several representative combinations, we study the decidability and complexity of the identified computational problems. As a by-product, we isolate (and solve) variants of classical decision problems in description logics, that are interesting in their own right.

cs.LO↗
arXiv2018

Finite Query Answering in Expressive Description Logics with Transitive Roles

We study the problem of finite ontology mediated query answering (FOMQA), the variant of OMQA where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We adopt the most typical setting with unions of conjunctive queries and ontologies expressed in description logics (DLs). The study of FOMQA is relevant in settings that are not finitely controllable. This is the case not only for DLs without the finite model property, but also for those allowing transitive role declarations. When transitive roles are allowed, evaluating queries is challenging: FOMQA is undecidable for SHOIF and only known to be decidable for the Horn fragment of ALCIF. We show decidability of FOMQA for three proper fragments of SOIF: SOI, SOF, and SIF. Our approach is to characterise models relevant for deciding finite query entailment. Relying on a certain regularity of these models, we develop automata-based decision procedures with optimal complexity bounds.

cs.AI↗
arXiv2015

Entropy bounds for conjunctive queries with functional dependencies

We study the problem of finding the worst-case bound for the size of the result $Q(\mathbb{ D})$ of a fixed conjunctive query $Q$ applied to a database $\mathbb{ D}$ satisfying given functional dependencies. We provide a precise characterization of this bound in terms of entropy vectors, and in terms of finite groups. In particular, we show that an upper bound provided by Gottlob, Lee, Valiant and Valiant is tight, answering a question from their paper. Our result generalizes the bound due to Atserias, Grohe and Marx, who consider the case without functional dependencies. Our result shows that the problem of computing the worst-case size bound, in the general case, is closely related to difficult problems from information theory.

cs.DB↗
arXiv2015

Red Spider Meets a Rainworm: Conjunctive Query Finite Determinacy Is Undecidable

We solve a well known and long-standing open problem in database theory, proving that Conjunctive Query Finite Determinacy Problem is undecidable. The technique we use builds on the top of our Red Spider method which we developed in our paper [GM15] to show undecidability of the same problem in the "unrestricted case" -- when database instances are allowed to be infinite. We also show a specific instance $Q_0$, ${\cal Q}= \{Q_1, Q_2, \ldots Q_k\}$ such that the set $\cal Q$ of CQs does not determine CQ $Q_0$ but finitely determines it. Finally, we claim that while $Q_0$ is finitely determined by $\cal Q$, there is no FO-rewriting of $Q_0$, with respect to $\cal Q$, and we outline a proof of this claim

cs.DB↗
arXiv2014

On the BDD/FC Conjecture

Bounded Derivation Depth property (BDD) and Finite Controllability (FC) are two properties of sets of datalog rules and tuple generating dependencies (known as Datalog +/- programs), which recently attracted some attention. We conjecture that the first of these properties implies the second, and support this conjecture by some evidence proving, among other results, that it holds true for all theories over binary signature.

cs.DB↗
arXiv2014

Termination of oblivious chase is undecidable

We show that all--instances termination of chase is undecidable. More precisely, there is no algorithm deciding, for a given set $\cal T$ consisting of Tuple Generating Dependencies (a.k.a. Datalog$^\exists$ program), whether the $\cal T$-chase on $D$ will terminate for every finite database instance $D$. Our method applies to Oblivious Chase, Semi-Oblivious Chase and -- after a slight modification -- also for Standard Chase. This means that we give a (negative) solution to the all--instances termination problem for all version of chase that are usually considered. The arity we need for our undecidability proof is three. We also show that the problem is EXPSPACE-hard for binary signatures, but decidability for this case is left open. Both the proofs -- for ternary and binary signatures -- are easy. Once you know them.

cs.DB↗
arXiv2012

On regular groups and fields

Regular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that each regular field is algebraically closed. Standard arguments show that a generically stable regular field is algebraically closed. Let $K$ be a regular field which is not generically stable and let $p$ be its global generic type. We observe that if $K$ has a finite extension $L$ of degree $n$, then $p^{(n)}$ has unbounded orbit under the action of the multiplicative group of $L$. Known to be true in the minimal context, it remains wide open whether regular, or even quasi-minimal, groups are abelian. We show that if it is not the case, then there is a counter-example with a unique non-trivial conjugacy class, and we notice that a classical group with one non-trivial conjugacy class is not quasi-minimal, because the centralizers of all elements are uncountable. Then we construct a group of cardinality $ω_1$ with only one non-trivial conjugacy class and such that the centralizers of all non-trivial elements are countable.

math.LO↗