Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1810.02132

A Single Approach to Decide Chase Termination on Linear Existential Rules

Michel Leclere·Marie-Laure Mugnier·Michael Thomazo·Federico Ulliana
View original source ↗Read source document ↗Export metadata ↓

Abstract

Existential rules, long known as tuple-generating dependencies in database theory, have been intensively studied in the last decade as a powerful formalism to represent ontological knowledge in the context of ontology-based query answering. A knowledge base is then composed of an instance that contains incomplete data and a set of existential rules, and answers to queries are logically entailed from the knowledge base. This brought again to light the fundamental chase tool, and its different variants that have been proposed in the literature. It is well-known that the problem of determining, given a chase variant and a set of existential rules, whether the chase will halt on any instance, is undecidable. Hence, a crucial issue is whether it becomes decidable for known subclasses of existential rules. In this work, we consider linear existential rules, a simple yet important subclass of existential rules that generalizes inclusion dependencies. We show the decidability of the all instance chase termination problem on linear rules for three main chase variants, namely semi-oblivious, restricted and core chase. To obtain these results, we introduce a novel approach based on so-called derivation trees and a single notion of forbidden pattern. Besides the theoretical interest of a unified approach and new proofs, we provide the first positive decidability results concerning the termination of the restricted chase, proving that chase termination on linear existential rules is decidable for both versions of the problem: Does every fair chase sequence terminate? Does some fair chase sequence terminate?

Explore related subjects

cs.LO

Keep this discovery

BibTeXRIS

Michel Leclere, Marie-Laure Mugnier, Michael Thomazo, Federico Ulliana. 2018-10-04. A Single Approach to Decide Chase Termination on Linear Existential Rules. https://arxiv.org/abs/1810.02132

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Four-Valued Graph Model for Conflict Resolution: Core Framework and a Machine-Checked Formalization in Lean 4

This note consolidates the core of the Quasi-Closed World Graph Model for Conflict Resolution (QCW-GMCR), which extends the standard Graph Model for Conflict Resolution with Belnap's four-valued logic to represent option-level epistemic ambiguity, and pairs the framework with a machine-checked Lean 4 formalization. QCW-GMCR combines: (1) FOUR-valued option assignments with compositional propagation to state-level feasibility; (2) graded reachability (definite, credible, possible) based on an FDE-inspired transition-warrant semantics, with definite reachability related to FDE consequence in the Boolean fragment; (3) axiomatized deterministic reductions from four-valued assessments to binary decisions, including four canonical operators reflecting distinct risk attitudes; and (4) catastrophe-avoiding equilibrium concepts with a quasi-closed-world safety invariant. A four-valued hypergame extension captures heterogeneous subjective assessments across decision makers. We state the core definitions and results and report the parts verified in Lean 4 with mathlib, including the classical GMCR stability hierarchy, algebraic and compositional properties of FOUR-valued conjunction, properties of the canonical reductions, and the graded reachability hierarchy. The formalization also helped identify and correct earlier claims, including a knowledge-monotonicity axiom replaced by truth monotonicity. This preprint provides a stable, citable record of the framework and its current formal verification status.

cs.LO↗
arXiv2026

The Semantic Elevation Operator and the Closure of the Undecidable Class under Preservation

The undecidability of a program's static semantic properties is governed by Rice's theorem. Self-modifying systems, however, require analysing not whether a property holds now, but whether it is preserved when the system rewrites itself. We formalise this transition through a semantic elevation operator {\Lambda}{\Phi}, which turns the static question "does x satisfy P?" into the dynamic question "is P preserved after x is transformed by {\Phi}?". We prove that when {\Phi} is intensional (depending on the source code, not only on the computed function), the elevated property remains undecidable even though it breaks the extensionality that Rice's theorem requires; the proof rests on Kleene's recursion theorem, not on Rice. Consequently the class U of non-verifiable properties is closed under the elevation operator. Unbounded iteration of the operator climbs the arithmetical hierarchy -to {\Pi}02-completeness- consolidating non-verifiability as a structural fact. We further show that the supervisory regress does not terminate: no fnite tower of increasingly capable verifiers yields an unconditional certificate. A categorical reading of these results in the efective topos, in which elevation appears as an instance of Lawvere's fxed-point theorem, is left as a direction for future work.

cs.LO↗
arXiv2026

Statistical Symmetry Release for Equivariant Quantum Learning

Hard symmetry constraints reduce model complexity, but can also erase label information. Statistical symmetry release determines when finite data and quantum measurements justify relaxing such a constraint, which directions to open, and how far to move. We connect global signal detection to local, loss-dependent improvement. A two-copy twirl--swap gate estimates task information in the symmetry-breaking complement with a dimension-independent copy count under paired-state and group-unitary access; reweighting the same records resolves representation sectors. An exact duality distinguishes this Hilbert--Schmidt signal from the larger signal accessible to bounded-outcome readouts. Local improvement is governed by the release gradient and a loss-corrected double-commutator matrix. Simultaneous confidence bounds convert empirical direction selection into certified descent, using either shared Pauli measurements or scalar probes with state-independent truncation bounds. Gaussian testing lower bounds quantify the cost of searching over unknown directions in the calibrated local experiment. Independent validation controls adaptively generated models, and a fast squared-loss bound preserves the approximation--estimation rate of a nested release path. On an eight-qubit Ising model, shared measurements certify release with 6300 times fewer shots than the specified scalar estimator on the tested budget grids. Quotient quantum natural gradient then controls parameter redundancy during training. Together, these results turn symmetry relaxation into a statistically justified model-selection decision.

cs.LO↗