Search arXivSearch

arXiv · 2109.08295

Geolog: Scalable Logic Programming on Spatial Data

Abstract

Spatial data is ubiquitous in our data-driven society. The Logic Programming community has been investigating the use of spatial data in different settings. Despite the success of this research, the Geographic Information System (GIS) community has rarely made use of these new approaches. This has mainly two reasons. First, there is a lack of tools that tightly integrate logical reasoning into state-of-the-art GIS software. Second, the scalability of solutions has often not been tested and hence, some solutions might work on toy examples but do not scale well to real-world settings. The two main contributions of this paper are (1) the Relation Based Programming paradigm, expressing rules on relations instead of individual entities, and (2) Geolog, a tool for spatio-logical reasoning that can be installed on top of ArcMap, which is an industry standard GIS. We evaluate our new Relation Based Programming paradigm in four real-world scenarios and show that up to two orders of magnitude in performance gain can be achieved compared to the prevalent Entity Based Programming paradigm.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Tobias Grubenmann, Jens Lehmann. 2021-09-17. Geolog: Scalable Logic Programming on Spatial Data. https://doi.org/10.4204/eptcs.345.34

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

KEEP EXPLORING

Related papers

PICID: Proof-Driven Clause Learning in Neural Network Verification

Current Deep Neural Network (DNN) verifiers are typically designed to prioritize scalability over reliability. Reliability can be reinforced through the generation of proofs that are checkable by trusted, external proof checkers. To date, only a handful of verifiers support proof production; and these rely on verifier-specific formats, and balance between scalability, proof detail, and the trustworthiness of their proof checker. In this tool paper, we introduce PICID, a DNN verifier that produces proofs in the standard Alethe format for SMT solving, checkable by an independent checker. PICID implements a parallel CDCL(T) architecture that integrates the state-of-the-art, proof-producing CaDiCaL SAT solver with the Marabou DNN verifier. Furthermore, PICID leverages UNSAT proofs to derive conflict clauses. Our evaluation shows that PICID generates valid proofs in the vast majority of cases and significantly outperforms existing tools that produce comparable proofs.

cs.LO

Confluence of conditional rewriting modulo

Sets of equations E play an important computational role in rewriting-based systems R. The equivalence relation =E induced by E introduces a partition of terms into E-equivalence classes on which rewriting computations, denoted ->R/E and called rewriting modulo E, are issued. This paper investigates confluence of ->R/E, usually called E-confluence, for conditional rewriting-based systems, where rewriting steps are determined by conditional rules. We rely on Jouannaud and Kirchner's framework to investigate confluence of an abstract relation R modulo an abstract equivalence relation E on a set A. We show how to particularize such a framework to be used with conditional systems. Then, we show how to define appropriate finite sets of conditional pairs to prove and disprove E-confluence. We introduce (i) Logic-based Conditional Critical Pairs, which do not require the use of (often infinitely many) E-unifiers to provide a finite representation of the local peaks considered in the abstract framework. We also introduce (ii) parametric Conditional Variable Pairs which are essential to deal with conditional rules in the analysis of E-confluence. Finally, we introduce (iii) Down Conditional Pairs which are often necessary to disprove E-confluence. Our results apply to well-known classes of rewriting-based systems, improving on previous results. As for unconditional systems, our results apply to Equational Term Rewriting Systems, first investigated by Huet and then by Jouannaud, and Jouannaud and Kirchner, among others. As for conditional systems, our results also apply to conditional rewrite theories and Maude.

cs.LO

Verifying Numerical Methods with Isabelle/HOL

Modern machine learning pipelines are built on numerical algorithms. Reliable numerical methods are thus a prerequisite for trustworthy machine learning and cyber-physical systems. Therefore, we contribute a framework for verified numerical methods in Isabelle/HOL based on ITrees. Our user-friendly specification language enables the direct declaration of numerical programs that can be annotated with variants and invariants for reasoning about correctness specifications. The generated verification conditions can be discharged via automated proof methods and lemmas from the HOL-Analysis library. The ITrees foundation interacts with Isabelle's code generator to export source code. This provides an end-to-end path from formal specifications with machine-checked guarantees to executable sources. We illustrate the process of modelling numerical methods and demonstrate the effectiveness of the verification by focusing on two well-known methods, the bisection method and the fixed-point iteration method. We also contribute crucial extensions to the libraries of formalised mathematics required for this objective: higher-order derivatives and Taylor's theorem in Peano form. Finally, we qualitatively evaluate the use of the framework for verifying numerical methods.

cs.LO