Improving Model Finding for Integrated Quantitative-qualitative Spatial Reasoning With First-order Logic Ontologies

Many spatial standards are developed to harmonize the semantics and specifications of GIS data and for sophisticated reasoning. All these standards include some types of simple and complex geometric features, and some of them incorporate simple mereotopological relations. But the relations as used in these standards, only allow the extraction of qualitative information from geometric data and lack formal semantics that link geometric representations with mereotopological or other qualitative relations. This impedes integrated reasoning over qualitative data obtained from geometric sources and “native” topological information – for example as provided from textual sources where precise locations or spatial extents are unknown or unknowable. To address this issue, the first contribution in this dissertation is a first-order logical ontology that treats geometric features (e.g. polylines, polygons) and relations between them as specializations of more general types of features (e.g. any kind of 2D or 1D features) and mereotopological relations between them. Key to this endeavor is the use of a multidimensional theory of space wherein, unlike traditional logical theories of mereotopology (like RCC), spatial entities of different dimensions can co-exist and be related. However terminating or tractable reasoning with such an expressive ontology and potentially large amounts of data is a challenging AI problem. Model finding tools used to verify FOL ontologies with data usually employ a SAT solver to determine the satisfiability of the propositional instantiations (SAT problems) of the ontology. These solvers often experience scalability issues with increasing number of objects and size and complexity of the ontology, limiting its use to ontologies with small signatures and building small models with less than 20 objects. To investigate how an ontology influences the size of its SAT translation and consequently the model finder’s performance, we develop a formalization of FOL ontologies with data. We theoretically identify parameters of an ontology that significantly contribute to the dramatic growth in size of the SAT problem. The search space of the SAT problem is exponential in the signature of the ontology (the number of predicates in the axiomatization and any additional predicates from skolemization) and the number of distinct objects in the model. Axiomatizations that contain many definitions lead to large number of SAT propositional clauses. This is from the conversion of biconditionals to clausal form. We therefore postulate that optional definitions are ideal sentences that can be eliminated from an ontology to boost model finder’s performance. We then formalize optional definition elimination (ODE) as an FOL ontology preprocessing step and test the simplification on a set of spatial benchmark problems to generate smaller SAT problems (with fewer clauses and variables) without changing the satisfiability and semantic meaning of the problem. We experimentally demonstrate that the reduction in SAT problem size also leads to improved model finding with state-of-the-art model finders, with speedups of 10-99%. Altogether, this dissertation improves spatial reasoning capabilities using FOL ontologies – in terms of a formal framework for integrated qualitative-geometric reasoning, and specific ontology preprocessing steps that can be built into automated reasoners to achieve better speedups in model finding times, and scalability with moderately-sized datasets

An Ontological Framework for Characterizing Hydrological Flow Processes

The spatio-temporal processes that describe hydrologic flow - the movement of water above and below the surface of the Earth -- are currently underrepresented in formal semantic representations of the water domain. This paper analyses basic flow processes in the hydrology domain and systematically studies the hydrogeological entities, such as different rock and water bodies, the ground surface or subsurface zones, that participate in them. It identifies the source and goal entities and the transported water (the theme) as common participants in hydrologic flow and constructs a taxonomy of different flow patterns based on differences in source and goal participants. The taxonomy and related concepts are axiomatized in first-order logic as refinements of DOLCE\u27s participation relation and reusing hydrogeological concepts from the Hydro Foundational Ontology (HyFO). The formalization further enhances HyFO and contributes to improved knowledge integration in the hydrology domain

Formal Qualitative Spatial Augmentation of the Simple Feature Access Model

The need to share and integrate heterogeneous geospatial data has resulted in the development of geospatial data standards such as the OGC/ISO standard Simple Feature Access (SFA), that standardize operations and simple topological and mereotopological relations over various geometric features such as points, line segments, polylines, polygons, and polyhedral surfaces. While SFA\u27s supplied relations enable qualitative querying over the geometric features, the relations\u27 semantics are not formalized. This lack of formalization prevents further automated reasoning - apart from simple querying - with the geometric data, either in isolation or in conjunction with external purely qualitative information as one might extract from textual sources, such as social media. To enable joint qualitative reasoning over geometric and qualitative spatial information, this work formalizes the semantics of SFA\u27s geometric features and mereotopological relations by defining or restricting them in terms of the spatial entity types and relations provided by CODIB, a first-order logical theory from an existing logical formalization of multidimensional qualitative space

Ontological Analysis and Formal Grounding of the Groundwater Markup Language (GWML2) with the Hydro Foundational Ontology (HYFO)

An abundance of formal ontologies and data models, including a number of standards, exist for the hydrology domain. While some standards have achieved a level of technical interoperability for water data integration and exchange, semantic integration of water data remains a challenge, for a number of reasons. Existing ontologies and data models (1) are mostly fragmented and disconnected, (2) lack foundational grounding, and (3) semantically differ in how hydrological and hydrogeological terms are used. We investigate the use of an emerging, rigorously axiomatized reference ontology for the hydro domain, the Hydro Foundational Ontology (HyFO), to overcome these heterogeneities by integrating the existing hydro ontologies and data models with HyFO. HyFO formalizes general concepts that are central to water storage below and above the ground surface through rigorous and detailed axiomatization in first-order logic. This work presents first results of integrating the Ground Water Markup Language (GWML2), a conceptual model specific for the exchange of groundwater information, with HyFO by grounding GWML2 concepts logically in HyFO’s concepts and relations. The rigorous logical axiomatization of GWML2’s concepts by way of adding semantic precision and clarity results in a first order logic merged ontology that is a consistent extension of HyFO and the foundational ontology DOLCE. It also leads to the development of a stratified subclass hierarchy that realizes three levels of semantic distinctions in GWML2 concepts: (1) the top layer contains generic to earth and physical sciences, (2) the intermediate layer contains HyFO specific concepts that are universal for the surface and subsurface domain, and (3) the bottom layer encapsulates groundwater specific GWML2 concepts. More generally, this work provides a broader benefit by demonstrating how to effectively utilize formal ontological analysis and rigorous axiomatizations in the development and integration of geoscience ontologies. In addition, this thesis presents a preliminary ontological model that formalizes different hydrologic flow patterns as perdurant processes. Endurant concepts that participate in a flow process are described by a refined set of participation relations. Flow that is confined to a single geophysical endurant, and flow between two different endurants are modeled as Intraflow and Interflow respectively

Identifying Bottlenecks in Practical SAT-Based Model Finding for First-Order Logic Ontologies with Datasets

Satisfiability of first-order logic (FOL) ontologies is typically verified by translation to propositional satisfiability (SAT) problems, which is then tackled by a SAT solver. Unfortunately, SAT solvers often experience scalability issues when reasoning with FOL ontologies and even moderately sized datasets. While SAT solvers have been found to capably handle complex axiomatizations, finding models of datasets gets considerably more complex and time-intensive as the number of clause exponentially increases with increase in individuals and axiomatic complexity. We identify FOL definitions as a specific bottleneck and demonstrate via experiments that the presence of many defined terms of the highest arity significantly slows down model finding. We also show that removing optional definitions and substituting these terms by their definiens leads to a reduction in the number of clauses, which makes SAT-based model finding practical for over 100 individuals in a FOL theory

Using a hydro-reference ontology to provide improved computer-interpretable semantics for the groundwater markup language (GWML2)

<p>Comprehensive water data management requires semantically integrating various data models and ontologies that represent hydrologic knowledge. But integration is hampered by nuances in the use of water-related vocabulary (e.g. terms such as water body, aquifer, reservoir, well, etc.) across water representations and by the reliance on a mix of formal and informal specifications of how these terms are interpreted in each representation. Reconciliation of only partially formal encodings of the semantics of water representations requires manual inspection using tools from ontological analysis. This paper investigates as to what extent a domain reference ontology that is fully formalized in first-order logic can guide the ontological analysis.</p> <p>In particular, it is studied as to what extent the Hydro Foundational Ontology (HyFO), which encodes the semantics of a small set of unifying water concepts and associated relations in first-order logic, can serve as a reference ontology for the water domain to steer the ontological analysis of individual water representations, and to formalize their semantics more fully. This is specifically tested on the Groundwater Markup Language (GWML2). The result is GWML2-FOL, a concise logical description of GWML2’s key terms as a logical extension of HyFO. GWML2-FOL is structured into three layers of terms (mostly classes) of increasing specificity. The top layer consists of terms shareable across the earth and physical sciences, an intermediate layer includes HyFO’s hydro terms that span surface and subsurface water storage, and the bottom layer encapsulates groundwater specific GWML2 terms. The analysis and stratification uncover semantic ambiguities in GWML2 and suggest terminological and semantic clarifications and modifications in preparation for integrating GWML2 with other semantic water representations.</p> <p>The analysis also identifies two necessary additions to the HyFO: the concept of a hydro rock body as a hybrid of water and solid matter, which generalizes key groundwater terms such as aquifers or wells, and the concept of dependent hydrologic features such as springs, water tables, or divides. More broadly, differences between domain ontologies and a domain-reference ontology and their respective complementary roles in semantic-enabled geosciences are outlined.</p