Finitely inseparable first-order axiomatized mereotopological theories

This paper will first introduce first-order mereotopological axioms and axiomatized theories which can be found in some recent literature and it will also give a survey of decidability, undecidability as well as other relevant notions. Then the main result to be given in this paper will be the finite inseparability of any mereotopological theory up to atomic general mereotopology (AGEMT) or strong atomic general mereotopology (SAGEMT). Besides, a more comprehensive summary will also be given via making observations about other properties stronger than undecidability

Notes on models of first-order mereological theories

This paper will consider some interesting mereological models and, by looking into them carefully, will clarify some important metalogical issues, such as definability, atomicity and decidability. More precisely, this paper will inquire into what kind of subsets can be defined in certain mereological models, what kind of axioms can guarantee that any member is composed of atoms and what kind of axioms are crucial, by regulating the models in a certain way, for an axiomatized mereological theory to be decidable

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

Semantic-driven modeling and reasoning for enhanced safety of cyber-physical systems

This dissertation is concerned with the development of new methodologies and semantics for model-based systems engineering (MBSE) procedures for the behavior modeling of cyber-physical systems (CPS). Our main interest is to enhance system-level safety through effective reasoning capabilities embedded in procedures for CPS design. This class of systems is defined by a tight integration of software and physical processes, the need to satisfy stringent constraints on performance, safety and a reliance on automation for the management of system functionality. Our approach employs semantic–driven modeling and reasoning : (1) for the design of cyber that can understand the physical world and reason with physical quantities, time and space, (2) to improve synthesis of component-based CPS architectures, and (3) to prevent under-specification of system requirements (the main cause of safety failures in software). We investigate and understand metadomains, especially temporal and spatial theories, and the role ontologies play in deriving formal, precise models of CPS. Description logic-based semantics and metadomain ontologies for reasoning in CPS and an integrated approach to unify the semantic foundations for decision making in CPS are covered. The research agenda is driven by Civil Systems design and operation applications, especially the dilemma zone problem. Semantic models of time and space supported respectively by Allen’s Temporal Interval Calculus (ATIC) and Region Connectedness Calculus (RCC-8) are developed and demonstrated thanks to the capabilities of Semantic Web technologies. A modular, flexible, and reusable reasoning-enabled semantic-based platform for safety-critical CPS modeling and analysis is developed and demonstrated. The platform employs formal representations of domains (cyber, physical) and metadomains (temporal and spatial) entities using decidable web ontology language (OWL) formalisms. Decidable fragments of temporal and spatial calculus are found to play a central role in the development of spatio-temporal algorithms to assure system safety. They rely on formalized safety metrics developed in the context of cyber-physical transportation systems and collision avoidance for autonomous systems. The platform components are integrated together with Whistle, a small scripting language (under development) able to process complex datatypes including physical quantities and units. The language also enables the simulation, visualization and analysis of safety tubes for collision prediction and prevention at signalized and non-signalized traffic intersections

Investigation of the tradeoff between expressiveness and complexity in description logics with spatial operators

Le Logiche Descrittive sono una famiglia di formalismi molto espressivi per la rappresentazione della conoscenza. Questi formalismi sono stati investigati a fondo dalla comunit\ue0 scientifica, ma, nonostante questo grosso interesse, sono state definite poche Description Logics con operatori spaziali e tutte centrate sul Region Connection Calculus. Nella mia tesi considero tutti i pi\uf9 importanti formalismi di Qualitative Spatial Reasoning per mereologie, mereo-topologie e informazioni sulla direzione e studio alcune tecniche generali di ibridazione. Nella tesi presento un\u2019introduzione ai principali formalismi di Qualitative Spatial Reasoning e le principali famiglie di Description Logics. Nel mio lavoro, introduco anche le tecniche di ibridazione per estendere le Description Logics al ragionamento su conoscenza spaziale e presento il potere espressivo dei linguaggi ibridi ottenuti. Vengono presentati infine un risultato generale di para-decidibilit\ue0 per logiche descrittive estese da composition-based role axioms e l\u2019analisi del tradeoff tra espressivit\ue0 e propriet\ue0 computazionali delle logiche descrittive spaziali.Description Logics are a family of expressive Knowledge-Representation formalisms that have been deeply investigated. Nevertheless the few examples of DLs with spatial operators in the current literature are defined to include only the spatial reasoning capabilities corresponding to the Region Connection Calculus. In my thesis I consider all the most important Qualitative Spatial Reasoning formalisms for mereological, mereo-topological and directional information and investigate some general hybridization techniques. I will present a short overview of the main formalisms of Qualitative Spatial Reasoning and the principal families of DLs. I introduce the hybridization techniques to extend DLs to QSR and present the expressiveness of the resulting hybrid languages. I also present a general paradecidability result for undecidable languages equipped with composition-based role axioms and the tradeoff analysis of expressiveness and computational properties for the spatial DLs

Semantic Interoperability of Geospatial Ontologies: A Model-theoretic Analysis

People sometimes misunderstand each other, even when they use the same language to communicate. Often these misunderstandings happen when people use the same words to mean different things, in effect disagreeing about meanings. This thesis investigates such disagreements about meaning, considering them to be issues of semantic interoperability. This thesis explores semantic interoperability via a particular formal framework used to specify people’s conceptualizations of a given domain. This framework is called an ‘ontology,’ which is a collection of data and axioms written in a logical language equipped with a modeltheoretic semantics. The domain under consideration is the geospatial domain. Specifically, this thesis investigates to what extent two geospatial ontologies are semantically interoperable when they ‘agree’ on the meanings of certain basic terms and statements, but ‘disagree’ on others. This thesis defines five levels of semantic interoperability that can exist between two ontologies. Each of these levels is, in turn, defined in terms of six ‘compatibility conditions,’ which precisely describe how the results of queries to one ontology are compatible with the results of queries to another ontology. Using certain assumptions of finiteness, the semantics of each ontology is captured by a finite number of models, each of which is also finite. The set of all models of a given ontology is called its model class. The five levels of semantic interoperability are proven to correspond exactly to five particular relationships between the model classes of the ontologies. The exact level of semantic interoperability between ontologies can in some cases be computed; in other cases a heuristic can be used to narrow the possible levels of semantic interoperability. The main results are: (1) definitions of five levels of semantic interoperability based on six compatibility conditions; (2) proofs of the correspondence between levels of semantic interoperability and the model-class relation between two ontologies; and (3) a method for computing, given certain assumptions of finiteness, the exact level of semantic interoperability between two ontologies. These results define precisely, in terms of models and queries, the often poorly defined notion of semantic interoperability, thus providing a touchstone for clear definitions of semantic interoperability elsewhere