Logical Foundations of Object-Oriented and Frame-Based Languages

We propose a novel logic, called Frame Logic (abbr., F-logic), that accounts in a clean, declarative fashion for most of the structural aspects of object-oriented and frame-based languages. These features include object identity, complex objects, inheritance, polymorphic types, methods, encapsulation, and others. In a sense, F-logic stands in the same relationship to the object-oriented paradigm as classical predicate calculus stands to relational programming. The syntax of F-logic is higher-order, which, among other things, allows the user to explore data and schema using the same declarative language. F-logic has a model-theoretic semantics and a sound and complete resolution-based proof procedure. This paper also discusses various aspects of programming in declarative object-oriented languages based on F-logic

Answering Deep Queries Specified in Natural Language with Respect to a Frame Based Knowledge Base and Developing Related Natural Language Understanding Components

abstract: Question Answering has been under active research for decades, but it has recently taken the spotlight following IBM Watson's success in Jeopardy! and digital assistants such as Apple's Siri, Google Now, and Microsoft Cortana through every smart-phone and browser. However, most of the research in Question Answering aims at factual questions rather than deep ones such as ``How'' and ``Why'' questions. In this dissertation, I suggest a different approach in tackling this problem. We believe that the answers of deep questions need to be formally defined before found. Because these answers must be defined based on something, it is better to be more structural in natural language text; I define Knowledge Description Graphs (KDGs), a graphical structure containing information about events, entities, and classes. We then propose formulations and algorithms to construct KDGs from a frame-based knowledge base, define the answers of various ``How'' and ``Why'' questions with respect to KDGs, and suggest how to obtain the answers from KDGs using Answer Set Programming. Moreover, I discuss how to derive missing information in constructing KDGs when the knowledge base is under-specified and how to answer many factual question types with respect to the knowledge base. After having the answers of various questions with respect to a knowledge base, I extend our research to use natural language text in specifying deep questions and knowledge base, generate natural language text from those specification. Toward these goals, I developed NL2KR, a system which helps in translating natural language to formal language. I show NL2KR's use in translating ``How'' and ``Why'' questions, and generating simple natural language sentences from natural language KDG specification. Finally, I discuss applications of the components I developed in Natural Language Understanding.Dissertation/ThesisDoctoral Dissertation Computer Science 201

Principles of KLM-style Defeasible Description Logics

The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both preferen- tial and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our seman- tics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of entailment and present an algorithm for the computation of rational closure of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL ALC

Understanding and Reasoning about Implicit Meaning in Language

Enabling machines to interact with humans requires understanding what people mean, even when they do not say it explicitly. For example, machines should understand that ``selfish people oppose gun control'' implies a pro-gun control viewpoint (i.e., is taking a stance in support of gun control) despite the negative tone of the statement. Understanding these types of pragmatic inferences allows humans to grasp meaning (e.g., intentions, relevant facts) beyond what is literally expressed in an utterance. Furthermore, pragmatic inferences conveyed through generalizations (e.g., referring to generic ``selfish people'' rather than specific individuals in order to be more persuasive) support flexible and efficient reasoning. Therefore, in this thesis we focus on improving computational understanding of two inter-related types of pragmatic inferences: stancetaking and linguistic generalizations. This thesis is divided into two parts. In Part II, we focus on stance detection. One major challenge for stance detection models is the large and continually growing set of stance targets (i.e., topics to take a stance on). Therefore, to address this we define and study zero-shot stance detection (i.e., evaluation on topics for which there is no training data). Our work develops both datasets and models for this task and analyzes the ongoing challenges for future work. This work has stimulated increasing and ongoing research in zero-shot stance detection in NLP. Then in Part I we study generics --- a specific type of linguistic generalization that does not contain explicit quantifiers (e.g., ``most'', ``some''). These statements can have strong persuasive force and are also related to complex patterns of reasoning. To probe the current understanding capabilities of computational models, we focus on generating generics exemplars --- specific cases when a generic holds true or false. In particular, we propose computational frameworks grounded in linguistic theory to generate the first datasets of exemplars. We then use our datasets to highlight the challenges generics pose for natural language reasoning and the current generic-understanding capabilities of large language models

Practical reasoning for defeasable description logics.

Doctor of Philosophy in Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Durban 2016.Description Logics (DLs) are a family of logic-based languages for formalising ontologies. They have useful computational properties allowing the development of automated reasoning engines to infer implicit knowledge from ontologies. However, classical DLs do not tolerate exceptions to speci ed knowledge. This led to the prominent research area of nonmonotonic or defeasible reasoning for DLs, where most techniques were adapted from seminal works for propositional and rst-order logic. Despite the topic's attention in the literature, there remains no consensus on what \sensible" defeasible reasoning means for DLs. Furthermore, there are solid foundations for several approaches and yet no serious implementations and practical tools. In this thesis we address the aforementioned issues in a broad sense. We identify the preferential approach, by Kraus, Lehmann and Magidor (KLM) in propositional logic, as a suitable abstract framework for de ning and studying the precepts of sensible defeasible reasoning. We give a generalisation of KLM's precepts, and their arguments motivating them, to the DL case. We also provide several preferential algorithms for defeasible entailment in DLs; evaluate these algorithms, and the main alternatives in the literature, against the agreed upon precepts; extensively test the performance of these algorithms; and ultimately consolidate our implementation in a software tool called Defeasible-Inference Platform (DIP). We found some useful entailment regimes within the preferential context that satisfy all the KLM properties, and some that have scalable performance in real world ontologies even without extensive optimisation