Implicitly Learning to Reason in First-Order Logic

We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed probability distribution. PAC semantics, introduced by Valiant, is one rigorous, general proposal for learning to reason in formal languages: although weaker than classical entailment, it allows for a powerful model theoretic framework for answering queries while requiring minimal assumptions about the form of the distribution in question. To date, however, the most significant limitation of that approach, and more generally most machine learning approaches with robustness guarantees, is that the logical language is ultimately essentially propositional, with finitely many atoms. Indeed, the theoretical findings on the learning of relational theories in such generality have been resoundingly negative. This is despite the fact that first-order logic is widely argued to be most appropriate for representing human knowledge. In this work, we present a new theoretical approach to robustly learning to reason in first-order logic, and consider universally quantified clauses over a countably infinite domain. Our results exploit symmetries exhibited by constants in the language, and generalize the notion of implicit learnability to show how queries can be computed against (implicitly) learned first-order background knowledge.Comment: In Fourth International Workshop on Declarative Learning Based Programming (DeLBP 2019

Compiling Unit Clauses for the Warren Abstract Machine

This thesis describes the design, development, and installation of a computer program which compiles unit clauses generated in a Prolog-based environment at Argonne National Laboratories into Warren Abstract Machine (WAM) code. The program enhances the capabilities of the environment by providing rapid unification and subsumption tests for the very significant class of unit clauses. This should improve performance substantially for large programs that generate and use many unit clauses

Probabilistic inference on uncertain semantic link network and its application in event identification

The Probabilistic Semantic Link Network (P-SLN) is a model for enhancing the ability of Semantic Link Network in representing uncertainty. Probabilistic inference over uncertain semantic links can process the likelihood and consistency of uncertain semantic links. This work develops the P-SLN model by incorporating probabilistic inference rules and consistency constraints. Two probabilistic inference mechanisms are incorporated into the model. The application of probabilistic inference on SLN of events for joint event identification verifies the effectiveness of the proposed model

Quantified epistemic logics for reasoning about knowledge in multi-agent systems

AbstractWe introduce quantified interpreted systems, a semantics to reason about knowledge in multi-agent systems in a first-order setting. Quantified interpreted systems may be used to interpret a variety of first-order modal epistemic languages with global and local terms, quantifiers, and individual and distributed knowledge operators for the agents in the system. We define first-order modal axiomatisations for different settings, and show that they are sound and complete with respect to the corresponding semantical classes.The expressibility potential of the formalism is explored by analysing two MAS scenarios: an infinite version of the muddy children problem, a typical epistemic puzzle, and a version of the battlefield game. Furthermore, we apply the theoretical results here presented to the analysis of message passing systems [R. Fagin, J. Halpern, Y. Moses, M. Vardi, Reasoning about Knowledge, MIT Press, 1995; L. Lamport, Time, clocks, and the ordering of events in a distributed system, Communication of the ACM 21 (7) (1978) 558–565], and compare the results obtained to their propositional counterparts. By doing so we find that key known meta-theorems of the propositional case can be expressed as validities on the corresponding class of quantified interpreted systems

A general approach to temporal reasoning about action and change

Reasoning about actions and change based on common sense knowledge is one of the most important and difficult tasks in the artificial intelligence research area. A series of such tasks are identified which motivate the consideration and application of reasoning formalisms. There follows a discussion of the broad issues involved in modelling time and constructing a logical language. In general, worlds change over time. To model the dynamic world, the ability to predict what the state of the world will be after the execution of a particular sequence of actions, which take time and to explain how some given state change came about, i.e. the causality are basic requirements of any autonomous rational agent. The research work presented herein addresses some of the fundamental concepts and the relative issues in formal reasoning about actions and change. In this thesis, we employ a new time structure, which helps to deal with the so-called intermingling problem and the dividing instant problem. Also, the issue of how to treat the relationship between a time duration and its relative time entity is examined. In addition, some key terms for representing and reasoning about actions and change, such as states, situations, actions and events are formulated. Furthermore, a new formalism for reasoning about change over time is presented. It allows more flexible temporal causal relationships than do other formalisms for reasoning about causal change, such as the situation calculus and the event calculus. It includes effects that start during, immediately after, or some time after their causes, and which end before, simultaneously with, or after their causes. The presented formalism allows the expression of common-sense causal laws at high level. Also, it is shown how these laws can be used to deduce state change over time at low level. Finally, we show that the approach provided here is expressive

SIMILARITY METRICS APPLIED TO GRAPH BASED DESIGN MODEL AUTHORING

Model reuse is typically facilitated by search and retrieval tools, matching the sought model with models in a database. This research aims at providing similar assistance to users authoring design exemplars, a data structure to represent parametric and geometric design problems. The design exemplar represents design problems in the form of a bi-partite graph consisting of entities and relations. Authoring design exemplars for relatively complex design problems can be time consuming and error prone. This forms the motivation of developing a search and retrieval tool, capable of retrieving exemplars that are similar to the exemplar that a user is trying to author, from a database of previously authored exemplars. In order to develop such a tool, similarity measures have been developed to evaluate the similarity between the exemplar that a user is trying to author and target exemplars in the database. Two exemplars can be considered similar based on the number and types of entities and relations shared by them. However, exemplars meant for the same purpose can be authored using different entities and relations. Hence, the two main challenges in developing a search and retrieval tool are to evaluate the similarity between exemplars based on structure and semantics. In this research, four distinct similarity metrics are developed to evaluate the structural similarity between exemplars for exemplar retrieval: entity similarity, relation similarity, attribute similarity, and graph matching similarity. As well, a thorough understanding of semantics in engineering design has been developed. Different types of semantic information found in engineering design have been identified and classified. Design intent and rationale have been proposed as the two main types of semantic information necessary to evaluate the semantic similarity between exemplars. The semantic and structural similarity measures have been implemented as separate modules in an interactive modeling environment. Several experiments have been conducted in order to evaluate the accuracy and effectiveness of the proposed similarity measures. It is found that for most queries, the semantic retrieval module retrieves exemplars that are not retrieved by structural retrieval module and vice versa

Language acquisition

This project investigates acquisition of a new language by example. Syntax induction has been studied widely and the more complex syntax associated with Natural Language is difficult to induce without restrictions. Chomsky conjectured that natural languages are restricted by a Universal Grammar. English could be used as a Universal Grammar and Punjabi derived from it in a similar way as the acquisition of a first language. However, if English has already been acquired then Punjabi would be induced from English as a second language. [Continues.

Information access and retieval with semantic background knowledge

Thesis (Ph. D.)--Massachusetts Institute of Technology, Program in Media Arts & Sciences, 1995.Includes bibliographical references (p. 161-174).Anil Srinivasa Chakravarthy.Ph.D