Foundations for Uniform Interpolation and Forgetting in Expressive Description Logics

We study uniform interpolation and forgetting in the description logic ALC. Our main results are model-theoretic characterizations of uniform inter- polants and their existence in terms of bisimula- tions, tight complexity bounds for deciding the existence of uniform interpolants, an approach to computing interpolants when they exist, and tight bounds on their size. We use a mix of model- theoretic and automata-theoretic methods that, as a by-product, also provides characterizations of and decision procedures for conservative extensions

The PIE Environment for First-Order-Based Proving, Interpolating and Eliminating

Abstract The PIE system aims at providing an environment for creating complex applications of automated first-order theorem proving techniques. It is embedded in Prolog. Beyond actual proving tasks, also interpolation and second-order quantifier elimination are supported. A macro feature and a L A T E X formula pretty-printer facilitate the construction of elaborate formalizations from small, understandable and documented units. For use with interpolation and elimination, preprocessing operations allow to preserve the semantics of chosen predicates. The system comes with a built-in default prover that can compute interpolants

Dual Forgetting Operators in the Context of Weakest Sufficient and Strongest Necessary Conditions

Forgetting is an important concept in knowledge representation and automated reasoning with widespread applications across a number of disciplines. A standard forgetting operator, characterized in [Lin and Reiter'94] in terms of model-theoretic semantics and primarily focusing on the propositional case, opened up a new research subarea. In this paper, a new operator called weak forgetting, dual to standard forgetting, is introduced and both together are shown to offer a new more uniform perspective on forgetting operators in general. Both the weak and standard forgetting operators are characterized in terms of entailment and inference, rather than a model theoretic semantics. This naturally leads to a useful algorithmic perspective based on quantifier elimination and the use of Ackermman's Lemma and its fixpoint generalization. The strong formal relationship between standard forgetting and strongest necessary conditions and weak forgetting and weakest sufficient conditions is also characterized quite naturally through the entailment-based, inferential perspective used. The framework used to characterize the dual forgetting operators is also generalized to the first-order case and includes useful algorithms for computing first-order forgetting operators in special cases. Practical examples are also included to show the importance of both weak and standard forgetting in modeling and representation

A Knowledge Graph Based Approach to Social Science Surveys

Peer reviewedPublisher PD

A Knowledge Graph Based Approach to Social Science Surveys

Recent success of knowledge graphs has spurred interest in applying them in open science, such as on intelligent survey systems for scientists. However, efforts to understand the quality of candidate survey questions provided by these methods have been limited. Indeed, existing methods do not consider the type of on-the-fly content planning that is possible for face-to-face surveys and hence do not guarantee that selection of subsequent questions is based on response to previous questions in a survey. To address this limitation, we propose a dynamic and informative solution for an intelligent survey system that is based on knowledge graphs. To illustrate our proposal, we look into social science surveys, focusing on ordering the questions of a questionnaire component by their level of acceptance, along with conditional triggers that further customise participants' experience. Our main findings are: (i) evaluation of the proposed approach shows that the dynamic component can be beneficial in terms of lowering the number of questions asked per variable, thus allowing more informative data to be collected in a survey of equivalent length; and (ii) a primary advantage of the proposed approach is that it enables grouping of participants according to their responses, so that participants are not only served appropriate follow-up questions, but their responses to these questions may be analysed in the context of some initial categorisation. We believe that the proposed approach can easily be applied to other social science surveys based on grouping definitions in their contexts. The knowledge-graph-based intelligent survey approach proposed in our work allows online questionnaires to approach face-to-face interaction in their level of informativity and responsiveness, as well as duplicating certain advantages of interview-based data collection