A Modal Logic for Explaining some Graph Neural Networks

In this paper, we propose a modal logic in which counting modalities appear in linear inequalities. We show that each formula can be transformed into an equivalent graph neural network (GNN). We also show that each GNN can be transformed into a formula. We show that the satisfiability problem is decidable. We also discuss some variants that are in PSPACE

A Markov chain model for changes in users’ assessment of search results

Previous research shows that users tend to change their assessment of search results over time. This is a first study that investigates the factors and reasons for these changes, and describes a stochastic model of user behaviour that may explain these changes. In particular, we hypothesise that most of the changes are local, i.e. between results with similar or close relevance to the query, and thus belong to the same ”coarse” relevance category. According to the theory of coarse beliefs and categorical thinking, humans tend to divide the range of values under consideration into coarse categories, and are thus able to distinguish only between cross-category values but not within them. To test this hypothesis we conducted five experiments with about 120 subjects divided into 3 groups. Each student in every group was asked to rank and assign relevance scores to the same set of search results over two or three rounds, with a period of three to nine weeks between each round. The subjects of the last three-round experiment were then exposed to the differences in their judgements and were asked to explain them. We make use of a Markov chain model to measure change in users’ judgments between the different rounds. The Markov chain demonstrates that the changes converge, and that a majority of the changes are local to a neighbouring relevance category. We found that most of the subjects were satisfied with their changes, and did not perceive them as mistakes but rather as a legitimate phenomenon, since they believe that time has influenced their relevance assessment. Both our quantitative analysis and user comments support the hypothesis of the existence of coarse relevance categories resulting from categorical thinking in the context of user evaluation of search results

Analysis of change in users' assessment of search results over time

We present the first systematic study of the influence of time on user judgements for rankings and relevance grades of web search engine results. The goal of this study is to evaluate the change in user assessment of search results and explore how users' judgements change. To this end, we conducted a large-scale user study with 86 participants who evaluated two different queries and four diverse result sets twice with an interval of two months. To analyse the results we investigate whether two types of patterns of user behaviour from the theory of categorical thinking hold for the case of evaluation of search results: (1) coarseness and (2) locality. To quantify these patterns we devised two new measures of change in user judgements and distinguish between local (when users swap between close ranks and relevance values) and non-local changes. Two types of judgements were considered in this study: 1) relevance on a 4-point scale, and 2) ranking on a 10-point scale without ties. We found that users tend to change their judgements of the results over time in about 50% of cases for relevance and in 85% of cases for ranking. However, the majority of these changes were local

Logical models for bounded reasoners

This dissertation aims at the logical modelling of aspects of human reasoning, informed by facts on the bounds of human cognition. We break down this challenge into three parts. In Part I, we discuss the place of logical systems for knowledge and belief in the Rationality Debate and we argue for systems that formalize an alternative picture of rationality -- one wherein empirical facts have a key role (Chapter 2). In Part II, we design logical models that encode explicitly the deductive reasoning of a single bounded agent and the variety of processes underlying it. This is achieved through the introduction of a dynamic, resource-sensitive, impossible-worlds semantics (Chapter 3). We then show that this type of semantics can be combined with plausibility models (Chapter 4) and that it can be instrumental in modelling the logical aspects of System 1 (“fast”) and System 2 (“slow”) cognitive processes (Chapter 5). In Part III, we move from single- to multi-agent frameworks. This unfolds in three directions: (a) the formation of beliefs about others (e.g. due to observation, memory, and communication), (b) the manipulation of beliefs (e.g. via acts of reasoning about oneself and others), and (c) the effect of the above on group reasoning. These questions are addressed, respectively, in Chapters 6, 7, and 8. We finally discuss directions for future work and we reflect on the contribution of the thesis as a whole (Chapter 9)

Business cycles, interest rates and market volatility : estimation and forecasting using DSGE macroeconomic models under partial information

Even long before the recent financial and economic crisis of 2007/2008 economists were more than aware of the insufficiencies and a lack of realism in macroeconomic modelling and model calibration methods, including those with DSGE methods and models, and spelled the need for further enhancements. The issues this research started addressing even before the 2008 crisis imposed demand for improvements, was use of single, fully informed rational agents in those modes. Consequently, the first part of this research project was aiming to improve the DSGE econometric methods by introducing novel solution for DSGE models with imperfect, partial information about the current values of deep variables and shocks, and apply this solution to imperfectly informed multiple agents with their different, inner-rationality models. Along these lines, this research also shows that DSGE models can be extended and suited to both, fitting and estimation of long-term yield curve, and to estimating with rich data sets by extending further its inner-mechanism. In the aftermath of the 2008 crises, which struck at the beginning of this research project, and the subsequent, extensive criticism of DSGE models, this research analyses the alternative causes of the crisis. It then focuses on identifying its possible causes, such as yet unknown debt accelerator mechanism and the related, probable model miss-specifications, rational inattention, and as well, a role of institutional policies in both the development of the crisis and its resolution. And finally, in a response to many of the critiques of the, usually monetary policy oriented DSGE models, this research project provides another set of novel extensions to such models, aiming to bring more of Keynesian characteristics suited to a more active, endogenous fiscal policy deemed needed in the aftermath of the crisis. This project, henceforth, extends the NK-Neo-Classical synthesis monetary DSGE models with a novel, endogenous, counter-cyclical fiscal policy rule driven by news and unemployment changes. It then also shows overall benefits of the resulting, mutually active, monetary-fiscal policy for both capital utilisation and overall economic stability