Explanation in constraint satisfaction: A survey

Much of the focus on explanation in the field of artificial intelligence has focused on machine learning methods and, in particular, concepts produced by advanced methods such as neural networks and deep learning. However, there has been a long history of explanation generation in the general field of constraint satisfaction, one of the AI's most ubiquitous subfields. In this paper we survey the major seminal papers on the explanation and constraints, as well as some more recent works. The survey sets out to unify many disparate lines of work in areas such as model-based diagnosis, constraint programming, Boolean satisfiability, truth maintenance systems, quantified logics, and related areas

Quantified Constraints in Twenty Seventeen

I present a survey of recent advances in the algorithmic and computational complexity theory of non-Boolean Quantified Constraint Satisfaction Problems, incorporating some more modern research directions

Finding counterfactual explanations through constraint relaxations

Interactive constraint systems often suffer from infeasibility (no solution) due to conflicting user constraints. A common approach to recover infeasibility is to eliminate the constraints that cause the conflicts in the system. This approach allows the system to provide an explanation as: "if the user is willing to drop out some of their constraints, there exists a solution". However, one can criticise this form of explanation as not being very informative. A counterfactual explanation is a type of explanation that can provide a basis for the user to recover feasibility by helping them understand which changes can be applied to their existing constraints rather than removing them. This approach has been extensively studied in the machine learning field, but requires a more thorough investigation in the context of constraint satisfaction. We propose an iterative method based on conflict detection and maximal relaxations in over-constrained constraint satisfaction problems to help compute a counterfactual explanation

Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support

A framework and methodology---termed LogiKEy---for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and governance of intelligent autonomous systems. LogiKEy's unifying formal framework is based on semantical embeddings of deontic logics, logic combinations and ethico-legal domain theories in expressive classic higher-order logic (HOL). This meta-logical approach enables the provision of powerful tool support in LogiKEy: off-the-shelf theorem provers and model finders for HOL are assisting the LogiKEy designer of ethical intelligent agents to flexibly experiment with underlying logics and their combinations, with ethico-legal domain theories, and with concrete examples---all at the same time. Continuous improvements of these off-the-shelf provers, without further ado, leverage the reasoning performance in LogiKEy. Case studies, in which the LogiKEy framework and methodology has been applied and tested, give evidence that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure

The interpretation and use of numerically-quantified expressions

This thesis presents a novel pragmatic account of the meaning and use of numerically-quantified expressions. It can readily be seen that quantities can typically be described by many semantically truthful expressions – for instance, if "more than 12" is true of a quantity, so is "more than 11", "more than 10", and so on. It is also intuitively clear that some of these expressions are more suitable than others in a given situation, a preference which is not captured by the semantics but appears to rely upon on wider-ranging considerations of communicative effectiveness. Motivated by these observations, I lay out a set of criteria that are demonstrably relevant to the speaker's choice of utterance in such cases. Observing further that it is typically impossible to satisfy all these criteria with a single utterance, I suggest that the speaker's choice of utterance can be construed as a problem of multiple constraint satisfaction. Using the formalism of Optimality Theory (Prince and Smolensky 1993), I proceed to specify a model of speaker behaviour for this domain of usage. The model I propose can be used to draw predictions both about the speaker's choice of utterance and the hearer's interpretation of utterances. I discuss the relation between these two aspects of the model, showing how constraints on the speaker's choice of utterance are predicted to make pragmatic enrichments available to the hearer. I then consider applications of this idea to specific issues that have been discussed in the literature. Firstly, with respect to superlative quantifiers, I show how this model provides an alternative account to that of Geurts and Nouwen (2007), building upon that offered by Cummins and Katsos (2010), and I present empirical evidence in its favour. Secondly, I show how this model yields the novel prediction that comparative quantifiers give rise to implicatures that are conditioned both by granularity and by prior mention of the numeral, and demonstrate these implicatures empirically. Finally I discuss the predictions that the model makes about the frequency of quantifiers in corpora, and investigate their validity. I conclude that the model presented here proves its worth as a source of hypotheses about speaker and hearer behaviour in the numerical domain. In particular, it serves as a way to integrate insights from distinct domains of enquiry including psycholinguistics, theoretical semantics and numerical cognition. I discuss the claim of this model to psychological plausibility, its relation to existing approaches, and its potential utility when applied to broader domains of language use.This work was supported by a University of Cambridge (Trinity College) Domestic Research Studentship