RankPL: A Qualitative Probabilistic Programming Language

In this paper we introduce RankPL, a modeling language that can be thought of as a qualitative variant of a probabilistic programming language with a semantics based on Spohn's ranking theory. Broadly speaking, RankPL can be used to represent and reason about processes that exhibit uncertainty expressible by distinguishing "normal" from" surprising" events. RankPL allows (iterated) revision of rankings over alternative program states and supports various types of reasoning, including abduction and causal inference. We present the language, its denotational semantics, and a number of practical examples. We also discuss an implementation of RankPL that is available for download

Embedding abduction in nonmonotonic theories

An important ampliative inference schema that is commonly used is abduction. Abduction plays a central role in many applications, such as diagnosis, expert systems, and causal reasoning. In a very broad sense we can state that abduction is the inference process that goes from observations to explanations within a more general context or theoretical framework. That is to say, abductive inference looks for sentences (named explanations), which, added to the theory, enable deductions for the observations. Most of the times there are several such explanations for a given observation. For this reason, in a narrower sense, abduction is regarded as an inference to the best explanation. However, a problem that faces abduction is the explanation of anomalous observations, i. e., observations that are contradictory with the current theory. It is perhaps impossible to do such inferences in monotonic theories. For this reason, in this work we will consider the problem of characterizing abduction in nonmonotonic theories. Our inference system is based on a natural deduction presentation of the implicational segment of a relevant logic, much similar to the R! system of Anderson and Belnap. Then we will discuss some issues arising the pragmatic acceptance of abductive inferences in nonmonotonic theories.Eje: Aspectos teóricos de inteligencia artificialRed de Universidades con Carreras en Informática (RedUNCI

A comparative survey of integrated learning systems

This paper presents the duction framework for unifying the three basic forms of inference - deduction, abduction, and induction - by specifying the possible relationships and influences among them in the context of integrated learning. Special assumptive forms of inference are defined that extend the use of these inference methods, and the properties of these forms are explored. A comparison to a related inference-based learning frame work is made. Finally several existing integrated learning programs are examined in the perspective of the duction framework

Theory formation by abduction : initial results of a case study based on the chemical revolution

Abduction is the process of constructing explanations. This chapter suggests that automated abduction is a key to advancing beyond the "routine theory revision" methods developed in early AI research towards automated reasoning systems capable of "world model revision" — dramatic changes in systems of beliefs such as occur in children's cognitive development and in scientific revolutions. The chapter describes a general approach to automating theory revision based upon computational methods for theory formation by abduction. The approach is based on the idea that, when an anomaly is encountered, the best course is often simply to suppress parts of the original theory thrown into question by the contradiction and to derive an explanation of the anomalous observation based on relatively solid, basic principles. This process of looking for explanations of unexpected new phenomena can lead by abductive inference to new hypotheses that can form crucial parts of a revised theory. As an illustration, the chapter shows how some of Lavoisier's key insights during the Chemical Revolution can be viewed as examples of theory formation by abduction

A comparison of techniques for learning and using mathematics and a study of their relationship to logical principles

Various techniques exist for learning mathematical concepts, like experimentation and exploration, respectively using mathematics, like modelling and simulation. For a clear application of such techniques in mathematics education, there should be a clear distinction between these techniques. A recently developed theory of fuzzy concepts can be applied to analyse the four mentioned concepts. For all four techniques one can pose the question of their relationship to deduction, induction and abduction as logical principles. An empirical study was conducted with 12-13 aged students, aiming at checking the three reasoning processes

Query-Answer Causality in Databases: Abductive Diagnosis and View-Updates

Causality has been recently introduced in databases, to model, characterize and possibly compute causes for query results (answers). Connections between query causality and consistency-based diagnosis and database repairs (wrt. integrity constrain violations) have been established in the literature. In this work we establish connections between query causality and abductive diagnosis and the view-update problem. The unveiled relationships allow us to obtain new complexity results for query causality -the main focus of our work- and also for the two other areas.Comment: To appear in Proc. UAI Causal Inference Workshop, 2015. One example was fixe

Theory formation by abduction : a case study based on the chemical revolution

Abduction is the process of constructing explanations. This chapter suggests that automated abduction is a key to advancing beyond the "routine theory revision" methods developed in early AI research towards automated reasoning systems capable of "world model revision" - dramatic changes in systems of beliefs such as occur in children's cognitive development and in scientific revolutions. The chapter describes a general approach to automating theory revision based upon computational methods for theory formation by abduction. The approach is based on the idea that, when an anomaly is encountered, the best course is often simply to suppress parts of the original theory thrown into question by the contradiction and to derive an explanation of the anomalous observation based on relatively solid, basic principles. This process of looking for explanations of unexpected new phenomena can lead by abductive inference to new hypotheses that can form crucial parts of a revised theory. As an illustration, the chapter shows how some of Lavoisier's key insights during the Chemical Revolution can be viewed as examples of theory formation by abduction