Dagmar Provijn

Ampliative Adaptive Logics and the Foundation of Logic-Based Approaches to Abduction

In this paper, we propose a reconstruction of logic-based approaches to abductive reasoning in terms of ampliative adaptive logics. A main advantage of this reconstruction is that the resulting logics have a proof theory. As abductive reasoning is non-monotonic, the latter is necessarily dynamic (conclusions derived at some stage may at a later stage be rejected). The proof theory warrants, however, that the conclusions derived at a given stage are justified in view of the insight in the premises at that stage. Thus, it even leads to justified conclusions for undecidable fragments. Another advantage of the proposed logics is that they are much closer to natural reasoning than the existing systems. Usually, abduction is viewed as a form of “backward reasoning”. The search procedure by which this is realized (for instance, some form of linear linear resolution) is very different from the search procedures of human reasoners. The proposed logics treat abduction as a form of “forward reasoning” (Modus Ponens in the “wrong direction”). As a result, abductive steps are very natural, and are moreover nicely integrated with deductive steps. We present two new adaptive logics for abduction, and illustrate both with some examples from the history of the sciences (the discovery of Uranus and of Neptune). We also present some alternative systems that are better suited for non-creative forms of abductive reasoning.

Some Adaptive Logics for Diagnosis

A logic of diagnosis proceeds in terms of a set of data and one or more (prioritized) sets of expectancies. In this paper we generalize the logics of diagnosis from [27] and present some alternatives. The former operate on the premises and expectancies themselves, the latter on their consequences.

Adaptive Logics for Non-Explanatory and Explanatory Diagnostic Reasoning

In this paper we discuss diagnosis of faults in systems. The latter are understood as structured wholes of components. Three types of diagnosis can be distinguished and are defined: non-explanatory, weak explanatory and strong explanatory. After the analysis of the reasoning process that leads to non-explanatory diagnosis, we argue that the predicative adaptive logic D* is an adequate tool for modeling this kind of diagnostic reasoning. Subsequently, we follow the same pattern for weak and strong diagnosis and describe the logic D* which adequately formalizes weak diagnostic reasoning, even when underlying theoretical knowledge is taken into account. Finally it is argued that the same logic can be applied in the case of strong diagnostic reasoning whenever a number of conditions are fulfilled.

Bloody Analogical Reasoning

In this paper I will study some of William Harvey’s applications of analogies in the Prelectiones Anatomiae Universalis and the Exercitatio anatomica de motu cordis et sanguinis in animalibus. I will show that Harvey applied analogies in many different ways and that some contributed to the discovery of the characteristic ‘action’ of the heart and pulse and even to the discovery of the blood circulation. The discovery process will be approached as a problem solving process as described in Batens’ contextual model. The focus on constraints allows to see Harvey both as a modern because of his extensive use of experimental results and as strongly influenced by an Aristotelian ‘natural philosophy interpretation’ of anatomy and physiology as, for instance, propagated by Fabricius of Aquapendente.