Online research in philosophy

In the companion paper (Towards a “sophisticated” model of belief dynamics. Part I), a general framework for realistic modelling of instantaneous states of belief and of the operations involving them was presented and motivated. In this paper, the framework is applied to the case of belief revision. A model of belief revision shall be obtained which, firstly, recovers the Gärdenfors postulates in a well-specified, natural yet simple class of particular circumstances; secondly, can accommodate iterated revisions, recovering several proposed revision operators for iterated revision as special cases; and finally, offers an analysis of Rott’s recent counterexample to several Gärdenfors postulates [32], elucidating in what sense it fails to be one of the special cases to which these postulates apply.

duction; so we think it prudent to proceed with a certain diffidence. That our own account of abduction is itself abductive is methodological expression of this diffi- dence. A second objective is to test our conception of abduction’s logical structure against some of the more promising going accounts of abductive reasoning.

In this paper I critically examine the notion of explanation used in artificial intelligence in general, and in the theory of belief revision in particular. I focus on two of the best known accounts in the literature: Pagnucco’s abductive expansion functions and Gärdenfors’ counterfactual analysis. I argue that both accounts are at odds with the way in which this notion has historically been understood in philosophy. They are also at odds with the explanatory strategies used in actual scientific practice. At the end of the paper I outline a set of desiderata for an epistemologically motivated, scientifically informed belief revision model for explanation.

The theory of belief revision deals with (rational) changes in beliefs in response to new information. In the literature a distinction has been drawn between belief revision and belief update (see [6]). The former deals with situations where the objective facts describing the world do not change (so that only the beliefs of the agent change over time), while the letter allows for situations where both the facts and the doxastic state of the agent change over time. We focus on belief revision and propose a temporal framework that allows for iterated revision. We model the notion of “minimal” or “conservative” belief revision by considering logics of increasing strength. We move from one logic to the next by adding one or more axioms and show that the corresponding logic captures more stringent notions of minimal belief revision. The strongest logic that we propose provides a full axiomatization of the well-known AGM theory of belief revision.

One of our purposes here is to expose something of the elementary logical structure of abductive reasoning, and to do so in a way that helps orient theorists to the various tasks that a logic of abduction should concern itself with. We are mindful of criticisms that have been levelled against the very idea of a logic of abduction; so we think it prudent to proceed with a certain diffidence. That our own account of abduction is itself abductive is methodological expression of this diffi- dence. A second objective is to test our conception of abduction’s logical structure against some of the more promising going accounts of abductive reasoning. We offer our various suggestions in a benignly advisory way. The primary targets of our advice is ourselves, meant as guides to work we have yet to complete or, in some instances, start. It is possible that our colleagues in the abduction research communities will find our counsel to be of some interest. But we repeat that our first concern is to try to get ourselves straight about what a logic of abduction should encompass.

This paper discusses abductive reasoning---that is, reasoning in which explanatory hypotheses are formed and evaluated. First, it criticizes two recent formal logical models of abduction. An adequate formalization would have to take into account the following aspects of abduction: explanation is not deduction; hypotheses are layered; abduction is sometimes creative; hypotheses may be revolutionary; completeness is elusive; simplicity is complex; and abductive reasoning may be visual and non-sentential. Second, in order to illustrate visual aspects of hypothesis formation, the paper describes recent work on visual inference in archaeology. Third, in connection with the evaluation of explanatory hypotheses, the paper describes recent results on the computation of coherence.

What I call theoretical abduction (sentential and model-based)certainly illustrates much of what is important in abductive reasoning, especially the objective of selecting and creating a set of hypotheses that are able to dispense good (preferred) explanations of data, but fails to account for many cases of explanation occurring in science or in everyday reasoning when the exploitation of the environment is crucial. The concept of manipulative abduction is devoted to capture the role of action in many interesting situations: action provides otherwise unavailable information that enables the agent to solve problems by starting and performing a suitable abductive process of generation or selection of hypotheses. Many external things, usually inert from the epistemological point of view, can be transformed into what I call epistemic mediators, which are illustrated in the last part of the paper, together with an analysis of the related notions of ``perceptual and inceptual rehearsal'' and of ``external representation''.

This is an examination of similarities and differences between two recent models of abductive reasoning. The one is developed in Atocha Aliseda’s Abductive Reasoning: Logical Investigations into the Processes of Discovery and Evaluation (2006). The other is advanced by Dov Gabbay and the present author in their The Reach of Abduction: Insight and Trial (2005). A principal difference between the two approaches is that in the Gabbay-Woods model, but not in the Aliseda model, abductive inference is ignorance-preserving. A further differ-ence is that Aliseda reconstructs the abduction relation in a semantic tableaux environment, whereas the Woods-Gabbay model, while less systematic, is more general. Of particular note is the connection between abduction and legal reasoning.

We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a belief set. We also show that a simple modification to the AGM framework can allow belief revision to be a function of epistemic states. We establish a model-based representation theorem which characterizes the proposed postulates and constrains, in turn, the way in which entrenchment orderings may be transformed under iterated belief revision.

The motivation behind the collection of papers presented in this THEORIA forum on Abductive reasoning is my book Abductive Reasoning: Logical Investigations into the Processes of Discovery and Explanation. These contributions raise fundamental questions. One of them concerns the conjectural character of abduction. The choice of a logical framework for abduction is also discussed in detail, both its inferential aspect and search strategies. Abduction is also analyzed as inference to the best explanation, as well as a process of epistemic change, both of which chal-lenge the argument-like format of abduction. Finally, the psychological question of whether humans reason abduc-tively according to the models proposed is also addressed. I offer a brief summary of my book and then comment on and respond to several challenges that were posed to my work by the contributors to this issue.