Most logic–based approaches characterize abduction as a kind of backwards deduction plus additional conditions, which means that a number of conditions is specified that enable one to decide whether or not a particular abductive inference is sound . Despite the fact that these approaches succeed in specifying which formulas count as valid consequences of abductive inference steps, they do not explicate the way people actually reason by means of abductive inferences. This is most clearly shown by the absence of a (...) decent proof theory. Instead, search procedures are provided that enable one to determine the right abductive consequences. However, these do not by far resemble human reasoning. In order to explicate abductive reasoning more realistically, an alternative approach will be provided in this article, namely, one that is based on the adaptive logics programme. Proof theoretically, this approach interprets the argumentation schema affirming the consequent as a defeasible rule of inference. This comes down to the fact that the abductive consequences obtained by means of AC are accepted only for as long as certain conditions are satis.ed—e.g. as long as their negation has not been derived from the background theory. In the end, only the unproblematic applications of AC are retained, while the problematic ones are rejected. In this way, the adaptive logics approach to abduction succeeds to provide a more realistic explication of the way people reason by means of abductive inferences. Moreover, as multiple abduction processes will be characterized, this article may be considered as the first step in the direction of a general formal approach to abduction based on the adaptive logics programme. (shrink)

Counterfactuals is David Lewis' forceful presentation of and sustained argument for a particular view about propositions which express contrary to fact conditionals, including his famous defense of realism about possible worlds and his theory of laws of nature.

In an adaptive logic APL, based on a (monotonic) non-standardlogic PL the consequences of can be defined in terms ofa selection of the PL-models of . An important property ofthe adaptive logics ACLuN1, ACLuN2, ACLuNs1, andACLuNs2 logics is proved: whenever a model is not selected, this isjustified in terms of a selected model (Strong Reassurance). Theproperty fails for Priest's LP m because its way of measuring thedegree of abnormality of a model is incoherent – correcting thisdelivers the property.

The paper explains how a paraconsistent logician can appropriate all classical reasoning. This is to take consistency as a default assumption, and hence to work within those models of the theory at hand which are minimally inconsistent. The paper spells out the formal application of this strategy to one paraconsistent logic, first-order LP. (See, Ch. 5 of: G. Priest, In Contradiction, Nijhoff, 1987.) The result is a strong non-monotonic paraconsistent logic agreeing with classical logic in consistent situations. It is shown (...) that the logical closure of a theory under this logic is trivial only if its closure under LP is trivial. (shrink)

John Horty effectively develops deontic logic (the logic of ethical concepts like obligation and permission) against the background of a formal theory of agency. He incorporates certain elements of decision theory to set out a new deontic account of what agents ought to do under various conditions over extended periods of time. Offering a conceptual rather than technical emphasis, Horty's framework allows a number of recent issues from moral theory to be set out clearly and discussed from a uniform point (...) of view. (shrink)

Theoria, Volume 88, Issue 3, Page 494-528, June 2022.

We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A second lesson is the (...) possibility of rational inconsistent belief; this leads us to formulate criteria for deciding when an inconsistent set of beliefs may reasonably be retained. (shrink)

An extended review of what is known about the formal behaviour of nonmonotonic inference operations, including those generated by the principal systems in the artificial intelligence literature. Directed towards computer scientists and others with some background in logic.