Joke Meheus

In this paper, I present the discussive adaptive logic DLI r . As is the case for other discussive logics, the intended application context of DLI r is the interpretation of discussions. What is new about the system is that it does not lead to explosion when some of the premises are self-contradictory. It is argued that this is important in view of the fact that human reasoners are not logically omniscient, and hence, that it may not be evident to discover the inconsistencies in one's beliefs. In addition to this, DLI r can handle cases in which different participants contradict each other. It is shown that, in both kinds of cases, DLI r leads to an interpretation of the discussion that is as rich as possible (even though no discussive connectives are introduced).

In the early eighties, philosophers of science came to the conviction that discovery and creativity form an integral part of scientific rationality. Ever since, the?positivists? have been criticised for their neglect of these topics. It is the aim of this paper to show that the positivists' approach to scientific discovery is not only much richer than is commonly recognized, but that they even defended an important thesis which some of the `friends of discovery' seem to have forgotten. Contrary to what is generally accepted, I shall also show that there is no reason at all why the positivists should have ignored discovery.

We present the inconsistency-adaptive deontic logic DP r, a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts such as O A ∧ O ∼A, O A ∧ P ∼A or even O A ∧ ∼O A. On the other hand, DP r still verifies all intuitively reliable inferences valid in Standard Deontic Logic (SDL). DP r interprets a given premise set ‘as normally as possible’ with respect to SDL. Whereas some SDL-rules are verified unconditionally by DP r, others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of DP r.

In this paper, I present two adaptive logics for paraconsistent compatibility. The consequence relation defined by these logics leads from a (possibly inconsistent) set of premises to all the sentences that are compatible with them. Their proof theory is dynamic, but is proven sound and complete with respect to a static semantics. For the consistent case, both logics lead to exactly the same results as the logics for classical compatibility that were presented in [11]. It is shown that paraconsistent compatibility cannot be defined with respect to a monotonic paraconsistent logic, but only with respect to an inconsistency-adaptive logic. The paper contains modal versions of two well-studied inconsistency-adaptive logics. These modal versions form the basis for the logics for paraconsistent compatibility, but are also interesting with respect to other applications. © 2011 Elsevier B.V., All rights reserved.