This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argued consequence relation, taking into account the existence of consistent arguments in favour of a conclusion and the absence of consistent arguments in favour of its contrary, is particularly investigated. Flat knowledge bases, i.e., without any priority between their elements, are studied under different inconsistency-tolerant consequence relations, namely the so-called argumentative, free, universal, existential, cardinality-based, and paraconsistent consequence relations. The syntax-sensitivity of these consequence relations is (...) studied. A companion paper is devoted to the case where priorities exist between the pieces of information in the knowledge base. (shrink)

It is shown that the consequence relations defined from theRescher-Manor Mechanism are all inconsistency-adaptive logics combined with a specific interpretation schema for the premises. Each of the adaptive logics isobtained by applying a suitable adaptive strategy to the paraconsistent logicCLuN.This result provides all those consequence relations with a proof theory and with a static semantics.

This paper describes the adaptive logic of compatibility and its dynamic proof theory. The results derive from insights in inconsistency-adaptive logic, but are themselves very simple and philosophically unobjectionable. In the absence of a positive test, dynamic proof theories lead, in the long run, to correct results and, in the short run, sometimes to final decisions but always to sensible estimates. The paper contains a new and natural kind of semantics for S5from which it follows that a specific subset of (...) the standard worlds-models is characteristic for S5. (shrink)

In [BAT 00b], the flat Rescher–Manor consequence relations — the Free, Strong, Argued, C-Based, andWeak consequence relation—were shown to be characterized by inconsistency-adaptive logics defined from the paraconsistent logic CLuN. This provided these consequence relations with a dynamic proof theory. In the present paper we show that the detour via an inconsistency-adaptive logic is not necessary. We present a direct dynamic proof theory, formulated in the language of Classical Logic, and prove its adequacy. The present paper contains the first direct (...) dynamic proof theory for consequence relations that are characterized by an adaptive logic. (shrink)

This paper spells out a dynamic proof format for the pure logic of relevant implication. (A proof is dynamic if a formula derived at some stage need not be derived at a later stage.) The paper illustrates three interesting points. (i) A set of properties that characterizes an inference relation on the (very natural) dynamic proof interpretation, need not characterize the same inference relation (or even any inference relation) on the usual settheoretical interpretation. (ii) A proof format may display an (...) internal dynamics (defeasible conclusions) in the absence of an external dynamics (non-monotonicity). (iii) A monotonic logic may have a non-monotonic characterization. (shrink)

This is a philosophical and historical investigation of the role of inconsistent representations of the same scientific phenomenon. The logical difficulties associated with the simultaneous application of inconsistent models are discussed. Internally inconsistent scientific proposals are characterized as structures whose application is necessarily tied to the confirming evidence that each of its components enjoys and to a vision of the general form of the theory that will resolve the inconsistency. Einstein's derivation of the black body radiation law is used as (...) an example application of such a strategy and is contrasted with planck's derivation. (shrink)

In this paper, I present two ampliative adaptive logics: LA and LAk. LA is an adaptive logic for abduction that enables one to generate explanatory hypotheses from a set of observational statements and a set of background assumptions. LAk is based on LA and has the peculiar property that it selects those explanatory hypotheses that are empirically most successful. The aim of LAk is to capture the notion of empirical progress as studied by Theo Kuipers.

In this paper I present a simple and straightforward logic of induction: a consequence relation characterized by a proof theory and a semantics. This system will be called LI. The premises will be restricted to, on the one hand, a set of empirical data and, on the other hand, a set of background generalizations. Among the consequences will be generalizations as well as singular statements, some of which may serve as predictions and explanations.