Diderik Batens

A Universal Logic Approach to Adaptive Logics

Abstract.In this paper, adaptive logics are studied from the viewpoint of universal logic (in the sense of the study of common structures of logics). The common structure of a large set of adaptive logics is described. It is shown that this structure determines the proof theory as well as the semantics of the adaptive logics, and moreover that most properties of the logics can be proved by relying solely on the structure, viz. without invoking any specific properties of the logics themselves.

The Need for Adaptive Logics In Epistemology

After it is argued that philosophers of science have lost interest in logic because they applied the wrong type of logics, examples are given of the forms of dynamic reasoning that are central for philosophy of science and epistemology. Adaptive logics are presented as a means to understand and explicate those forms of reasoning. All members of a specific (large) set of adaptive logics are proved to have a number of properties that warrant their formal decency and their suitability with respect to understanding and explicating dynamic forms of reasoning. Most of the properties extend to other adaptive logics.

A Formal Logic for Abductive Reasoning

This paper presents and illustrates a formal logic for the abduction of singular hypotheses. The logic has a semantics and a dynamic proof theory that is sound and complete with respect to the semantics. The logic presupposes that, with respect to a specific application, the set of explananda and the set of possible explanantia are disjoint (but not necessarily exhaustive). Where an explanandum can be explained by different explanantia, the logic allows only for the abduction of their disjunction.

TOWARDS THE UNIFICATION OF INCONSISTENCY HANDLING MECHANISMS

It is shown that the (flat) consequence relations defined from the Rescher-Manor Mechanism (that is: in terms of maximal consistent subsets of the premises) are all inconsistency-adaptive logics combined with a specific interpretation schema for the premises. Each of the adaptive logics is obtained by applying a suitable adaptive strategy to the paraconsistent logic CLuN. This result provides all those consequence relations with a (dynamic) proof theory and with a static (as well as a dynamic) semantics.

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.

The Adaptive Logic of Compatibility

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.

A procedural criterion for final derivability in inconsistency-adaptive logics

Abstract This paper concerns a (prospective) goal directed proof procedure for the propositional fragment of the inconsistency-adaptive logic ACLuN1. At the propositional level, the procedure forms an algorithm for final derivability. If extended to the predicative level, it provides a criterion for final derivability. This is essential in view of the absence of a positive test. The procedure may be generalized to all flat adaptive logics.

A Tableau Method for Inconsistency-Adaptive Logics

We present a tableau method for inconsistency-adaptive logics and illustrate it in terms of the two best studied systems. The method is new in that adaptive logics require a more complex structure of the tableaus and of some rules and conditions. As there is no positive test for derivability in inconsistency-adaptive logics, the tableau method is important for providing criteria for derivability.

Shortcuts and dynamic marking in the tableau method for adaptive logics

Adaptive logics typically pertain to reasoning procedures for which there is no positive test. In [7], we presented a tableau method for two inconsistency-adaptive logics. In the present paper, we describe these methods and present several ways to increase their efficiency. This culminates in a dynamic marking procedure that indicates which branches have to be extended first, and thus guides one towards a decision — the conclusion follows or does not follow — in a very economical way.

Minimally Abnormal Models In Some Adaptive Logics

In an adaptive logic APL, based on a (monotonic) non-standardlogic PL the consequences of Γ can be defined in terms ofa selection of the PL-models of Γ. 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 Priests LPm because its way of measuring thedegree of abnormality of a model is incoherent – correcting thisdelivers the property.