Joke Meheus

Ampliative Adaptive Logics and the Foundation of Logic-Based Approaches to Abduction

In this paper, we propose a reconstruction of logic-based approaches to abductive reasoning in terms of ampliative adaptive logics. A main advantage of this reconstruction is that the resulting logics have a proof theory. As abductive reasoning is non-monotonic, the latter is necessarily dynamic (conclusions derived at some stage may at a later stage be rejected). The proof theory warrants, however, that the conclusions derived at a given stage are justified in view of the insight in the premises at that stage. Thus, it even leads to justified conclusions for undecidable fragments. Another advantage of the proposed logics is that they are much closer to natural reasoning than the existing systems. Usually, abduction is viewed as a form of “backward reasoning”. The search procedure by which this is realized (for instance, some form of linear linear resolution) is very different from the search procedures of human reasoners. The proposed logics treat abduction as a form of “forward reasoning” (Modus Ponens in the “wrong direction”). As a result, abductive steps are very natural, and are moreover nicely integrated with deductive steps. We present two new adaptive logics for abduction, and illustrate both with some examples from the history of the sciences (the discovery of Uranus and of Neptune). We also present some alternative systems that are better suited for non-creative forms of abductive reasoning.

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.

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 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.

An inconsistency-adaptive deontic logic for normative conflicts

We present the inconsistency-adaptive deontic logic DPr, 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 OA ∧ O ∼A, OA ∧ P ∼A or even OA ∧ ∼OA. On the other hand, DPr still verifies all intuitively reliable inferences valid in Standard Deontic Logic (SDL). DPr interprets a given premise set ‘as normally as possible’ with respect to SDL. Whereas some SDL-rules are verified unconditionally by DPr, 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 DPr.

Analogical Reasoning in Creative Problem Solving Processes: Logico-Philosophical Perspectives

One of the central questions any model of analogical reasoning has to provide an answer for concerns the derivation of new information from an analogy: what logic allows one to draw sensible inferences from an analogy ? In order to formulate an answer to this question, one should take into account that analogies play a different role in different kinds of processes. An important distinction here is that between communication processes (where analogies are used to convey information on a certain topic) and problem solving processes (where they are used to generate a solution to the problem one is dealing with). A further important distinction is that between creative problem solving processes (where novel analogies are discovered and gradually developed) and non-creative ones (where inferences are drawn from well-established analogies).

Deductive and ampliative adaptive logics as tools in the study of creativity

In this paper, I argue that logic hasan important role to play in the methodological studyof creativity. I also argue, however, that onlyspecial kinds of logic enable one to understand thereasoning involved in creative processes. I show thatdeductive and ampliative adaptive logics areappropriate tools in this respect.

Model-Based Reasoning in Creative Processes

Combining a contextual approach to problem solving with results on some recently developed (non-standard) logics, I present in this paper a general frame for the methodological study of model-based reasoning in creative processes. I argue that model-based reasoning does not require that we turn away from logic. I also argue, however, that in order to better understand and evaluate creative processes that involve model-based reasoning, and in order to formulate guidelines for them, we urgently need to extend the existing variety of logics.