This paper answers the philosophical contentions defended in Horsten and Welch (2007, Synthese, 158, 41–60). It contains a description of the standard format of adaptive logics, analyses the notion of dynamic proof required by those logics, discusses the means to turn such proofs into demonstrations, and argues that, notwithstanding their formal complexity, adaptive logics are important because they explicate an abundance of reasoning forms that occur frequently, both in scientific contexts and in common sense contexts.

For centuries, inconsistencies were seen as a hindrance to good reasoning, and their role in the sciences was ignored. In recent years, however, logicians as well as philosophers and historians have showed a growing interest in the matter. Central to this change were the advent of paraconsistent logics, the shift in attention from finished theories to construction processes, and the recognition that most scientific theories were at some point either internally inconsistent or incompatible with other accepted findings. The new interest (...) gave rise to important questions. How is `logical anarchy' avoided? Is it ever rational to accept an inconsistent theory? In what sense, if any, can inconsistent theories be considered as true? The present collection of papers is the first to deal with this kind of questions. It contains case studies as well as philosophical analyses, and presents an excellent overview of the different approaches in the domain. (shrink)

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 . Where an explanandum can be explained by different explanantia, the logic allows only for the abduction of their disjunction.

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 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.

It is generally agreed upon today that scientific reasoning, like everyday reasoning, proceeds in a dynamic way: inferences derived at some stage in the reasoning process may at a later stage be rejected. This dynamics may be extrinsic or intrinsic. I shall call it extrinsic when previously derived conclusions are rejected on non-logical grounds, and intrinsic when their rejection is based on a purely logical analysis.

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. (shrink)

In this paper, I present the modal adaptive logic $AJ^{r}$ (based on S5) as well as the discussive logic $D_{2}^{r}$ that is defined from it. $D_{2}^{r}$ is a (nonmonotonic) alternative for Jaśkowski's paraconsistent system D₂. Like D₂, $D_{2}^{r}$ validates all single-premise rules of Classical Logic. However, for formulas that behave consistently, $D_{2}^{r}$ moreover validates all multiple-premise rules of Classical Logic. Importantly, and unlike in the case of D₂, this does not require the introduction of discussive connectives. It is argued that (...) this has clear advantages with respect to one of the main application contexts of discussive logics, namely the interpretation of discussions. (shrink)

The aim of this paper is twofold. First, I want to argue that the distinction between induction and deduction is less clear-cut than traditionally assumed, and that, moreover, most reasoning processes in the sciences involve an integration of inductive and deductive steps. Next, I want to show how so-called adaptive logics may lead to a better understanding of this integrated use of induction and deduction.

In this paper, we present a goal-directed proof procedure for abductive reasoning. This procedure will be compared with Aliseda’s approach based on semantic tableaux. We begin with some comments on Aliseda’s algorithms for computing conjunctive abductions and show that they do not entirely live up to their aims. Next we give a concise account of goal-directed proofs and we show that abductive explanations are a natural spin-off of these proofs. Finally, we show that the goal-directed procedure solves the problems we (...) encountered in Aliseda’s algorithms. (shrink)

In this paper, we present a goal-directed proof procedure for abductive reasoning. This procedure will be compared with Aliseda’s approach based on semantic tableaux. We begin with some comments on Aliseda’s algorithms for computing conjunctive abductions and show that they do not entirely live up to their aims. Next we give a concise account of goal-directed proofs and we show that abductive explanations are a natural spin-off of these proofs. Finally, we show that the goal-directed procedure solves the problems we (...) encountered in Aliseda’s algorithms. (shrink)

In this paper, we present the outline for a goal-directed proof procedure for abductive reasoning and compare this procedure with Aliseda’s approach.

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). (shrink)

In this paper, I discuss the main difficulties one encounters whensolving problems with inconsistent constraints. I argue that in order to meetthese difficulties we need an inconsistency-adaptive logic that enables one toderive as many consequences as possible, but that at the sametime allows one to determine which consequences can be accepted. I showthat the inconsistency-adaptive logic ANA satisfies these requirements.

The present paper introduces a belief merging procedure by majority using the standard format of Adaptive Logics. The core structure of the logic ADM c (Adaptive Doxastic Merging by Counting) consists in the formulation of the conflicts arising from the belief bases of the agents involved in the procedure. A strategy is then defined both semantically and proof-theoretically which selects the consistent contents answering to a majority principle. The results obtained are proven to be equivalent to a standard majority operator (...) for bases with partial support. (shrink)

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)

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.

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.

In order to deal with the possibility of deontic conflicts Lou Goble developed a group of logics (DPM) that are characterized by a restriction of the inheritance principle. While they approximate the deductive power of standard deontic logic, they do so only if the user adds certain statements to the premises. By adaptively strengthening the DPM logics, this paper presents logics that overcome this shortcoming. Furthermore, they are capable of modeling the dynamic and defeasible aspect of our normative reasoning by (...) their dynamic proof theory. This way they enable us to have a better insight in the relations between obligations and thus to localize deontic conflicts. (shrink)

This introduction clarifies the ideas behind the Logic, Reasoningand Rationality congress from which the papers in this issue are selected.These ideas are situated in the history of 20th century philosophy. We also give an overview of the papers in this issue.

This introduction clarifies the ideas behind the Logic, Reasoning and Rationality congress from which the papers in this issue are selected. These ideas are situated in the history of 20th century philosophy (Vienna Circle, Kuhn, ...). We also give an overview of the papers in this issue.

This book contains a selection of the papers presented at the Logic, Reasoning and Rationality 2010 conference in Ghent. The conference aimed at stimulating the use of formal frameworks to explicate concrete cases of human reasoning, and conversely, to challenge scholars in formal studies by presenting them with interesting new cases of actual reasoning. According to the members of the Wiener Kreis, there was a strong connection between logic, reasoning, and rationality and that human reasoning is rational in so far (...) as it is based on logic. Later, this belief came under attack and logic was deemed inadequate to explicate actual cases of human reasoning. Today, there is a growing interest in reconnecting logic, reasoning and rationality. A central motor for this change was the development of non-classical logics and non-classical formal frameworks. The book contains contributions in various non-classical formal frameworks, case studies that enhance our apprehension of concrete reasoning patterns, and studies of the philosophical implications for our understanding of the notions of rationality. (shrink)

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. (shrink)

This paper answers the philosophical contentions defended in Horsten and Welch . It contains a description of the standard format of adaptive logics, analyses the notion of dynamic proof required by those logics, discusses the means to turn such proofs into demonstrations, and argues that, notwithstanding their formal complexity, adaptive logics are important because they explicate an abundance of reasoning forms that occur frequently, both in scientific contexts and in common sense contexts.

This paper primarily deals with the conceptual prospects for generalizing the aim of abduction from the standard one of explaining surprising or anomalous observations to that of empirical progress or even truth approximation. It turns out that the main abduction task then becomes the instrumentalist task of theory revision aiming at an empirically more successful theory, relative to the available data, but not necessarily compatible with them. The rest, that is, genuine empirical progress as well as observational, referential and theoretical (...) truth approximation, is a matter of evaluation and selection, and possibly new generation tasks for further improvement. The paper concludes with a survey of possible points of departure, in AI and logic, for computational treatment of the instrumentalist task guided by the ‘comparative evaluation matrix’. (shrink)

Naturalism and scientific creativity: new tools for analyzing science Content Type Journal Article Pages 1-4 DOI 10.1007/s11016-010-9513-1 Authors Daniel Burnston, Department of Philosophy, Interdisciplinary Cognitive Science Program, University of California, San Diego, 9500 Gilman Drive # 0119, La Jolla, CA 92093-0119, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.