In this paper, I will characterize a new class of inconsistency-adaptive logics, namely inconsistency-adaptive modal logics. These logics cope with inconsistencies in a modal context. More specifically, when faced with inconsistencies, inconsistency-adaptive modal logics avoid explosion, but still allow the derivation of sufficient consequences to adequately explicate the part of human reasoning they are intended for.

The anti-exceptionalist debate brought into play the problem of what are the relevant data for logical theories and how such data affects the validities accepted by a logical theory. In the present paper, I depart from Laudan's reticulated model of science to analyze one aspect of this problem, namely of the role of logical data within the process of revision of logical theories. For this, I argue that the ubiquitous nature of logical data is responsible for the proliferation of several (...) distinct methodologies for logical theories. The resulting picture is coherent with the Laudanean view that agreement and disagreement between scientific theories take place at different levels. From this perspective, one is able to articulate other kinds of divergence that considers not only the inferential aspects of a given logical theory, but also the epistemic aims and the methodological choices that drive its development. (shrink)

The term "non-monotonic logic" covers a family of formal frameworks devised to capture and represent defeasible inference , i.e., that kind of inference of everyday life in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further information. Such inferences are called "non-monotonic" because the set of conclusions warranted on the basis of a given knowledge base does not increase (in fact, it can shrink) with the size of the knowledge base itself. This is (...) in contrast to classical (first-order) logic, whose inferences, being deductively valid, can never be "undone" by new information. (shrink)

This paper defends a pragmatical approach to vagueness. The vagueness-adaptive logic VAL is a good reconstruction of and an excellent, instrument for human reasoning processes in which vague predicates are involved. Apart from its proof-theory and semantics, a Sorites-treating model based on it is presented, disarming the paradox. The paper opens perspectives with respect to the construction of theories by means of vague predicates.

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 this paper we present a comparison of certain inconsistencyadaptive logics and Jaśkowski’s logic.

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 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 aim of this paper is to lay bare the roots of dialetheism in discussions about dialectics and dialectical logic at the time of the first development of paraconsistent logics. In other words, th...

This paper presents Rasiowa–Sikorski deduction systems for logics \, \, \ and \. For each of the logics two systems are developed: an R–S system that can be supplemented with admissible cut rule, and a \-version of R–S system in which the non-admissible rule of cut is the only branching rule. The systems are presented in a Smullyan-like uniform notation, extended and adjusted to the aims of this paper. Completeness is proved by the use of abstract refutability properties which are (...) dual to consistency properties used by Fitting. Also the notion of admissibility of a rule in an R–S-system is analysed. (shrink)

This paper is a contribution to the program of constructing formal representations of pragmatic aspects of human reasoning. We propose a formalization within the framework of Adaptive Logics of the exclusivity implicature governing the connective ‘or’.Keywords: exclusivity implicature, Adaptive Logics.

We investigate and classify the notion of final derivability of two basic inconsistency-adaptive logics. Specifically, the maximal complexity of the set of final consequences of decidable sets of premises formulated in the language of propositional logic is described. Our results show that taking the consequences of a decidable propositional theory is a complicated operation. The set of final consequences according to either the Reliability Calculus or the Minimal Abnormality Calculus of a decidable propositional premise set is in general undecidable, and (...) can be -complete. These classifications are exact. For first order theories even finite sets of premises can generate such consequence sets in either calculus. (shrink)

In this paper I generalize the new approach to nonmonotonicreasoning that was presented in [6]. This generalization results in the inconsistency-adaptive logic PRL . I give proof theory, semantics, mention interesting properties,and comment on the reconstruction and amelioration of other nonmonotoniclogics and mechanisms.

The aim of the paper is to introduce the concept of adaptive logics (AL) or rather adaptive logical approach. In the introduction, a motivation and an emergence of AL are briefly discussed. In the second part of the paper, specifics of AL are analysed – especially nonmonotonic character, internal and external dynamics, as well as the structure of AL, namely the distinction between upper limit logic and lower limit logic. In this part, the dynamic proof is also described. Applications of (...) AL are presented in the third part. Three illustrations from three different branches of philosophy are presented. First one is an illustration of description of science – a traditional application of AL. Second one is an illustration of solving a deontic conflict – this is a new direction within in AL which has recently been researched. Third one is an illustration of analyses of metaphors – an example of an unusual application of AL. In the conclusion of the paper, contemporary results of AL are critically evaluated with respect to some problems of the project of AL. (shrink)

_Abduction of generalizations_ is the process in which explanatory hypotheses are formed for an observed, yet puzzling generalization such as ``pineapples taste sweet" or ``rainbows appear when the sun breaks through the rain". This phenomenon has received little attention in formal logic and philosophy of science. The current paper remedies this lacuna by first giving an overview of some general characteristics of this process, elaborating on its ubiquity in scientific and daily life reasoning. Second, the adaptive logic $\LAG$ is presented (...) to explicate this process formally. (shrink)

The aim of this paper is to offer an account of epistemic justification suitable for the context of theory pursuit, that is, for the context in which new scientific ideas, possibly incompatible with the already established theories, emerge and are pursued by scientists. We will frame our account paradigmatically on the basis of one of the influential systems of epistemic justification: Laurence Bonjour’s coherence theory of justification. The idea underlying our approach is to develop a set of criteria which indicate (...) that the pursued system is promising of contributing to the epistemic goal of robustness of scientific knowledge and of developing into a candidate for acceptance. In order to realize this we will (a) adjust the scope of Bonjour’s standards—consistency, inferential density, and explanatory power, and (b) complement them by the requirement of a programmatic character. In this way we allow for the evaluation of the “potential coherence” of the given epistemic system. (shrink)

This paper presents eight (previously unpublished) adaptive logics for belief revision, each of which define a belief revision operation in the sense of the AGM framework. All these revision operations are shown to satisfy the six basic AGM postulates for belief revision, and Parikh's axiom of Relevance. Using one of these logics as an example, we show how their proof theory gives a more dynamic flavor to belief revision than existing approaches. It is argued that this turns belief revision (that (...) obeys Relevance) into a more natural undertaking, where analytic steps are performed only as soon as they turn out to be necessary in order to uphold certain beliefs. (shrink)

This paper develops a new proof method for two propositional paraconsistent logics: the propositional part of Batens' weak paraconsistent logic CLuN and Schütte's maximally paraconsistent logic Φv. Proofs are de.ned as certain sequences of questions. The method is grounded in Inferential Erotetic Logic.

. This paper proposes a generalization of the theory of the process of explanation to include consistent as well as inconsistent situations. The generalization is strong, for example in the sense that, if the background theory and the initial conditions are consistent, it leads to precisely the same results as the theory from the lead paper (Halonen and Hintikka 2004). The paper presupposes (and refers to arguments for the view that) inconsistencies constitute problems and that scientists try to resolve them.

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)

ABSTRACT The present paper offers a new approach to non-monotonic logics and their reconstruction in terms of inconsistency-adaptive logics. By applying a special technique, universally quantified formulas are assigned instances that, given the paraconsistent framework, do not cause triviality even if they conflict with knowledge deriving from other sources. From the special instances, the usual instances may be derived conditionally, viz. provided they are not contradicted by statements derived with a higher preference ranking.

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.

Paraconsistent logics are logics that, in contrast to classical and intuitionistic logic, do not trivialize inconsistent theories. In this paper we take a paraconsistent view on two famous modal logics: B and S5. We use for this a well-known general method for turning modal logics to paraconsistent logics by defining a new negation as $\neg \varphi =_{Def} \sim \Box \varphi$. We show that while that makes both B and S5 members of the well-studied family of paraconsistent C-systems, they differ from (...) most other C-systems in having the important replacement property. We further show that B is a very robust C-system in the sense that almost any axiom which has been considered in the context of C-systems is either already a theorem of B or its addition to B leads to a logic that is no longer paraconsistent. There is exactly one notable exception, and the result of adding this exception to B leads to the other logic studied here, S5. (shrink)

In this paper I use the distinction between hard and soft information from the dynamic epistemic logic tradition to extend prior work on informational conceptions of logic to include non-monotonic consequence-relations. In particular, I defend the claim that at least some non-monotonic logics can be understood on the basis of soft or “belief-like” logical information, and thereby question the orthodox view that all logical information is hard, “knowledge-like”, information.

The three research questions of this study have been: what exactly is active ambiguity?; how should we assess active ambiguities in an argumentative discussion?; what does an adequate dialectical account of active ambiguity look like? These three questions have been answered by giving a definition of active ambiguity, and by elaborating on the properties of active ambiguity. Based on the survey of possible consequences of active ambiguities, and based on the basic division of labour in a persuasion dialogue, we arrived (...) at a set of requirements that a normative, procedural account of active ambiguity should satisfy. The model for ambiguity dialectic both provides a detailed account of evaluating active ambiguities, as well as a dialectical account of dealing with alleged active ambiguity. The distinction between constitutive and regulative rules for discussion has made it possible to provide a discussion model in which discussants can raise the issue of active ambiguity, and in which they can argue about the correctness of such points of order. This immanent dialectical approach has lead to a fourfold classification of fallacies: by using an actively ambiguous expression a party either violates a regulative, or a constitutive rule for persuasion dialogue, and if this party violates a rule, he or she either commits a fallacy of ambiguity, and possibly also the more complex fallacy of equivocation. This model for ambiguity dialectic has been shown to be useful for the analysis and evaluation of complex debates and discussions. The present study can be extended in various ways:  A model for critical discussion can be enriched so that it accommodates other regulative rules, such as the rule that requires arguments to be valid. By doing so, other points of order and other fallacy criticisms can be studied from the perspective of a critical metadiscussion.  The results concerning active ambiguity can be applied to other modes of reasoning, such as visual argumentation.  The results can be applied to ambiguity at the level of larger stretches of argumentative discourse. That could lead to a fruitful contribution to the theory of argument structures.  There still is a need for dialectical models that concern the use of usage declaratives different from providing a disambiguation, such as the use of definitions, clarifications of unfamiliar expressions, amplifications, etc., and the question would have to be answered how the rules with respect to active ambiguity would relate to those models.  The model can be enriched by inserting a specific ‘linguistic utterance meaning testing machine’. That would be a major step towards implementing the model in a computer program.  The use of descriptive profiles of dialogue could be improved further. In order to analyse the way parties respond to dialectically complex contributions, we are in need of a dialectical theory that provides the parties with specific rights and obligations for putting forward complex contributions and for responding to complex contributions. (shrink)

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)

Creativity is commonly seen as beyond the scope of rationality. In the present paper, it is argued that available insights in epistemology and available results in logic enable us to incorporate creativity within an independently sensible view on human rationality.

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)

This paper studies the question: How should one handle inconsistencies that derive from the inadequacy of the criteria by which one approaches the world. I compare several approaches. The adaptive logics defined from CLuN appear to be superior to the others in this respect. They isolate inconsistencies rather than spreading them, and at the same time allow for genuine deductive steps from inconsistent and mutually inconsistent premises. Yet, the systems based on CLuN seem to introduce an asymmetry betweennegated and non-negated (...) formulas, and this seems hard to justify. To clarify and understand the source of the asymmetry, the epistemological presuppositions of CLuN, viz. inadequate criteria, are investigated. This leads to a new type of paraconsistent logic that involves gluts with respect to all logical symbols. The larger part of the paper is devoted to this logic, to the adaptive logics defined from it, and to the properties of these systems. While the resulting logics are sensible and display interesting features, the search for variants of the justification leads to an unexpected justification for CLuN. (shrink)

In a rather general setting, we prove a number of basic theorems concerning computational complexity of derivability in adaptive logics. For that setting, the so-called standard format of adaptive logics is suitably adopted, and the corresponding completeness results are established in a very uniform way.

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.

For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms. A related property of Tarski logics is that the extensions of equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion does. (...) We also shall show that every monotonic logic weaker than an adaptive logic is weaker than the lower limit logic of the adaptive logic or identical to it. This highlights the role of the lower limit for settling the adaptive equivalence of extensions of equivalent premise sets. (shrink)

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

Scientific explanations arc subject to the occurrence of inconsistencies. To rule them out in many cases demands the construction of new theories. As the examples of complementary explanations show, that may take a while. Furthermore, even if possible in principle, it is not always reasonable to eliminate inconsistencies immediately, e.g., by bringing in a more sophisticated formal language. After all, under some circumstances a provisional, not fully coherent explanation may be better than none. In any case, we need a logically (...) controlled approach to such inconsistencies. Modern logic provides the tools which are necessary to solve this task. We will mention two alternative approaches. (shrink)

The paper contains a survey of (mainly unpublished) adaptive logics of inductive generalization. These defeasible logics are precise formulations of certain methods. Some attention is also paid to ways of handling background knowledge, introducing mere conjectures, and the research guiding capabilities of the logics.

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.