The article presents several adaptive fuzzy hedge logics. These logics are designed to perform a specific kind of hedge detection. Given a premise set Γ that represents a series of communicated statements, the logics can check whether some predicate occurring in Γ may be interpreted as being (implicitly) hedged by technically, strictly speaking or loosely speaking, or simply non-hedged. The logics take into account both the logical constraints of the premise set as well as conceptual information concerning the meaning of (...) potentially hedged predicates (stored in the memory of the interpreter in question). The proof theory of the logics is non-monotonic in order to enable the logics to deal with possible non-monotonic interpretation dynamics (this is illustrated by means of several concrete proofs). All the adaptive fuzzy hedge logics are also sound and strongly complete with respect to their [0,1]-semantics. (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.

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.

. 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.

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.

Proof theory and semantics of an adaptive logic that deals adequately with change in individuals with or without a name are presented. New logical constants are introduced, viz. indicators. Within a given context they function as names, predicates and quantifiers at the same time. The thus extended language (of classical logic) has a big expressive power and solvespartly — the (classical) non-logical presuppositions with respect to ‘the existence of individuals’. Nevertheless, from a purely logical point of view, the here pre (...) - sented logic requires nothing but a very intuitive selection of classical models of the premises, viz. the minimally abnormal ones. (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)

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)