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.

%B Journal of Logic, Language and Information %V 18 %P 333–356 %G eng %U http://dx.doi.org/10.1007/s10849-009-9084-y %R 10.1007/s10849-009-9084-y %0 Generic %D 2009 %T Menselijke rationaliteit en identiteit. %A van der Waart van Gulik, Stephan %E Van den Bossche, M. %E Vandemeulebroecke, R. %XWat volgt is een aanzet tot een zuiver beschrijvende analyse van de relatie tussen de ontwikkeling van de menselijke identiteit en de drie sociaal- psychologische fenomenen xenofobie, etnocentrisme en tolerantie. Het werkkader voor deze analyse is een conceptueel, speculatief model van de menselijke rationaliteit.

%B Humanismen %I VUB Press %P 163-172 %G eng %0 Generic %D 2008 %T A Fuzzy Logic Approach to Non-Scalar Hedges %A van der Waart van Gulik, Stephan %E Makinson, David %E Wansing, Heinrich %XIn (Journal of Philosophical Logic, 2: 458508, 1973), George Lakoff proposes a fuzzy semantics for the non-scalar hedges *technically, strictly speaking, and loosely speaking*. These hedges are able to modify the meaning of a predicate. However, Lakoffs proposal is problematic. For example, his semantics only contains interpretations for hedged predicates using semantic information provided by selection functions. What kind of information these functions should provide for non-hedged predicates remains unspecified. This paper presents a solution for this deficit and other problems by means of a generic first-order fuzzy logic **FL**_{h} . A wide range of fuzzy logics can be used as a basis for **FL**_{h} . Next to a fully specified semantics, this solution also incorporates a proof theory for reasoning with these hedges. **FL**_{h} makes use of a special set of selection functions. These functions collect the kind of information a reasoner can retrieve from concepts in his or her memory when interpreting a (non-)hedged predicate. Despite this non-standard element, **FL**_{h} remains a conservative modification of its underlying fuzzy logic.

We present and discuss a new solution for reasoning with sorites series and their related paradoxes.We argue that a suitable logic for sorites series should be able to apply specific classical logic rules like modus ponens until and unless it becomes apparent that these applications generate unacceptable results. When the latter happens, the logic should be able to retract those applications of classical logic rules that are problematic. The formal core of our solution consists of several adaptive logics based on a Łukasiewicz fuzzy logic extended with the Baaz △-operator and a non-singleton interval of designated values. The natural dynamics characteristic of adaptive logics allows these logics to perform necessary retractions in an intuitive and elegant manner. © 2008 Elsevier B.V. All rights reserved.

%B Fuzzy Sets and Systems %V 159 %P 1869–1884 %G eng %R 10.1016/j.fss.2008.01.001 %0 Generic %D 2008 %T Vage logica's, concepten en betekenistransformatoren. %A van der Waart van Gulik, Stephan %I Ghent University %C Ghent %8 May 30 %9 phd %1Joke Meheus

%0 Conference Paper %B Proceedings of the European Cognitive Science Conference 2007 %D 2007 %T On the Implementation of Concept Structures in Fuzzy Logic. %A van der Waart van Gulik, Stephan %E Vosniadou, S. %E Kayser, D. %E Athanassios, P. %XA procedure is presented which can modify a large number of fuzzy logics in such a way that the result integrates a logically meaningful representation of the family resemblance structure of fuzzy concepts. The most important aspect of this modification is the implementation of so-called concept matrices. The interpretation and construction of these new formal objects is based upon Fintan Costellos Diagnostic Evidence Model (2000), a contemporary cognitive scientific model of concept structure and concept combination. As a result, it becomes possible to formalize, explain and simulate new logical aspects of cognitive fuzziness such as meaning transformations by means of non-scalar hedges, and interpretational and inferential operations over non-intersective concept combinations.

%B Proceedings of the European Cognitive Science Conference 2007 %G eng