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On the Psychology of Vague Predicates
, 1999
"... Most speakers experience unclarity about the application of predicates like tall and red to liminal cases. We formulate alternative psychological hypotheses about the nature of this unclarity, and report experiments that provide a partial test of them. A psychologized version of the #vaguenessas ..."
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Most speakers experience unclarity about the application of predicates like tall and red to liminal cases. We formulate alternative psychological hypotheses about the nature of this unclarity, and report experiments that provide a partial test of them. A psychologized version of the #vaguenessasignorance" theory is then advanced and defended. 1 Introduction If you examine monochromatic light from 650nm on down, the #rst hues will probably strikeyou as red and later ones as orange. Somewhere near 610nm, however, your judgment will become unstable, with neither the a#rmation #This hue is red" nor its denial aptly characterizing your belief. Such unclarity is called #vagueness," and as every amateur sophist knows, it infects virtually every predicate in natural language. Vagueness is more than an annoyance since it can obstruct the attempt to articulate valid principles of reasoning. A classic illustration concerns mathematical induction. #1# Principle of Mathematical Induction: ...
Style as Choice of Blending Principles
 In Style and Meaning in Language, Art, Music and Design, Proceedings of a Symposium at the 2004 AAAI Fall Symposium Series, Technical Report FS0407, AAAI
"... This paper proposes a new approach to style, arising from our work on computational media using structural blending, which enriches the conceptual blending of cognitive linguistics with structure building operations in order to encompass syntax and narrative as well as metaphor. We have implemented ..."
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This paper proposes a new approach to style, arising from our work on computational media using structural blending, which enriches the conceptual blending of cognitive linguistics with structure building operations in order to encompass syntax and narrative as well as metaphor. We have implemented both conceptual and structural blending, and conducted initial experiments with poetry, although the approach generalizes to other media. The central idea is to analyze style in terms of principles for blending, based on our £nding that very different principles from those of common sense blending are needed for some creative works. 1
Fuzzy Epistemicism ∗
, 2007
"... Please do not cite or quote without permission. It is taken for granted in much of the literature on vagueness that semantic and epistemic approaches to vagueness are fundamentally at odds. If we can analyze borderline cases and the sorites paradox in terms of degrees of truth, then we don’t need an ..."
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Please do not cite or quote without permission. It is taken for granted in much of the literature on vagueness that semantic and epistemic approaches to vagueness are fundamentally at odds. If we can analyze borderline cases and the sorites paradox in terms of degrees of truth, then we don’t need an epistemic explanation. Conversely, if an epistemic explanation suffices, then there is no reason to depart from the familiar simplicity of classical bivalent semantics. I question this assumption, showing that there is an intelligible motivation for adopting a manyvalued semantics even if one accepts a form of epistemicism. The resulting hybrid view has advantages over both classical epistemicism and traditional manyvalued approaches. It is taken for granted in much of the literature on vagueness that semantic and epistemic approaches to vagueness are fundamentally at odds. If we can analyze borderline cases and the sorites paradox in terms of degrees of truth, then we don’t need an epistemic explanation. Conversely, if an epistemic explanation suffices, then there is no reason to depart from the familiar simplicity of classical bivalent semantics. Thus, while an epistemic approach to vagueness is not logically incompatible with the view that truth comes in degrees, it is usually assumed that there could be no motivation for combining the two.
LBonds vs extents of direct product of two Lfuzzy contexts
"... Abstract. We focus on the direct product of two Lfuzzy contexts, which are defined with the help of a binary operation on a lattice of truthvalues L. This operation, essentially a disjunction, is defined as k ⋉ l = ¬k → l, for k, l ∈ L where negation is interpreted as ¬l = l → 0. We provide some r ..."
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Abstract. We focus on the direct product of two Lfuzzy contexts, which are defined with the help of a binary operation on a lattice of truthvalues L. This operation, essentially a disjunction, is defined as k ⋉ l = ¬k → l, for k, l ∈ L where negation is interpreted as ¬l = l → 0. We provide some results which extend previous work by Krötzsch, Hitzler and Zhang. 1
What is a fuzzy concept lattice? What is a fuzzy concept lattice?
"... Abstract. The paper is an overview of several approaches to the notion of a concept lattice from the point of view of fuzzy logic. The main aim is to clarify relationships between the various approaches. ..."
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Abstract. The paper is an overview of several approaches to the notion of a concept lattice from the point of view of fuzzy logic. The main aim is to clarify relationships between the various approaches.
Contextual Effects on Vagueness and the Sorites Paradox: A Preliminary Study
"... Abstract. Context is a prominent theme in accounts of the semantics of vagueness. Contextual theories of vagueness have been motivated in part by a desire to disarm skeptical arguments that make use of vagueness; another motive is the hope that they might help to resolve the Sorites Paradox. This pa ..."
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Abstract. Context is a prominent theme in accounts of the semantics of vagueness. Contextual theories of vagueness have been motivated in part by a desire to disarm skeptical arguments that make use of vagueness; another motive is the hope that they might help to resolve the Sorites Paradox. This paper is intended as part of a larger project, which aims at describing and comparing the leading theories that have been presented, to bring out the ways in which contextual theories have informed the semantic phenomenon of vagueness, and to make strategic assesments and suggestions concerning the crucial case of adjectives. It concentrates on Hans Kamp’s 1975 theory, and two recent contributions by Haim Gaifman and Joseph Halpern. The specific goal of this paper is to examine the role of context in the semantics of certain adjectives, and assess to what extent context can help to solve what I take to be the most challenging version of the Sorites Paradox. 1
PROPERTIES OF FUZZY LOGICAL OPERATIONS
, 2009
"... This thesis deals with geometrical and differential properties of triangular norms (tnorms for short), i.e. binary operations which implement logical conjunctions in fuzzy logic. It is divided into two main parts. The first part discusses the problem of a visual characterization of the associativit ..."
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This thesis deals with geometrical and differential properties of triangular norms (tnorms for short), i.e. binary operations which implement logical conjunctions in fuzzy logic. It is divided into two main parts. The first part discusses the problem of a visual characterization of the associativity of tnorms. The thesis adopts the results given by web geometry, mainly the concept of the Reidemeister closure condition, in order to characterize the shape of level sets of tnorms. This way, a visual characterization of the associativity is provided for general, continuous, and continuous Archimedean tnorms. The second part of the thesis deals with differential properties of continuous Archimedean tnorms. It is shown that partial derivatives of such a tnorm on a particular subset of its domain correspond directly to the generator (or to the derivative of the generator) of the tnorm. Namely, partial derivatives of tnorms along the annihilator, the unit element, a level set, and a vertical section are studied. As the result, several methods which reconstruct
A New Proof of Completeness of Fuzzy Logic and Some Conclusions for Approximate Reasoning
, 1995
"... this paper, we turn again to the problem of the completeness of firstorder fuzzy logic. The completeness theorem for propositional fuzzy logic was proved by J. Pavelka in [15]. Later, some other variations appeared [18] proving, however, completeness only for formulas in the degree 1. Extension of ..."
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this paper, we turn again to the problem of the completeness of firstorder fuzzy logic. The completeness theorem for propositional fuzzy logic was proved by J. Pavelka in [15]. Later, some other variations appeared [18] proving, however, completeness only for formulas in the degree 1. Extension of Pavelka's proof to firstorder fuzzy logic was done by the author in [5, 6]. The proof, however, is quite complicated based on ultrafilter trick and on several tricky axioms. An open question remained, whether this proof can be done in a different way following classical Henkin construction of a model from the constats. This has been done by P. H#jek for fuzzy propositional logic in [4] and independently on him for firstorder one by the author. This result, besides others, is presented in this paper. Let us remark, that motivation of both proofs was different. The main goal of H#jek was to prepare material for study of recursive properties of fuzzy logic. Some of the results, also independently, have been presented in [12]. The main problem consits in introducing names for all the truth values being special atomic formulas in the language. If we work with the interval [0; 1] of truth values then the language becomes immediately uncountable, which disqualifies it for study of recursive properties. However, as both papers demonstrate, it is possible to introduce only countably many names for rational numbers being dense subset of [0; 1] so that we may study recursive properties of fuzzy logic using classical tools. The latter was demonstrated by P. H#jek in [4]. In [14], we have demonstrated that the language can be further simplified when introducing a special unary connective