Abstract: 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, including interactive multimedia poetry, although the approach generalizes to other media. The central idea is to analyze style in terms of blending principles, based on our finding that different principles from those of common sense blending are often needed for some contemporary poetic metaphors. 1

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 #vagueness-as-ignorance" 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: ...

this paper, we turn again to the problem of the completeness of first-order 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 first-order 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 first-order 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

This thesis deals with geometrical and differential properties of triangular norms (t-norms 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 t-norms. 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 t-norms. This way, a visual characterization of the associativity is provided for general, continuous, and continuous Archimedean t-norms. The second part of the thesis deals with differential properties of continuous Archimedean t-norms. It is shown that partial derivatives of such a t-norm on a particular subset of its domain correspond directly to the generator (or to the derivative of the generator) of the t-norm. Namely, partial derivatives of t-norms along the annihilator, the unit element, a level set, and a vertical section are studied. As the result, several methods which reconstruct

Abstract. We focus on the direct product of two L-fuzzy contexts, which are defined with the help of a binary operation on a lattice of truth-values 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