ON THE MEASURE OF FUZZINESS AND NEGATION Part I: Membership in the Unit Interval

We investigate the meaning of the concept of fuzziness. It is suggested that fuzziness can be related to the lack of distinction between a set and its negation. Using fuzzy subsets with grades of membership in the unit interval, measures of fuzziness are suggested. First, a class of measures based on metric distances is used to derive numeric measures of fuzziness of a fuzzy set. Finally, the concept of compatibility is used to develop linguistic measures of fuzziness.     

MapReduce环境下的否定粗糙关联规则算法

为了解决Apriori关联规则算法在处理大数据时产生大量候选项集,且无法在大数据环境下挖掘出频繁事件中所隐藏的否定关系的问题,通过深度分析事务数据库的特征,结合Boolean矩阵原理,运用粗糙集的分类思想和MapReduce并行编程模型,提出在MapReduce框架下的否定粗糙关联规则算法,以处理大数据所隐藏的否定关系。实验结果表明了该并行算法的有效性,适合挖掘出海量数据的否定关系。     

无中生有

论文以"纽约五"、高科技派(伦敦四)、"解构建筑七人组"为例阐述创新求变是现代建筑发展的灵魂。     

On the relationship between annotated logic programs and nonmonotonic formalisms

Abstract

In the past we developed a semantics for a restricted annotated logic language for inheritance reasoning. Here we generalize it to annotated Horn logic programs. We first provide a formal account of the language, describe its semantics, and provide an interpreter written in Prolog for it. We then investigate its relationship to Belnap's 4-valued logic, Gelfond and Lifschitz's semantics for logic programs with negation, Brewka's prioritized default logics and other annotated logics due to Kifer et al.     

On the completeness of SLDENF-resolution

SLDENF-resolution combines the negation-as-failure principle for logic programs involving negation, and SLDE-resolution for logic programs with an underlying equational theory. Recently, J. Shepherdson proved the soundness of this resolution principle wrt. an extended completion semantics. In this note, we investigate the particular problems of obtaining completeness which are caused by adding equational theories. As a concrete result we show to what extent the classical result for hierarchical and allowed nonequational programs can be generalized.     

Reasoning with Intensional Negative Adjectivals: Semantics, Pragmatics, and Context

Intensional negative adjectives alleged , artificial , fake , false , former , and toy are unusual adjectives that depending on context may or may not be restricting functions. A formal theory of their semantics, pragmatics, and context that uniformly accounts for their complex mathematical and computational characteristics and captures some peculiarities of individual adjectives is presented.
Such adjectives are formalized as new concept builders, negation‐like functions that operate on the values of intensional properties of the concepts denoted by their arguments and yield new concepts whose intensional properties have values consistent with the negation of the old values. Understanding these new concepts involves semantics, pragmatics and context‐dependency of natural language. It is argued that intensional negative adjectives can be viewed as a special‐purpose, weaker, conntext‐dependent negationin natural language. The theory explains and predicts many inferences licensed by expressions involving such adjectives. Implementation of sample examples demonstrates its computational feasibility. Computation of context‐dependent interpretation is discussed.
The theory allows one to enhance a knowledge representation system with similar concept building, negation‐like, context‐dependent functions, the availability of which appears to be a distinct characteristic of natural languages.     

含蓄否定(英文)

一句话中,既可使用否定词也可使用肯定式来实现否定;后者叫做含蓄否定或是隐蔽否定。用含蓄否定所表达的否定意思要比一般否定语气更为含蓄、委婉、诙谐。在有些语境中,含蓄否定的语气更为有力、强烈。在英语中,可以通过反问句、虚拟从句、状语从句、词语搭配以及词汇等方法达到含蓄否定的目的。     

The Basic Constructive Logic for Negation-Consistency

In this paper, consistency is understood in the standard way, i.e. as the absence of a contradiction. The basic constructive logic B_Kc4, which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined. Then, it is shown how to define a series of logics by extending B_Kc4 up to minimal intuitionistic logic. All logics defined in this paper are paraconsistent logics.     

直觉模糊逻辑非算子与蕴涵算子的一些性质及证明

给出了直觉模糊逻辑非算子的定义,讨论了非算子的一些性质。提出了关于直觉蕴涵算子的两个重要定理,并给出了证明     

On querying simple conceptual graphs with negation

We consider basic conceptual graphs, namely simple conceptual graphs (SGs), which are equivalent to the existential conjunctive positive fragment of first-order logic. The fundamental problem, deduction, is performed by a graph homomorphism called projection. The existence of a projection from a SG Q to a SG G means that the knowledge represented by Q is deducible from the knowledge represented by G. In this framework, a knowledge base is composed of SGs representing facts and a query is itself a SG. We focus on the issue of querying SGs, which highlights another fundamental problem, namely query answering. Each projection from a query to a fact defines an answer to the query, with an answer being itself a SG. The query answering problem asks for all answers to a query.

This paper introduces atomic negation into this framework. Several understandings of negation are explored, which are all of interest in real world applications. In particular, we focus on situations where, in the context of incomplete knowledge, classical negation is not satisfactory because deduction can be proven but there is no answer to the query. We show that intuitionistic deduction captures the notion of an answer and can be solved by projection checking. Algorithms are provided for all studied problems. They are all based on projection. They can thus be combined to deal with several kinds of negation simultaneously. Relationships with problems on conjunctive queries in databases are recalled and extended. Finally, we point out that this discussion can be put in the context of semantic web databases.