The constructive negation rule has been introduced by Chan 5, 6] to overcome the main drawbacks of the negation-as-failure rule: the unsoundness of oundering programs and, consequently , the inability of providing answers for non-ground negative queries. In this paper we deene a bottom-up semantics for constructive negation which we prove sound and complete with respect to the three-valued comp...

Negation is known to vary considerably in both form and morphosyntactic function among the languages of the Arawak family (Aikhenvald 1999: 96), with even closely-related languages sometimes exhibiting negation elements with starkly different forms and functions. The purpose of this chapter is to present a typological overview of negation in Arawak languages and to develop a preliminary compara...

Though negation is unique and central to human language, it has so far received little attention in cognitive neuroscience. The goal of the present study was to investigate the contrast between affirmative and negative sentences using fMRI, focusing on two central aspects, namely, (1) a semantic difference: affirmation is upward entailing, whereas negation is downward entailing; (2) a syntactic...

In this article we present the two classical negations of Euclid’s Fifth Postulate (done by Lobachevski-Bolyai-Gauss, and respectively by Riemann), and in addition of these we propose a partial negation (or a degree of negation) of an axiom in geometry. The most important contribution of this article is the introduction of the degree of negation (or partial negation) of an axiom and, more gener...

Why do some negative sentences sound strange, even when they are both true and grammatical? Past work suggests that both adults (e.g., Clark & Chase, 1972) and children (e.g., Kim, 1985) find negation difficult, but context can facilitate the processing of negative sentences (e.g., Wason, 1965). We argue that the effect of context on negation is driven by general pragmatic principles rather tha...

In this paper we present a complete framework for the annotation of negation in Italian, which accounts for both negation scope and negation focus, and also for language-specific phenomena such as negative concord. In our view, the annotation of negation complements more comprehensive Natural Language Processing tasks, such as temporal information processing and sentiment analysis. We applied t...

Existing semantics for answer-set program updates fall into two categories: either they consider only strong negation in heads of rules, or they primarily rely on default negation in heads of rules and optionally provide support for strong negation by means of a syntactic transformation. In this paper we pinpoint the limitations of both these approaches and argue that both types of negation sho...

Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant 0, namely ¬φ isφ → 0. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which i...

In many practical situations, we only know the bounds on the distances. A natural question is: knowing these bounds, can we check whether there exists a metric whose distance always lie within these bounds – or such a metric is not possible and thus, the bounds are inconsistent. In this paper, we provide an answer to this question. We also describe possible applications of this result to a desc...

This essay proposes a procedural interpretation of negative information in terms of split negation as procedural prohibition. Information frames and models are introduced, with negation defined as the implication of bottom, 0. A method for extracting the procedures prohibited by complex formulas is outlined, and the relationship between types of prohibited procedures is identified. Definitions ...