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When negation is not negation
In this paper I will discuss the formation of different types of yes/no questions in Serbian (examples in (1)), focusing on the syntactically and semantically puzzling example (1d), which involves the negative auxiliary inversion. Although there is a negative marker on the fronted auxiliary, the construction does not involve sentential negation. This coincides with the fact that the negative quantifying NPIs cannot be licensed. The question formation and sentential negation have similar syntactic effects cross-linguistically. This has led to various attempts to formulate a unifying syntactic account of the phenomena (ever since Klima 1964). One striking fact about the two syntactic contexts is that both license weak NPIs (Negative Polarity Items). It has been suggested (cf. Laka 1990, Culicover 1991) that the derivation of both interrogatives and negatives involves the same type of functional projection PolP (polarity phrase). One such account of the formation of negative interrogatives in Serbo- Croatian is offered by Progovac (2005). She proposes that there are two PolPs optionally cooccurring in the same clause, in which both positive and negative polarity items check their positive or negative features (following Haegeman and Zanuttini (1991) feature-checking account of negative structures, and the insights of Brown(1999) on the negation in Russian). On her account, the negative auxiliary question in (1d), is the case when both polarity phrases are present. The higher has [-pos +neg] features, and the lower one (below TP) is [-pos -neg]. Although her account correctly predicts the ungrammaticality of (2a) in contrast with (1c), it wrongly predicts the (2b) to be grammatical. I will argue that Progovac’s theory regarding the nature of the PolP is wrong. It employs both the binary feature valuation on the polarity head and the hierarchical ordering of the two polarity phrases, which eventually leads to overgeneration. On the account presented here the nature of the question marker (li vs zar) is highly relevant. Notice that (1b) and (1d) express presuppositions regarding the truth value of the propositions. In this way they contrast with (1a) and (1c). In addition, the type (1b) (with the question particle zar) can introduce both the positive and negative presupposition as shown in (3), which, semantically, makes this construction compatible with negative auxiliary questions in English (4a). The polarity items licensed in the relevant structures are also of the same type in both languages. The fronted-negative-auxiliary questions (1d) in Serbian are only possible with the particle li. In this case the presupposition is exclusively positive. The peculiar question/focus marking function of li (in Bulgarian and Russian) is well known. However, it is always assumed that its focus marking role is not relevant for the formation of yes/no questions. This I believe is not correct. The syntactic explanation of the interpretational facts points to the following: A) The possibility of the separate lexical encoding (particle zar) of the ‘rhetorical’ yes/no questions in Serbian allows the embedding of both positive and negated sentences, in which case the (weak) NPIs can remain in local relation with the negated verb. B) Recall that Serbian is an NC language, which requires local/c-command relation between the verbal negative marker and the NPI. With the negative inverted auxiliary questions this condition is not met, and the licensing of an n-word is not possible. C) The impossibility of licensing a weak NPI (i-words in the examples below) is due to the nature of the question marker li. (1) a. Da li je Vera videla ikoga / nekoga / *nikoga? DA Q aux Vera see.part.F.Sg anyone someone noone “Did Vera see anyone/someone/noone?” b. Zar je Vera videla ikoga / nekoga / *nikoga? ZAR aux Vera see.part.F.Sg anyone someone noone “Is it really the fact that Vera saw anyone/someone?” c. Je li Vera videla ikoga / nekoga /*nikoga? aux Q Vera see.part.F.Sg anyone someone noone “Did Vera see anyone/someone/noone?” d. Nije li Vera videla *ikoga / nekoga / *nikoga? neg+aux Q Vera see.part.F.Sg anyone someone noone “Didn’t Vera see someone?”/ “Vera saw someone, didn’t she?” (2) a. *Nije li Vera videla nikoga? neg+aux Q Vera see.part.F.Sg noone b. *Nije li Vera videla ikoga? neg+aux Q Vera see.part.F.Sg anyone (3) a. Zar je Vera videla nekoga / ikoga? ZAR aux Vera see.part.F.Sg someone/anyone b. Zar Vera nije videla nekoga/nikoga? ZAR Vera neg+aux see.part.F.Sg someone/anyone (4) a. Didn’t Vera (NOT) see someone/anyone? b. Vera saw someone, didn’t she
Queries with Guarded Negation (full version)
A well-established and fundamental insight in database theory is that
negation (also known as complementation) tends to make queries difficult to
process and difficult to reason about. Many basic problems are decidable and
admit practical algorithms in the case of unions of conjunctive queries, but
become difficult or even undecidable when queries are allowed to contain
negation. Inspired by recent results in finite model theory, we consider a
restricted form of negation, guarded negation. We introduce a fragment of SQL,
called GN-SQL, as well as a fragment of Datalog with stratified negation,
called GN-Datalog, that allow only guarded negation, and we show that these
query languages are computationally well behaved, in terms of testing query
containment, query evaluation, open-world query answering, and boundedness.
GN-SQL and GN-Datalog subsume a number of well known query languages and
constraint languages, such as unions of conjunctive queries, monadic Datalog,
and frontier-guarded tgds. In addition, an analysis of standard benchmark
workloads shows that most usage of negation in SQL in practice is guarded
negation
Indefinites, negation and Jespersen's Cycle in the history of Low German
This paper offers a formal account of the diachronic changes in the interaction between indefinites in the scope of negation and the expression of sentential negation in the history of Low German. Different types of negative concord develop at the different historical stages. Parallel to that, the language underwent Jespersen's Cycle. In addition, I argue that, against common belief, Jespersen's Cycle is at best indirectly related to the type of interaction between indefinites and negation. Changes in the type of indefinites used in the scope of negation arise due to changes in the lexical properties of the indefinites involved, not as a result of changes in the expression of negation. Conversely, changes in the type of indefinites do not trigger changes in the expression of negation
Interval-valued contractive fuzzy negations
In this work we consider the concept of contractive interval-valued fuzzy negation, as a negation such that it does not increase the length or amplitude of an interval. We relate this to the concept of Lipschitz function. In particular, we prove that the only strict (strong) contractive interval-valued fuzzy negation is the one generated from the standard (Zadeh's) negation
Double-Negation Elimination in Some Propositional Logics
This article answers two questions (posed in the literature), each concerning
the guaranteed existence of proofs free of double negation. A proof is free of
double negation if none of its deduced steps contains a term of the form
n(n(t)) for some term t, where n denotes negation. The first question asks for
conditions on the hypotheses that, if satisfied, guarantee the existence of a
double-negation-free proof when the conclusion is free of double negation. The
second question asks about the existence of an axiom system for classical
propositional calculus whose use, for theorems with a conclusion free of double
negation, guarantees the existence of a double-negation-free proof. After
giving conditions that answer the first question, we answer the second question
by focusing on the Lukasiewicz three-axiom system. We then extend our studies
to infinite-valued sentential calculus and to intuitionistic logic and
generalize the notion of being double-negation free. The double-negation proofs
of interest rely exclusively on the inference rule condensed detachment, a rule
that combines modus ponens with an appropriately general rule of substitution.
The automated reasoning program OTTER played an indispensable role in this
study.Comment: 32 pages, no figure
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A privative derivational source for standard negation in Lokono (Arawakan)
Abstract
It has recently been argued that Arawakan languages of South America provide evidence for a novel historical
source for standard negation, a privative derivational affix. This hypothesis posits that the prefixal standard negation found in
some languages of the family developed from a privative prefix, ma-, present in Proto-Arawakan, that originally
derived privative stative verbs from nouns. According to this account, the function of this prefix extended, in many languages of
the family, to negating nominalized verbs in subordinate clauses, and then, via insubordination, to standard main clause negation,
in a smaller subset of languages. The purpose of this paper is to substantiate this hypothetical trajectory in detail in a
particular Arawakan language: Lokono, a highly endangered language of the Guianas. On the basis of modern linguistic fieldwork and
colonial-era language materials, we show that 18th-century Lokono exhibited a standard negation construction based on the
privative, and that this construction exhibits clear signs of its subordinate clause origin. We show that Lokono also exhibits the
full range of functions for the privative ma- that are predicted to be historical precursors to the standard
negation function, substantiating the historical trajectory from privative derivation to standard negation. We conclude by
observing that the prefixal standard negation strategy has lost ground since the 18th century to a standard negation particle that
originally expressed constituent negation, possibly due to contact with colonial languages that employ similar strategies
An Argument for Minimal Logic
The problem of negative truth is the problem of how, if everything in the world is positive, we can speak truly about the world using negative propositions. A prominent solution is to explain negation in terms of a primitive notion of metaphysical incompatibility. I argue that if this account is correct, then minimal logic is the correct logic. The negation of a proposition A is characterised as the minimal incompatible of A composed of it and the logical constant ¬. A rule based account of the meanings of logical constants that appeals to the notion of incompatibility in the introduction rule for negation ensures the existence and uniqueness of the negation of every proposition. But it endows the negation operator with no more formal properties than those it has in minimal logic
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