•A new family of fuzzy implications based on powers of t-norms is presented.•Their truth value is invariant with respect to powers of t-norms.•Other important additional properties are analyzed.•They ...do not intersect the main classes of fuzzy implications.
The modification (relaxation or intensification) of the antecedent or the consequent in a fuzzy “If, Then” conditional is an important asset for an expert in order to agree with it. The usual method to modify fuzzy propositions is the use of Zadeh's quantifiers based on powers of t-norms. However, the invariance of the truth value of the fuzzy conditional would be a desirable property when both the antecedent and the consequent are modified using the same quantifier. In this paper, a novel family of fuzzy implication functions based on powers of continuous t-norms which ensure the aforementioned property is presented. Other important additional properties are analyzed and from this study, it is proved that they do not intersect the most well-known classes of fuzzy implication functions.
This paper has two related goals. First, we develop an expressivist account of negation which, in the spirit of Alan Gibbard, treats disagreement as semantically primitive. Our second goal is to make ...progress toward a unified expressivist treatment of modality. Metaethical expressivists must be expressivists about deontic modal claims. But then metaethical expressivists must either extend their expressivism to include epistemic and alethic modals, or else accept a semantics for modal expressions that is radically disjunctive. We propose that expressivists look to Amie Thomasson’s work for a general strategy for offering a unified expressivist account of modality. Modals in general, we propose, are devices for expressing metalinguistic commitments within the object language, with deontic, epistemic, and metaphysical modals all expressing different kinds of metalinguistic commitments.
Die Buchreihe Linguistik - Impulse & Tendenzen (LIT) ist ein attraktives Forum für hochwertige Arbeiten zur Sprachwissenschaft - insbesondere zur germanistischen Linguistik. Sie sucht aktuelle ...Tendenzen aufzunehmen und widerzuspiegeln, gleichzeitig aber wegweisende Impulse für das Fach und seine weitere Entwicklung zu geben. Im Fokus steht die synchrone Sprachwissenschaft mit all ihren Facetten.
Abstract
This article offers a characterization of the biased polar interrogative with
¿a poco (no)?
, frequent in Mexican Spanish. This characterization is based on the system proposed by
Sudo ...(2013)
and shows that Sudo’s two notions of epistemic bias and evidential bias are necessary and sufficient to characterize the conventional non-propositional meaning associated with the three kinds of
a poco
questions in Mexican Spanish: the
a poco
positive polarity question codes a negative epistemic bias and a +positive or +negative evidential bias; the
a poco
negative polarity question with inside negation codes a positive epistemic bias and a +negative evidential bias; and the
a poco
negative polarity question with outside negation codes a positive epistemic bias and a −negative evidential bias. Lastly, the article discusses to what extent these characterizations are also compatible with the interactional uses of the short questions
¿a poco?
and
¿a poco no?
In this paper we study the conditions in which the implication operators satisfy the property
I(
x,
c(
x))=
c(
x) for all
x∈0,1,
c being any strong negation. This study has led us to present ...different implication operator characterization theorems from automorphisms, obtaining a theorem similar to the one presented by Smets and Magrez (Internat. J. Approx. Reason. 1 (1987) 327), in which the strong negation
c used is not generated by the same automorphism that generates the implication.
This paper investigates the deontic modal
in Cantonese. I argue that
is an NPI and a negative operator is induced at the sentence-initial position by the SFPs
or
in rhetorical questions. In SAI ...sentence,
must syntactically agree with the negative operator for licensing, and minimality and locality effects are found in such agreement. This study may provide evidence of a syntactic approach to NPI licensing and rhetorical questions.
According to the literature, negations such as "not" or "don't" reduce the accessibility in memory of the concepts under their scope. Moreover, negations applied to action contents (e.g., "don't ...write the letter") impede the activation of motor processes in the brain, inducing "disembodied" representations. These facts provide important information on the behavioral and neural consequences of negations. However, how negations themselves are processed in the brain is still poorly understood. In two electrophysiological experiments, we explored whether sentential negation shares neural mechanisms with action monitoring or inhibition. Human participants read action-related sentences in affirmative or negative form ("now you will cut the bread" vs "now you will not cut the bread") while performing a simultaneous Go/NoGo task. The analysis of the EEG rhythms revealed that theta oscillations were significantly reduced for NoGo trials in the context of negative sentences compared with affirmative sentences. Given the fact that theta oscillations are often considered as neural markers of response inhibition processes, their modulation by negative sentences strongly suggests that negation uses neural resources of response inhibition. We propose a new approach that views the syntactic operator of negation as relying on the neural machinery of high-order action-monitoring processes.
Previous studies have shown that linguistic negation reduces the accessibility of the negated concepts and suppresses the activation of specific brain regions that operate in affirmative statements. Although these studies focus on the consequences of negation on cognitive and neural processes, the proper neural mechanisms of negation have not yet been explored. In the present EEG study, we tested the hypothesis that negation uses the neural network of action inhibition. Using a Go/NoGo task embedded in a sentence comprehension task, we found that negation in the context of NoGo trials modulates frontal theta rhythm, which is usually considered a signature of action inhibition and control mechanisms.
This article introduces, studies, and applies a new system of logic which is called 'HYPE'. In HYPE, formulas are evaluated at states that may exhibit truth value gaps (partiality) and truth value ...gluts (overdeterminedness). Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE's logical connectives. Furthermore, HYPE's first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work.
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