A Non-deterministic View on Non-classical Negations

We investigate two large families of logics, differing from each other by the treatment of negation. The logics in one of them are obtained from the positive fragment of classical logic (with or without a propositional constant ff for “the false”) by adding various standard Gentzen-type rules for negation. The logics in the other family are similarly obtained from LJ⁺, the positive fragment of intuitionistic logic (again, with or without ff). For all the systems, we provide simple semantics which is based on non-deterministic four-valued or three-valued structures, and prove soundness and completeness for all of them. We show that the role of each rule is to reduce the degree of non-determinism in the corresponding systems. We also show that all the systems considered are decidable, and our semantics can be used for the corresponding decision procedures. Most of the extensions of LJ⁺ (with or without ff) are shown to be conservative over the underlying logic, and it is determined which of them are not.     

Combining Possibilities and Negations

Combining non-classical (or sub-classical) logics is not easy, but it is very interesting. In this paper, we combine nonclassical logics of negation and possibility (in the presence of conjunction and disjunction), and then we combine the resulting systems with intuitionistic logic. We will find that Kracht's results on the undecidability of classical modal logics generalise to a non-classical setting. We will also see conditions under which intuitionistic logic can be combined with a non-intuitionistic negation without corrupting the intuitionistic fragment of the logic.     

Dialectical Negations,Absolute Affirmation

Studies in Philosophy and Education -     

Maltreated Children Use More Grammatical Negations

Many studies reveal a strong impact of childhood maltreatment on language development, mainly resulting in shorter utterances, less rich vocabulary, or a delay in grammatical complexity. However, different theories suggest the possibility for resilience—a positive adaptation to an otherwise adverse environment—in children who experienced childhood maltreatment. Here, we investigated different measures for language development in spontaneous speech, examining whether childhood maltreatment leads to a language deficit only or whether it can also result in differences in language use due to a possible adaptation to a toxic environment. We compared spontaneous speech during therapeutic peer-play sessions of 32 maltreated and 32 non-maltreated children from the same preschool and equivalent in gender, age (2 to 5 years), home neighborhood, ethnicity, and family income. Maltreatment status was reported by formal child protection reports, and corroborated by independent social service reports. We investigated general language sophistication (i.e., vocabulary, talkativeness, mean length of utterance), as well as grammatical development (i.e., use of plurals, tense, grammatical negations). We found that maltreated and non-maltreated children showed similar sophistication across all linguistic measures, except for the use of grammatical negations. Maltreated children used twice as many grammatical negations as non-maltreated children. The use of this highly complex grammatical structure shows an advanced linguistic skill, which shows that childhood maltreatment does not necessarily lead to a language deficit. The result might indicate the development of a negativity bias in the structure of spontaneous language due to an adaptation to their experiences.     

Proof Systems Combining Classical and Paraconsistent Negations

New propositional and first-order paraconsistent logics (called L _ω and FL _ω , respectively) are introduced as Gentzen-type sequent calculi with classical and paraconsistent negations. The embedding theorems of L _ω and FL _ω into propositional (first-order, respectively) classical logic are shown, and the completeness theorems with respect to simple semantics for L _ω and FL _ω are proved. The cut-elimination theorems for L _ω and FL _ω are shown using both syntactical ways via the embedding theorems and semantical ways via the completeness theorems. Presented by Yaroslav Shramko and Heinrich Wansing     

A Hierarchy of Classical and Paraconsistent Logics

Journal of Philosophical Logic - In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a...     

Dual Intuitionistic Logic and a Variety of Negations: The Logic of Scientific Research

We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic. This logic can be labeled as “falsification logic”: it embodies the Popperian methodology of scientific discovery. Whereas intuitionistic logic deals with constructive truth and non-constructive falsity, and Nelson's logic takes both truth and falsity as constructive notions, in the falsification logic truth is essentially non-constructive as opposed to falsity that is conceived constructively. We also briefly clarify the relationships of our falsification logic to some other logical systems.     

When Cheap Isn't the Same as Not Expensive: Generic Price Terms and Their Negations

Generic price terms such as cheap, not expensive, not cheap, and expensive are used frequently in marketing, but little is known about how consumers interpret them. In typical consumer contexts, in which lower prices are preferred, we find that not cheap means essentially the same as expensive (i.e., not cheap = expensive). In contrast, not expensive does not mean the same as cheap, in that cheap is associated with lower prices (i.e., cheap < not expensive). As an implication, in a consumer survey we find different response distributions for rating scales that are anchored with endpoint labels of not expensive versus expensive as compared to cheap versus expensive or cheap versus not cheap (the latter two are equivalent). Furthermore, although cheap is associated with lower prices than not expensive, this does not necessarily translate into higher preferences for options that are described as cheap (vs. not expensive), because cheap may also evoke negative quality perceptions. Finally, we demonstrate an interesting reversal in the way price terms are interpreted: when higher prices are preferred, cheap is equal to not expensive (i.e., cheap = not expensive), whereas not cheap is associated with lower prices than expensive (i.e., not cheap < expensive).     

Negations and natural sampling in data selection: Ecological versus heuristic explanations of matching bias

Matching bias occurs when people ignore negations when testing a hypothesis--for example, if A, then not 2--and select possible data types that are named in the hypothesis (i.e., A and 2; Evans & Lynch, 1973). There are two explanations of this bias: the heuristic account and the contrast class account. The latter is part of Oaksford and Chater's (1994) ecological approach to data selection. On this account, a contrast set (i.e., birds that are not ravens) has a higher probability than the original set (i.e., birds that are ravens). This article reports two experiments in which these accounts make divergent predictions. The same materials were used as those in Yama (2001), who found more support for the heuristic approach. Experiment 1 replicated Yama with Western participants. Experiment 2 used a procedure introduced by Oaksford and Wakefield (2003). Rather than present participants with one of each of the four possible data types all at once, 50 were presented one at a time. The proportions of each data type reflected the relevant probabilities. The results supported the ecological approach, showing that people constructed contrast sets that strongly influenced their data selection behavior. The results were not consistent with the heuristic approach.     

A Stronger Doctrine of Double Effect

Many believe that intended harms are more difficult to justify than are harms that result as a foreseen side effect of one's conduct. We describe cases of harming in which the harm is not intended, yet the harmful act nevertheless runs afoul of the intuitive moral constraint that governs intended harms. We note that these cases provide new and improved counterexamples to the so-called Simple View, according to which intentionally phi-ing requires intending to phi. We then give a new theory of the moral relevance of intention. This theory yields the traditional constraint on intending harm as a special case, along with several stronger demands.     

Evaluating Violent Conduct in Sport: A Hierarchy of Vice

The landscape of sport shows conspicuous discursive and material disparities between the responses to openly violent on-field transgressors and the responses to other kinds of transgressor, most notably drug users. The former gets off significantly lighter in terms of ideological framing and formal punishment. The latter—and drug users in particular—are typically demonised and heavily punished, whilst the former are regularly lionised, dramatised, celebrated and punished less severely. The preceding disparities cannot be upheld from the standpoint of morality in general or from that of a Broad Internalist sport ethic. Consideration of the consequences, actions, motives and vices involved in the respective categories fails to support them. Nor is support provided by the notion that sports are tests of the physical skills and virtues that the obstacles presented are designed to foster and promote, and behaviour that threatens the opportunity to exercise those excellences or have competitions determined by them should be the subject of critical moral scrutiny. Openly violent on-field transgression does not fare at all well by the yardstick of Broad Internalism. Robust investigation of and ultimate change in the values underpinning the disparities is warranted.