The Non-Boolean Logic of Natural Language Negation

Resolving apparent contradictions: adults' and preschoolers' ability to cope with non-classical negation

“…First and foremost, they show that the logical model based on set theory is too simplistic because it cannot handle object structure. A logical model, in fact the only one there is, was worked out using KRIPKE TREES (La Palme Reyes, Macnamara, Reyes & Zolfaghari, 1994). One of the important properties of this new model is that its logic is, in general, non-classical.…”

“…It is as if the point that objects, like doorways and people, have structure is so basic that it has been missed. The main contribution of La Palme Reyes et al (1994) has therefore been to develop a non-classical logic that readily handles object structure.…”

Reasoning about a Structured Object: Three‐ and Four‐Year‐Olds' Grasp of a Borderline Case and an Unexcluded Middle

“…It is possible to describe nonset-theoretic structures that give rise to nonclassical logic that lends itself to modeling object structure and predicate inheritance (and of which classical logic based on set theory is a special case-see La Palme Reyes, Macnamara, Reyes, & Zolfaghari, 1994), but a purely formal approach gives little or no insight into how the capacities in question might arise in adults and children. Conversely, research that has examined how reasoning abilities arise has tended to focus on classical logic.…”

“…A similar pattern can be found in the linguistic and philosophical literature on the logic of natural language negation (e.g., no). The standard approach has been to assume that its logic is classical (barring nonlogical uses such as rejecting the assertability of an utterance on grounds of, say, incorrect pronunciationsee Horn, 1989), leaving the opposition relation between an open class of pairs of opposed predicates (e.g., loving versus hating, happy versus unhappy, and so forth) to be handled at the level of nonlogical, emotive force (see, for example, Englebretsen, 1976Englebretsen, , 1981Englebretsen, , 1990Horn, 1989Horn, , 1990Sommers, 1970Sommers, , 1974Sommers, , 1976 for an alternative account see La Palme Reyes et al, 1994). The standard approach therefore also sidesteps the question of object structure and predicate inheritance (Sharpe, Eakin, Saragovi, & Macnamara, 1996), leaving it to be handled case by case, pragmatically rather than semantically (B. Gillon, personal communication, December 12, 1996).…”