Restricting logical validity and consequence to normal worlds is a common move in worlds semantics that include non-normal or impossible worlds.
In this respect, logicians' prospects have been enhanced by the development of a semantical theory of modal logic, both in the narrower sense of modal logic, which is restricted to logical necessity and logical possibility, and in the wider sense, in which all concepts that exhibit similar logical behaviour are included.
But the Boolean model is restricted to logical relationships between variables.
It is often useful and intuitive to restrict the logical operators to AND (also called logical product), OR (also called logical sum), and NOT, and then to express the logical functions as sum of products (SOP) [ 78] (also known as disjunctive normal form (DNF)).
Assessing female association preferences under this restricted physical contact is logical, because females are generally choosier than males (that is, significant preferences can be more easily detected) and choice males often fight for a test female (that is, her final mating decision under free-swimming conditions may only reflect dominance hierarchy of the males).
Azzouni (2006), ch. 9, also defends the view that model-theoretic validity provides a correct conceptual analysis of logical truth (though restricted to first-order languages), on the basis of a certain deflationist conception of the (strong) modality involved in logical truth.
Unsurprisingly, Apple has applied a logical but highly restricted scope to how the feature can be accessed.
But far from showing that the logical form of 'The boy sang' diverges dramatically from its grammatical form, the restricted quantifier notation suggests that the logical form closely parallels the grammatical form.
It was restricted to just the universally acknowledged logical operators of first-order logic: ¬, ∧, ∨, →, ∃ and ∀.
To accomplish this, DNA molecules must be restricted to a wide window of thermodynamical and logical conditions, which in turn facilitate and control the algorithmic processes implemented by chemical reactions.
