Posibles efectos adversos

8.2

Special Strategies for Explanations

We proposed four special strategies to make explanations for difficult rules become more understandable. These strategies originated from an informal study in which the author and some colleagues proposed enhanced explanations for these rules, after which we col- lected together the strategies into four groups.

Strategy 1: Explicate premises to cancel the presupposition

In 1, 2, 5, 7, and 8 in Table 8.1 (namely ‘ObjAll’, ‘DatSom-DatRng’, ‘ObjVal-ObjVal- DifInd-ObjFun’, ‘ObjMin-ObjFun’, and ‘ObjSom-Bot-1’), the source of difficulty plausibly lies in presuppositions [Bea97] caused by the words ‘only’ and ‘every’. In rule 1, the word ‘only’ may cause the readers to presuppose that an X is anything that Ro one or more

things, and all of these things are Y s. In fact, the accurate meaning of rule is that an X is anything that either Ro nothing at all, or if it Ro one or more things then all of

these things are Y s. The first part of the meaning (i.e., things that Ro nothing at all) is

implicit in the word ‘only’. To help the readers cancel this presupposition, we explicate the original axiom by transforming it into an equivalent axiom by using a disjunction operator: X ≡ (∀Ro.⊥) t (∀Ro.Y). Hence, the new verbalisation for the axiom is “An X

is anything that Ro nothing at all, or Ro only Y s”.

In rules 2, 5, 7, and 8, the word ‘every’ in the verbalisations of v axioms like “Every X Ro

a Y ”, “Every X Rda Dr0value” etc. may cause the readers to presuppose that there exists

at least an instance of X. This presupposition contradicts the conclusion that “Nothing is an X”, so the readers may be confused whether rule is true. As before, we cancel this presupposition by transforming each v axiom into a new v axiom by using a disjunction operator—specifically, X v ∃Ro.Y is transformed into X v (∃Ro.Y) t ⊥, X v ∃Rd.Dr0

into X v (∃Rd.Dr0) t ⊥, and so on. The new verbalisations would be “Every X Ro a Y ,

or there are no Xs at all” and “Every X Rda Dr0 value, or there are no Xs” etc.

Another way to cancel the presupposition caused by the word ‘every’ is to use if-then statements. Specifically, we explicate the axiom X v ∃Ro.Y as “If there are any Xs then

they all Ro a Y ”, the axiom X v ∃Rd.Dr0 as “If there are any Xs then they all Rd a Dr0

value”, and so on. This strategy, however, is not applicable for rule 1 as its only premise is an ≡ axiom (but not a v axiom). In our empirical study, only the explication strategy

using a disjunction is tested for rule 1, but both of the explication strategies are tested for rules 2, 5, 7, and 8, as summarised in Table 8.1.

Strategy 2: Exemplify premises to show the contradiction

For rules that conclude a class is unsatisfiable, namely rules 2, 5, 7, and 8 in Table 8.1, an- other source of difficulty may be the visibility of the logical contradiction in the description of the class. To make it more visible to the readers, we propose a method that exemplifies the premises. Specifically, a named individual is assumed to be an instance of the class in the conclusion, and we show that the existence of this individual leads to a contradiction. For example, to explain the contradiction in rule 2, we propose the following template for an explanation:

Suppose there is an X named Rover. It follows from the premises that: - Rover Rd a Dr0,

- Rover Rd only Dr1s, and

- Dr0s are not Dr1s.

The existence of an X such as Rover leads to a contradiction. Therefore, there are no Xs.

In this template, the statement “Rover Rd a Dr0” is inferred from the axiom “X v

∃R_d.Dr0” (“Every X Rd a Dr0 value”) and the assumption, and “Rover Rd only Dr1

values” from Rng(Rd, Dr1) (“Any value that something Rdis a Dr1”). Similar templates

for rules 5, 7, and 8 can be created in the same way. Strategy 3: Paraphrase difficult axioms

Another source of difficulty of these rules may lies in the verbalisations of difficult axioms. We propose alternative verbalisations for several axioms, and compare them with the original ones to identify which ones are understood best by non-logicians. The list of possible difficult verbalisations and the new paraphrases we propose are listed in Table 8.2. These axioms occur once in rules 2-6, and twice in rule 7 in Table 8.1.

Strategy 4: Contextualise Invs axioms

Invs is a difficult axiom to reason with. For rules that contains an Invs axiom in their premises, namely rules 3, 4, and 6 in Table 8.1, we propose a method to contextualise this axiom in order to make it better connected to the remaining premises. Specifically, in rule 3 (‘ObjAll-ObjInv’) we rely on the first premise which says “Every X Ro only Y s”