ABSTRACT
The purpose of Experiment 1 was to test the psychological reality for adolescents of the derivations generated by o Lq . To this end, single- and multiple-operation arguments were prepared to allow a test of the inventory and additivity requirements. The 48 arguments derived in Section 3.6 constitute the multiple-operation arguments in Lq whose translations into English yield the multiple-ope ration arguments in the experiment. The translation into English will be described shortly. The single-operation arguments in Lq (i.e., the formulas of Lq, prior to translation into English) were constructed in the following way. The rewrite rule ϕ/ψ of each operation of o Lq was transformed into a single-operation argument by (a) replacing in ϕ and ψ every occurrence (if any) “A” with “F,” “B” with “G,” and “C” with “H,” (b) inserting the individual constant “a” after every occurrence (if any) of F that is not under the scope of a quantifier, and similarly for the individual constants “b” and “c” with respect to “G” and “H,” respectively, (c) dropping the individual variable “k” (from Operations 23 and 24), since it is superfluous after step (b), and finally (d) taking ϕ and ψ so transformed to be the premise and conclusion of an (single-operation) argument in Lq. 1 For example, the rule −A → B/A ∨ B becomes the argument −Fa → Gb/Fa ∨ Gb; the rule ∀(A & B)/∀A & ∀B becomes the argument ∀(F & G)/∀F & ∀G. 2
