Formalizing the Regulation

We have manually translated Sections 610.11 and 610.40 of the CFR into Refl. We

given an overview of the formalization. Then, we evaluate Refl qualitatively via

a discussion of four examples. Finally, we use the annotation of logical form (see Chapter 5) to provide some quantitative insights into the coverage of the logic.

Overview: Table 3.1 gives a breakdown of the various types of rules and formulas

that were used in translating CFR 610.11 and 610.40 intoRefl. The columns corre-

spond to the number of obligations, permissions, other rules (which typically consist

of list items), and intersentential references formalized using the says predicate. For

Document Obligations Permissions Other says

CFR 610.11 10 6 3 13

CFR 610.40 12 5 6 8

Table 3.1: Types of rules and formulas used in translating CFR 610.11 and 610.40

into RefL

corresponding to disease names, and a total of 8 instances of the sayspredicate were

used. There are a total of 42 rules (in both documents), and 21 instances of thesays

predicate. In other words, thesayspredicate is used once in every two rules. We now

turn to a discussion of examples.

Example 1: Figure 3.3 shows the translation of CFR 610.40 Paragraph (a) into

Refl. The predicate says is used twice in the precondition. says./∗list(z) is the

translation of the phrase “the following communicable disease agents”, and is under-

stood as follows. ./∗ is an expression to select the sub-paragraphs. The predicate

list(z) is a convenient way to represent lists of noun phrases. For example, the list

item “(3) Hepatitis B virus” is represented as: (3) z.fName = Hepatitis(B) 7→list(z)

This rule lists the object representing the disease name “Hepatitis B”, and the

utterance obtained can be used to access the object. The other says predicate in

Figure 3.3 is¬says[c,d]¬pTestFor(x, z), which is the translation of the clause “Except as specified in paragraphs (c) and (d) of this section”.

Example 2: Figure 3.4 shows the translation of CFR 610.40 Paragraph (d) into

Refl. Paragraph (d) provides exceptions to the tests required in Paragraph (a), for

“autologous donations”. Autologous donations are those that are made by a donor for herself, e.g., prior to surgery. Paragraph (d)(1) cancels this exemption under certain conditions, with the phrase “must be tested under this section”. A direct translation of Paragraph (d)(1) would give us an obligation of the form:

[a (** Except as specified in paragraphs (c) and (d) of this section, you ... must test each donation ... for evidence of infection due to the following communicable disease agents:

(1) Human immunodeficiency virus, type 1; (2) Human immunodeficiency virus, type 2; (3) Hepatitis B virus; ...**)

obligation (x : cDonation) (z : cDiseaseConst) =

(** x is a donation of human blood or blood component, used in a product or device **)

pHumanDonation x && (pUsedInProduct x || pUsedInDevice x) && (** z is a disease agent listed below

and no exception is granted by other laws **)

(says ( ./* ) (listDisease z)) && !(says ( [c, d] ) !(pTestFor x z)) -->

(* If I, II and III hold, x must be tested for z *) pTestFor x z

[1 rule (z : cDiseaseConst) = z.fName = HIV(Type1) --> list z] [2 rule (z : cDiseaseConst) = z.fName = HIV(Type2) --> list z] [3 rule (z : cDiseaseConst) = z.fName = Hepatitis(B) --> list z]

Figure 3.3: CFR 610.40 Paragraph (a) and its translation in logic

Whereϕ(x) checks some conditions on the donation. The obligation is understood

as “Ifϕ(x) holds and test(x) is required in this section, then xmust be tested”. This translation of (d)(1) gives rise to a circular reference to Paragraph (a), leaving (a), (d), and (d)(1) ungrounded at the least fixed point. However, there exists a maximal fixed point where the donation is required to be tested. There are three options when faced with such a circular reference:

[d (** Autologous donations. You,..., are not required to test donations of blood...from autologous donors for evidence of infection due to the disease agents listed in paragraph (a) of this section..., except: (1) If you allow any autologous donation to be used for allogeneic transfusion, you must assure that all autologous donations are tested under this section;... *)

permission (x : cDonation) (z : cDiseaseConst) =

(** x is an autologous donation, i.e., intended for the donor herself. And, z is a disease listed in paragraph (a) *)

pAutologousDonation x && (says ( [a]/* ) (list z)) && (** There is no exception *)

!(says (./[1-3]) (cancel x)) -->

!(there exists z in x.fTests : true) [1 rule (x : cDonation) = pAutologousDonation x && x.fCollector.fAllowsAutologousForAllogeneicTransfusion --> (cancel x) ]]

Figure 3.4: CFR 610.40 Paragraph (d) and its translation in logic. A direct translation of the phrase “tested under this section” in (d)(1) results in a circular reference to paragraph (a), leaving (a), (d), and (d)(1) ungrounded. The cancel predicate is used to break this cycle.

2. Issue a warning if the precondition of an obligation is ungrounded, and the postcondition is false

[(a) obligation (x : cDonation) (z : cDiseaseConst) =

(pHumanDonation x) && (pUsedInProduct x || pUsedInDevice x) && (z.fName = HIV Type1) || (z.fName = HIV Type2) ||

(z.fName = Hepatitis B) || (z.fName = Hepatitis C) || (z.fName = HTLymph Type1) || (z.fName = HTLymph Type2) && !((Exists (x15 : cThirtyDayPeriodConst):

(pDedicatedDonation x && !(pFirstDonationInPeriod x x15) && pUsedForTransfusion x)) || (pSourcePlasma x) &&

((z.fName = HTLymph Type1) || (z.fName = HTLymph Type2)) || (match x.fIntendedUse with

Device d -> !d.fContainsViableLeucocytes | _ -> false) && ((z.fName = HTLymph Type1) || (z.fName = HTLymph Type2)) || (match x.fIntendedUse with

ClinicalTesting | Research -> true | _ -> false) || (CFR61040.pAutologousDonation x) &&

!((x.fCollector.fAllowsAutologousForAllogeneicTransfusion) || (x.fOrgRecepient.fAllowsAutologousForAllogeneicTransfusion) || (Exists (x25 : cThirtyDayPeriodConst):

(pAutologousDonation x && pFirstDonationInPeriod x x25 && !x.fOrgRecepient.fAllowsAutologousForAllogeneic))))

-->

(CFR61040.pTestFor x z)]

Figure 3.5: CFR 610.40 Paragraph (a), after thesays predicate is compiled out.

The first option of computing maximal fixed points is infeasible, as there can be exponentially many. The second option is supported by our implementation. And, for the last option, we detect cycles and present them to the user, who can then

the cycle. We note that the cycle detection is carried out after we compile out the satisfiability tests (as in Section 3.3.2). This ensures that only cycles leading to ungrounded precondition are presented to the user.

Example 3: We now discuss some issues in sententially translating CFR 610.11 into

Refl. Consider the following sentences:

(18) A general safety test for the detection of extraneous toxic contaminants shall be performed on biological products intended for administration to humans.

(19) The general safety test is required in addition to other specific tests prescribed in the additional standards for individual products in this subchapter, except that, the test need not be performed on those products listed in paragraph (g) of this section.

It is not possible to translate (18) and (19) separately into Refl. (18) conveys a

requirement to perform “a general safety test”, and (19) reiterates this requirement, while providing exceptions. The problem arises because: (A) there is an incomplete- ness in (18), i.e., the exception is not provided, and (B) there is a redundancy in

(19), i.e., the requirement is reiterated. To translate these sentences into Refl, we

combine them into the following obligation:

(20) Except as specified in paragraph (g) of this section, a general safety test ... shall be performed on biological products ...

It is easy to translate (20) into Refl. We note that the permission given by (19)

is restated in paragraph (g) of CFR 610.11.

Example 4: Consider the following sentences:

(21) The general safety test shall be performed as specified in this section...

a. The general safety test shall be conducted upon a representative sample of the product in the final container from every final filling of each lot of the product. b. The duration of the general safety test shall be 7 days for both species, except that a longer period may be established for specific products in accordance with Sec. 610.9.

It is unclear how to translate (21) into Refl, due to the phrase “as specified in

one conforms to the rest of the requirements (such as (21a) and (21b)), one conforms to (21). However, we will need to interpret (21a) and (21b) as quantifying over all general safety tests. For example, we can interpret (21a) as:

(22) If a general safety test is required to be performed on a product, then it shall be conducted upon a representative sample of the product...

It is easy to translate (22) into Refl. However, the question is whether there is a

way to translate (21) into Refl, so that we can avoid such paraphrases. We believe

that the central problem is the analysis of the phrase “the general safety test” – what is the test that is being referred to? There are several possibilities for formalization

within Refl, and we leave an investigation to future work.

Coverage: The discussion of examples gives us a qualitative way to evaluateRefl. A question arises as to whether there is a more quantitative way to do it. The best

test is, of course, to translate large bodies of regulation into Refl, and evaluate how

it corresponds to the text. However, doing this would be quite time consuming. In Chapter 5, we describe an annotation of logical form on about 200 sentences of Section 610 of the CFR. While logical form is not quite the same as logic, our hope is that it can serve as an approximation to the logic, in order to evaluate it quantitatively. We take a preliminary step toward this end, here, by studying the distribution of clause a verb phrase modifiers.

Number of Temporal and Purpose Other References Other

Instances Conditional to Laws

333 29.1% 28% 30.2% 12.7%

Table 3.2: Subtypes of clause and verb phrase modifiers.

Table 3.2 gives a breakdown of clause and verb phrase modifiers found in Section

610 of the CFR. Temporal and conditonal modifiers (29.1%) include, for example,

“before”, “after”, “if”, and “except as”. The purpose modifiers (28%) are signalled

“according to”. Note that the temporal and conditional (and exceptional) modifiers introduce references to laws as well. The other modifiers include cases which we have not categorized yet, e.g., “regardless”, “notwithstanding”.

The temporal and conditional/exceptional modifiers are adequately handled by

Refl. However, the modifers conveying references to laws need further investigation.

Reflprovides no special capabilities for purpose modifiers, but the notions of purpose

in the CFR 610.40 are simple, and constant symbols suffice. We conclude that the

Refl accomodates approximately 57.1% of modifiers (the first two columns), needs

to be extended to accomodate another 30.2%, and the remaining 12.7% needs to

be categorized. We note that 57.1% is an upper bound, because the temporal and

conditional modifiers may include contain some other constructs that we do not know how to formalize.