2.1 Overview of XSD says
As it is used in this specification, the term "schema-validity assessment" has two aspects:
1 Determining local schema-validity, that is whether an element or attribute information item satisfies the constraints embodied in the relevant components of an XSD schema;
2 Synthesizing an overall validation outcome for the item, combining local schema-validity with the results of schema-validity assessments of its descendants, if any, and adding appropriate augmentations to the infoset to record this outcome.
Throughout this specification, [Definition:]  the word valid and its derivatives are used to refer to clause 1 above, the determination of local schema-validity.
Throughout this specification, [Definition:]  the word assessment is used to refer to the overall process of local validation, schema-validity assessment and infoset augmentation.

Comment 1: although it is in bold and called "the term", schema-validity 
           assessment is not rendered with the usual [Definition:] flag nor 
           does it appear in the glossary.

Comment 2: one might be tempted to think schema-validity assessment and 
           assessment are synonyms - I am keeping them separate, as I think you 
           intend

Comment 3: "validation" seems to me like a derivative of "valid".  According to 
           that reasoning, 'validation' should not be used in any context other 
           than local schema-validity.  This reasoning conflicts with its usage 
           in clause 2 (overall VALIDATION outcome).

Comment 4: If I try substituting definitions just within this excerpt above, it 
           becomes either circular or self-inconsistent.
> SVA = (LSV + OVO); OVO = LSV + SVA(desc) + InfosetAug; 
  assessment = L(S?)V + SVA(desc?) + InfosetAug
If I take it as written:
> SVA = (LSV + OVO); OVO = LSV + SVA(desc) + InfosetAug; 
  assessment = LV + SVA + InfosetAug
  - it's using a term (LV) that's not defined. 
If I take it as written and make the (small, likely) leap that LV should have been LSV
> SVA = (LSV + OVO); OVO = LSV + SVA(desc) + InfosetAug; 
  assessment = LSV + SVA + InfosetAug
  - Solving for SVA, since it is used in two places
    (LSV + (LSV+SVA(desc)+ InfosetAug) = LSV + InfosetAug - assessment
  - further assuming the two LSV l-values collapse into one, and cancelling 
    like terms
    SVA(desc) = (-) assessment
    If it weren't for (desc) on one side only, I'd call it close enough.
If instead I take it as I think you probably meant it:
> SVA(x) = (LSV(x) + OVO); OVO = LSV(x) + SVA(desc) + InfosetAug(x+desc); 
> assessment(x) = LSV(x) + SVA(desc) + InfosetAug(x+desc)
  - This leads to 
    SVA(x) = assessment(x) = LSV(x) + SVA(desc(x)) + InfosetAug(x+desc(x))
    - I think it functions, but it's just my best guess at what I think you 
      meant (and fwiw, doing it this way was the only thing that led me to see 
      the descendants qualifier in the OVO text)
  - Of course, SVA as a term sounds a lot like a derivation of validity to me, 
    which would be a contradiction.
  - Since you did not say what you meant by derivation, no way to know if we 
    are interpreting that word similarly.

1.5 Documentation Conventions and Terminology - error entry
note 1: "Failure of an XML document to be valid against a particular schema..."
By your own definitions in 2.1, I should interpret this to mean local schema validity of the document element, not the more conventional interpretation of assessment of the document element?

1.5 Documentation Conventions and Terminology - error entry
note 2: Notwithstanding the fact that (as just noted) failure to be schema-valid 
Same question.  Since term is not defined (here, or in - non-normative, why? - Glossary), I assume it is a derivation of valid.
	 
2.2 XSD Abstract Data Model - last paragraph of section before 2.2.1
"·Validation·, defined in detail in Schema Component Details (§3), is a relation between information items and schema components. For example, an attribute information item is ·validated·  with respect to an attribute declaration, a list of element information items with respect to a content model, and so on. The following sections briefly introduce the kinds of components in the schema abstract data model, other major features of the abstract model, and how they contribute to ·validation·."
So this is all about local schema-validity too?  Sounds like assessment to my unwashed ears.

2.2.1.1 Type Definition Hierarchy
"[Definition:]  A type defined with the same constraints as its ·base type definition·, or with more, is said to be a restriction.  The added constraints might include narrowed ranges or reduced alternatives. Given two types A and B, if the definition of A is a ·restriction· of the definition of B, then members of type A are always locally valid against type B as well."
By your own definitions in 2.1, I should interpret this to mean local schema validity of the element, not the more conventional interpretation of assessment of the document element?  I'm pretty sure this is your intent here, since you 
use a (new!) term: LOCALLY valid.  Seems like a pretty good one to use throughout where local validity is the intent, IMO.
Strictly speaking though, as narrowly defined today, I should be saying "locally valid" is definitionally redundant.

2.2.2.1 Element Declaration
"Element declarations contribute to ·validation· as part of model group ·validation·, when their defaults and type components are checked against an element information item with a matching name and namespace, and by triggering identity-constraint definition ·validation·."
·validation· does link back to 2.1 clause 1, fwiw.
The contextual use often makes me think you are trying to define a new term, for which the (lack of) [Definition:] rendering signals your presumed intent NOT to do so.

2.2.3.2 Particle
"Their validity does affect whether their parent is (recursively) valid as well as locally valid."
Local schema-validity is probably your intent here, but "(recursively) valid" leads to questions.

2.3 Constraints and Validation Rules
Schema Information Set Contribution
"[Definition:]  Augmentations to ·post-schema-validation infoset·s expressed by schema components, which follow as a consequence of ·validation· and/or ·assessment·."
In contrast to 2.1's definitions, this indicates that validation (local schema-validity _?_something but no not assessment____) also augments the infoset.
2.1 and 2.3 need to be consistent about it, and 2.1 usage of augmentation should likely link here.

3.1.3 The Mapping between XML Representations and Components
"items in a document being ·validated·."
Seems like this wants to be different: document element (if local is intended), being assessed (if assessment), document element being validated or assessed (if either, as I might imagine)

3.4.4.3 Element Sequence Locally Valid (Complex Content)
"[Definition:]    A sequence of element information items is locally valid with respect to a Content Type if and only if ..."
Here you define (on page 94 printed, when it was first used in the 20s) "locally valid", then do so in an element-specific way.
You actually define it again later (two Glossary entries), and use the same term in other places (with varying definitions, e.g. for attributes) without ever defining it.  Unless this document is intended only for wg participants, this does make it harder to read and understand unambiguously.

3.8.4.1 Language Recognition by Groups
"By contrast, V(M) takes account of those constraints and includes only the sequences which are ·locally valid· against M."
-This- "locally valid" links to 3.8.4.2 Principles of Validation against Groups (so the link is 'as intended' I think).

3.10.1 The Wildcard Schema Component - {process contents} strict + lax
"There must be a top-level declaration for the item available, or the item must have an xsi:type, and the item must be ·valid· as appropriate."
Both link to local schema-validity, hope that's your intent here.

3.13.4.1 Assertion Satisfied clause 1.1
"Note: It is a consequence of this rule that the [attributes] and [children] of E will be validated in the usual way."
Descendants sure makes it sounds like assessment.  No mention of descendants in the definition of valid (or its derivations).