Reference in Document: p.14, 5th paragraph (Section 6.2)
Nature of Defect: mention of "universe" without qualification "of reference"
Proposed Solution: Replace
"If E is a subset of UD_I, then the restriction of I to E is an
interpretation K of the same vocabulary and over the
same universe and with int_K = int_I and seq_K = seq_I,
but where UD_K = E, rel_K(v) is the restriction of rel_I(v) to E*
and fun_K(v) is the restriction of fun_I(v) to E*->E, for all v in the vocabulary of I."
with
"If E is a subset of UD_I, then the restriction of I to E is an
interpretation K of the same vocabulary and over the
same universe of reference (UR_K = UR_I)
and with int_K = int_I and seq_K = seq_I,
but where UD_K = E, rel_K(v) is the restriction of rel_I(v) to E*
and fun_K(v) is the restriction of fun_I(v) to E*->E, for all v in the vocabulary of I."
Discussion: this clarification has bearing on Issues #24, #25 and #35. This passage indicates that even unsegregated dialects (those that do not have a syntax for functions and relations separate from that of individuals) inherently have the concept of segregated interpretations (interpretations whose universe of discourse is a proper subset of the universe of reference) if they adopt the CL abstract semantics.
Reference in Document: p.14, 5th paragraph (Section 6.2)
Nature of Defect: mention of "universe" without qualification "of reference"
Proposed Solution: Replace "If E is a subset of UD_I, then the restriction of I to E is an interpretation K of the same vocabulary and over the same universe and with int_K = int_I and seq_K = seq_I, but where UD_K = E, rel_K(v) is the restriction of rel_I(v) to E* and fun_K(v) is the restriction of fun_I(v) to E*->E, for all v in the vocabulary of I."
with
"If E is a subset of UD_I, then the restriction of I to E is an interpretation K of the same vocabulary and over the same universe of reference (UR_K = UR_I) and with int_K = int_I and seq_K = seq_I, but where UD_K = E, rel_K(v) is the restriction of rel_I(v) to E* and fun_K(v) is the restriction of fun_I(v) to E*->E, for all v in the vocabulary of I."
Discussion: this clarification has bearing on Issues #24, #25 and #35. This passage indicates that even unsegregated dialects (those that do not have a syntax for functions and relations separate from that of individuals) inherently have the concept of segregated interpretations (interpretations whose universe of discourse is a proper subset of the universe of reference) if they adopt the CL abstract semantics.