Hypergendered Logic Source

Hypergendered Logic — Page 44

HGL Source Framework · Page 44 of 293 · Source: Hypergendered Logic

SF1≡PAx∧PA¬y. 
Status: strict HGL axiom consequence. 
Worked Example 3 — SF2 conjunction elimination 
From 
SF2 = IH(SF1) AND IH(NOT SM1) AND PH(SF1) AND NOT PH(SM1) AND UD(SF1) AND PA(x) AND 
PA(NOT y) AND NOT FD(SF1) 
infer each of the eight conjuncts: IH(SF1), IH(NOT SM1), PH(SF1), NOT PH(SM1), UD(SF1), PA(x), PA(NOT 
y), and NOT FD(SF1). 
Status: classical deduction. 
Worked Example 4 — SF2 inherits SF1 
SF2⇒IHSF1⇒SF1. 
Status: deduction using conjunction elimination and IH projection. 
Worked Example 5 — SF2 is non-SM1 
SF2⇒IH¬SM1⇒¬SM1. 
Status: deduction. 
Worked Example 6 — Noninheritance is weaker than inherited negation 
Assume ¬IHSM1. This tells us only that SM1 is not inherited. It does not entail ¬SM1. 
But 
IH¬SM1⇒¬SM1. 
Status: deduction/countermodel distinction. 
Worked Example 7 — Negating SF2 
NOT SF2 = NOT IH(SF1) OR NOT IH(NOT SM1) OR NOT PH(SF1) OR PH(SM1) OR NOT UD(SF1) OR 
NOT PA(x) OR NOT PA(NOT y) OR FD(SF1) 
Status: De Morgan deduction. 
Worked Example 8 — De Morgan does not move NOT through IH 
From ¬IHSF1 one may not infer IH¬SF1. 
Status: invalid inference demonstration. 
Worked Example 9 — De Morgan does not move NOT through PA 
From 
 one may not infer 
. 
¬𝑃𝐴𝑥
( )
𝑃𝐴¬𝑥
(
)
Status: invalid inference demonstration. 
Worked Example 10 — SF3 immediate inheritance 
SF3 = IH(SF2) AND IH(NOT SM2) AND PH(SF2) AND NOT PH(SM2) AND UD(SF2) AND NOT FD(SF2)

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:44.