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Deductively Sound Formal Proofs --- (v9)
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peteolcott
May 15, 2019, 2:13:35 PM5/15/19
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In AI research the following can be used to anchor the notion of
[truth conditional semantics] in a single [axiom schema True(x) predicate]
for the [knowledge ontology inheritance hierarchy].
Because valid deduction from true premises necessarily derives
a true consequent we know that the following predicate pair
consistently decides every deductively sound argument.
The notion of complete and consistent formal systems is exhaustively
elaborated as conventional formal proofs to theorem consequences
where axioms are stipulated to be finite strings with the semantic
property of Boolean true.
// LHS := RHS the LHS is defined as an alias for the RHS
∀x True(x) := ⊢x
∀x False(x) := ⊢¬x
Introduction to Mathematical logic Sixth edition Elliott Mendelson (2015) Pages 27-28
http://liarparadox.org/Provable_Mendelson.pdf
--
Copyright 2019 Pete Olcott
All rights reserved
[truth conditional semantics] in a single [axiom schema True(x) predicate]
for the [knowledge ontology inheritance hierarchy].
Because valid deduction from true premises necessarily derives
a true consequent we know that the following predicate pair
consistently decides every deductively sound argument.
The notion of complete and consistent formal systems is exhaustively
elaborated as conventional formal proofs to theorem consequences
where axioms are stipulated to be finite strings with the semantic
property of Boolean true.
// LHS := RHS the LHS is defined as an alias for the RHS
∀x True(x) := ⊢x
∀x False(x) := ⊢¬x
Introduction to Mathematical logic Sixth edition Elliott Mendelson (2015) Pages 27-28
http://liarparadox.org/Provable_Mendelson.pdf
--
Copyright 2019 Pete Olcott
All rights reserved
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