Can someone please check my logic proof?

Thread starter BondKing
Start date Oct 11, 2014
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Logic Proof

AI Thread Summary

The discussion revolves around a logic proof involving premises and deductions. The user presents a series of logical steps to derive the conclusion regarding the variable 'm.' Initially, the proof appears to follow a structured approach using Modus Ponens and elimination techniques. However, the user ultimately concludes that their reasoning is incorrect, indicating a flaw in their logic. The conversation highlights the complexities of formal logic proofs and the importance of careful analysis in deriving conclusions.

Oct 11, 2014

BondKing

(c v ~ h) - > ~ m (prem 1)

T -> ~ c (prem 2)

T ^ h (prem 3)

trying to get m 1) T (spec prem 3)

2) ~ c ( M.PON prem 2, 1)

3) ~ h (ELIM prem 1 (c v ~ h), 2)

4) ~ h - > ~ m (replace (c v ~ h) with ~h)

5) m -> h (Contrap. 4)

6) ~m v h (M.TOL 5,3)

6) m

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Oct 11, 2014

BondKing

Nevermind. This is wrong.

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...

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