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UNISA Chatter – Formal Logic: Propositional Logic Conditional Symbols

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See UNISA – Summary of 2010 Posts for a list of related UNISA posts. This post is one of the summary posts I will be building up over the next couple of months, so if you are following this topic or completing the same course as I this year, you may want to bookmark this post and come back occasionally for a peek and to give “candid” feedback.

The following truth tables summarise the main conditional symbols used as part of first-order-language (FOL):

Conditional Symbol Ù

In English we typically use terms such as and, moreover and but. Also known as the conjunction symbol.

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Conditional Symbol Ú

In English we typically use the term or.  Also known as disjunction symbol.

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Conditional Symbol Ø

When using English we typically use terms such as not, it is not the case, non- and un-. Also known as the negation symbol.

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See UNISA Chatter – Formal Logic: Propositional Logic Proofs for examples using the three symbols covered above.

Conditional Symbol ®

Also known as the material conditional symbol, it states that P®Q is true if and only if either P is false or Q is true, or both.

P®Q  could be expressed as ØP Ú Q.

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We will cover this one in this post and work through an example which gave me nightmares for days … then suddenly it clicked.

Some basics first.

If we have to prove a one (®) directional conditional symbol, the process is as follows:

  • If the goal is to show that P®Q, then …
  • Sketch a sub proof with P as an assumption and Q as the final step
  • Q will become intermediate goal while checking the proof and by proving that we can rely on assumption P
  • Example …
    image

If we have a bidirectional situation («), the process changes to:

  • If the goal is to show that (P®Q)«(ØP®ØQ), then …
  • Sketch the two sub proofs ahead of time, i.e. P®Q and ØP®ØQ
  • Cite the sub proof in support
  • Fill the sub proofs, which could become long.

Comments

  • Anonymous
    February 17, 2011
    Thank you... your explainations and views on this subject have given me a clear understanding about Propositional Logic.