Skip to main contentCal State San Bernardino / [CNS] / [Comp Sci Dept] / [R J Botting] >> [MATHS] >> logic_2_Proofs
[Contents] [Source Text] || [Notation] || [Copyright] || [Contact] [Search ]
Tue Mar 6 14:29:50 PST 2007

Contents

    Proofs -- Old Page

      For an introduction see [ logic_20_Proofs100.html ] which give informal hints and discusses some philophical ideas associated with proofs and some tools and automation, or [ logic_25_Proofs.html ] which presents an attempt at a practical yet formal way of presenting proofs in a machine readable, renderable, and checkable form.

      Tools for Proofs


      (ProofBuilder): hamburger helper for budding logicians [ poster.html ]

    . . . . . . . . . ( end of section Proofs and Demonstrations) <<Contents | End>>

    Notes on MATHS Notation

    Special characters are defined in [ intro_characters.html ] that also outlines the syntax of expressions and a document.

    Proofs follow a natural deduction style that start with assumptions ("Let") and continue to a consequence ("Close Let") and then discard the assumptions and deduce a conclusion. Look here [ Block Structure in logic_25_Proofs ] for more on the structure and rules.

    The notation also allows you to create a new network of variables and constraints, and give them a name. The schema, formal system, or an elementary piece of documentation starts with "Net" and finishes "End of Net". For more, see [ notn_13_Docn_Syntax.html ] for these ways of defining and reusing pieces of logic and algebra in your documents.

    For a complete listing of pages in this part of my site by topic see [ home.html ]

    Notes on the Underlying Logic of MATHS

    The notation used here is a formal language with syntax and a semantics described using traditional formal logic [ logic_0_Intro.html ] plus sets, functions, relations, and other mathematical extensions.

    For a more rigorous description of the standard notations see

  1. STANDARD::= See http://www.csci.csusb.edu/dick/maths/math_11_STANDARD.html

    Glossary
  2. above::reason="I'm too lazy to work out which of the above statements I need here", often the last 2 or three statements.
  3. given::reason="I've been told that...", used to describe a problem.
  4. given::variable="I'll be given a value or object like this...", used to describe a problem.
  5. goal::theorem="The result I'm trying to prove right now".
  6. goal::variable="The value or object I'm trying to find or construct".
  7. let::reason="For the sake of argument let...", intoduces a temporary hypothesis that survives until the end of the surrounding "Let...Close.Let" block or Case.
  8. hyp::reason="I assumed this in my last Let/Case/Po/...".
  9. QED::conclusion="Quite Easily Done" or "Quod Erat Demonstrandum", indicates that you have proved what you wanted to prove.
  10. QEF::conclusion="Quite Easily Faked", -- indicate that you have proved that the object you constructed fitte the goal you were given.
  11. RAA::conclusion="Reducto Ad Absurdum".

End