(logic.info)Introduction to logic

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1.1 Introduction to logic
=========================

This is a draft version of logic algebra package for Maxima.  It is
being developed by Alexey Beshenov (al@beshenov.ru).  All source code is
available uder the terms of GNU GPL 2.1.

   List of recognized operators:

Operator    Type    Binding Description                      Properties
                    power
----------------------------------------------------------------------------
'not'       Prefix  '70'    Logical NOT (negation)
'and'       N-ary   '65'    Logical AND (conjunction)        Commutative
'nand'      N-ary   '62'    Sheffer stroke (alternative      Commutative
                            denial, NAND)
'nor'       N-ary   '61'    Webb-operation or Peirce arrow   Commutative
                            (Quine's dagger, NOR)
'or'        N-ary   '60'    Logical OR (disjunction)         Commutative
'implies'   Infix   '59'    Implication
'eq'        N-ary   '58'    Equivalence                      Commutative
'xor'       N-ary   '58'    Sum modulo 2 (exclusive or)      Commutative

1.2 TeX output
==============

logic.mac assigns the following TeX output:

'not'
     '\neg'
'and'
     '\wedge'
'nand'
     '\mid'
'nor'
     '\downarrow'
'or'
     '\vee'
'implies'
     '\rightarrow'
'eq'
     '\sim'
'xor'
     '\oplus'

   Examples:

     (%i1) load ("logic.mac")$
     (%i2) tex (a implies b)$
     $$a \rightarrow b$$
     (%i3) tex ((a nor b) nand c)$
     $$\left(a \downarrow b\right) \mid c$$
     (%i4) tex (zhegalkin_form (a or b or c))$
     $$a \wedge b \wedge c \oplus a \wedge b \oplus a \wedge c \oplus b
       \wedge c \oplus a \oplus b \oplus c$$
     (%i5) tex (boolean_form (a implies b implies c));
     $$ \neg \left( \neg a \vee b\right) \vee c$$
     (%i6) tex (a eq b eq c);
     $$a \sim b \sim c$$