Where can I find Nuel Belnap’s publications? Thanks for Your help.

dbier…@polbox.com

Use mathematical Induction to show that for n >= 1,
    Fn < 2^n

Where Fn is a Fibinocci number.

why logic.

I am attempting to do some proofs of simple statements using the Peano
Axioms expressed in first order predicate logic (FOPL), but I have been
having a few difficulties. I would be grateful if anyone could provide me
with or at least give me a few pointers towards proving (in FOPL) the
statement ’2 is not equal to 1′ using the Peano Axioms.

Thanks

Pete

I was looking at Dekedend’s problem,
ie, calculate the number of monotone Boolean functions
having at most N variables.

I have no idea what monotone Boolean functions are good for.
Any hints would be appreciated.

A monotone Boolean function uses AND and/or OR but not NOT.
I’ve found a simple way to generate the truth tables for monotone functions.

The best way I’ve found to
actually calculate the number of such functions
is to generate all of the truth tables and count them.
I hope there is a better way.

Let M(n) be the number of monotone Boolean expressions.

Define M(0)=2.
These are the truth tables (TT) for the two monotone functions with 0
variables:

0 index position
————————-
1  True (T)
0  False (F)

To create the truth tables (TT) for N variable functions,
start with the TT of monotone functions having N-1 variables.

Put the first N-1 TT on the left side
of the N variable truth table.

Now combine each N-1 truth table with this first one
by putting each N-1 TT on the right side
of the N variable TT.

The TT on the right must be a subset of the TT on the left.
(I define subset such that a set is a subset of itself.)

All combinations of two N-1 TT that meet this subset criteria
are TT of N variable monotone Boolean functions.

M(1)=3

10 index of variable A
———————————
11  T
10  A
00  F

Note that 01 is not legal because 1 is not a subset of 0.

M(2)=6

1100  index B
1010  index A
—————–
1111  T
1110  A+B   (A OR B)
1100  B
1010  A
1000  AB   (A AND B)
0000  F

Note that 1011 is illegal because 11 is not a subset of 10.

M(3)=20

11110000  index of C
11001100  index of B
10101010  index of A
———————————
11111111  T
11111110  A+B+C
11111100  B+C
11111010  A+C
11111000  C+AB
11110000  C
11101110  A+B
11101100  B+AC
11101010  A+BC
11101000  AB+AC+BC
11100000  AC+BC
11001100  B
11001000  AB+BC
11000000  BC
10101010  A
10101000  AB+AC
10100000  AC
10001000  AB
10000000  ABC
00000000  F

A modification of this method can determine
if an arbitary truth table is a monotonic function.

Compare the left half of the TT to the right half.
The right half must be a subset of the left.
Now compare the left quarter of the the left half
to the right quarter of the left half.
The right quarter must be a subset of the left.
Continue dividing the TT and verify
that the right side is always a subset of the left.
If this is true for every combination then the function is monotone.

Russell
-2 many 2 count

I dont know if this is the right place to post this but is there an
algorithm for finding the most general unifier for given expressions?

                         UCLA LOGIC COLLOQUIUM
                       Friday, November 19, 1999
                               4:00 p.m.
                       Mathematical Sciences 6627
                                 UCLA

                            NORMAN DANNER

                                (UCLA)

         "CAPTURING FUNCTION CLASSES WITH THE LAMBDA CALCULUS"

     One of the first results regarding Church’s untyped lambda
calculus is that, relative to an appropriate encoding of the natural
numbers, exactly the total recursive functions are representable.  Much
of the power of the untyped calculus arises from its (intentional)
failure to distinguish between function and argument (i.e., the same
term can be used in both capacities).  A typing discipline for the
lambda calculus reinstates this distinction, and when a typing
discipline is imposed, the collection of representable numeric
functions decreases dramatically.
     In this talk, I will survey some of the main typing disciplines
and their corresponding classes of representable functions.  I will
start with so-called simple typing, characterized by Schwichtenberg and
Statman in the late 60′s, and work through to some recent results of
Daniel Leivant and myself on systems of ramified polymorphism.

_________________________________________________________________________

                           http://www.math.ucla.edu/~hbe/logic.html

If you are interested in the philosophy of The Universe, The True Nature
of Reality and our place in all Existence, please visit the following
pages.
http://www.earthpoetry.demon.co.uk/sciph.html
http://www.earthpoetry.demon.co.uk
—
Reason
RC

This speculation is not grounded in fact;
nor in known theory;
nor even in hallucination.

If this makes this post unwanted in your group, please forgive me
for polluting your living space.

Under what circumstances could the laws of logic change?
What physical phenomena could cause such change, on a local
or Universe-Wide scale?

What would be the consequences of such?
Is it even theoretically possible to predict this?

***
Could some parts of the universe work according to logical laws
that are different from "ours"? This is not an entirely ridiculous
query. We may have evolved in a region of space where logic-defying
anomalies (workable time travel, etc.) do not exist or are not
commonplace,
and therefore our brains are not equipped to think about them. This is
why
time travel – related violations of causality seem impossible. It is
probable
that they are possible, but we are physically incapable of reasoning
about
them.

In short, there may exist physical phenomena which are outside of the
human scope of reasoning; our minds are not capable of thinking properly
about them.

See the short easy read at
http://members.aol.com/randaminor/mathuniv.html
Regards,
john reed