Logic — math, philosophy & computational aspects

using encoder as MUX

Hi ,
Can anyone here help me to solve one task from my study. I tried to
find a solution for it by myself but hanged up.
I have a logic function F(A,B,C). After a simplification I received a
simple function as following:
 F(A,B,C)= A XOR C.
I was said to implemented the function with 4*1  MUX and 2*1 MUX. And
it is OK, I did it.
Now I have to implemetent it with  2-to-4 decoder and NAND gate. The
decoder is 74LS139 .
(This decoder has Enable pin) How can I do it ?

Thank you in advance.

Links

Appeared excellent way to facebook hack password. Get access to any account. .
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OT: Apples = Oranges Article in the Onion

After receiving an e-mail from Mr. Jablome, and exchanging a few more,
he wrote and said that he will be submitting the following article to
The Onion, a newspaper published in Denver, Colorado. I thought you all
might like a preview. (As I told him, I’m not technically a professor,
but he quoted "artistic license", as I was a Visiting Assistant
Professor at ASU from Fall 2000-Spring 2001.)

     — Christopher Heckman

e-mail begins here:
———————————————————————————————-

Prof. Heckman,

Here’s the article I’m sending to the Onion. Thanx for suggesting I
look
up A.P. on Wikipedia.

     – H.wood.

————————————————–

"Apples Now Comparable to Oranges"
Internet "Crank" Responsible

by Heywood Jablome

DENVER, CO. Remember the saying "You can’t compare apples with
oranges?" Well,
it’s not true any more, thanks to one "Archimedes Plutonium".

"Archimedes Plutonium" is the pseudonym of Ludwig Poehlmann, born in
1950, in
Germany, and who has moved around the world and lived in Australia,
Colorado,
and South Dakota. Mr. Plutonium, as he prefers to be called,
accomplished this
by his submission to Wikipedia which re-defined an apple as a
"spherical fruit
which is usually the color of orange."

"I never liked that old saying about apples and oranges," Mr. Plutonium

explained in his submission. "But then I realized that ancient grocers
had
simply defined an apple the wrong way. Once I found the right
definition, well,
everything came together.

"I will be the most famous person in Grocery Theory, a hundred years
from
now," he added. (Mr. Plutonium is evidently unfamiliar with the term
‘biology’.) "Horace Banana will be one of a thousand people who you
will never
hear of again."

"Grocery theory" is only one subject that Mr. Plutonium will leave his
mark
on. He has new theories for physics, mathematics, and chemistry, which
he has
also submitted to Wikipedia.

One submission refered to a ‘quake’ [sic] by the name of Chris Heckman.
This
reporter decided to track down this ‘quake’, who turned out to be
Professor
Christopher Heckman, teaching at Arizona State University. I asked the
good
professor  about his opinion of Mr. Plutonium. He replied, via e-mail,
"Perhaps
you should check Wikipedia for yourself."

It was a good thing I did, because this is the source of information
available
with the fewest mistakes per article, even beating out the Encyclopedia

Britannica. Any source which was less credible would have raised doubts
in my
mind as to the facts it contained.

Mr. Plutonium claims to have obtained a mathematics degree at the
University
of Cincinnati in th elate 1960s and done graduate work at a university
in Utah.
He then moved inexplicably to Australia, where he became a professional
tutor,
joined the Navy (and was discharged with a Section 8, for mental
unfitness),
and moved back to the United States, when he inexplicably made money
off the
stock market. The past twenty years he has posted to the Internet under
the
names of "Ludwig Plutonium" and "Archimedes Plutonium". His current
whereabouts
could not be determined, as he refused to respond to this reporter’s
e-mails.

– H.J.

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junk

obfuskacja_test…@tlen.pl
obfuskacja_test_02[at]tlen.pl

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logic professionals opinion – Geometry in the Bible Text

Hi, I’d like to know logical arguments of the logic professionals – pro
and contra (if any) about unusual facts found by me in printed book of
TANAkH (BIBLE in Hebrew):
Atoll Project
http://www.atoll-geocad.com/The-Message/Atoll-ENG.html

Thanks,
Boris

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Is Relativism Always Self-Refuting Or Just Sometimes?

Relativism is sometimes identified (usually by its critics) as the
thesis that all points of view are equally valid. In ethics, this
amounts to saying that all moralities are equally good; in epistemology
it implies that all beliefs, or belief systems, are equally true.
Critics of relativism typically dismiss such views as incoherent since
they imply the validity even of the view that relativism is false. They
also charge that such views are pernicious since they undermine the
enterprise of trying to improve our ways of thinking.

http://www.iep.utm.edu/r/relativi.htm

The first clear statement of relativism comes with the Sophist
Protagoras, as quoted by Plato, "The way things appear to me, in that
way they exist for me; and the way things appears to you, in that way
they exist for you" (Theaetetus 152a). Thus, however I see things, that
is actually true — for me. If you see things differently, then that is
true — for you. There is no separate or objective truth apart from how
each individual happens to see things. Consequently, Protagoras says
that there is no such thing as falsehood. Unfortunately, this would
make Protagoras’s own profession meaningless, since his business is to
teach people how to persuade others of their own beliefs. It would be
strange to tell others that what they believe is true but that they
should accept what you say nevertheless. So Protagoras qualified his
doctrine: while whatever anyone believes is true, things that some
people believe may be better than what others believe.

Plato thought that such a qualification reveals the inconsistency of
the whole doctrine. His basic argument against relativism is called the
"Turning the Tables" (Peritropé, "turning around") argument, and it
goes something like this: "If the way things appear to me, in that way
they exist for me, and the way things appears to you, in that way they
exist for you, then it appears to me that your whole doctrine is
false." Since anything that appears to me is true, then it must be true
that Protagoras is wrong [1]. Relativism thus has the strange logical
property of not being able to deny the truth of its own contradiction.
Indeed, if Protagoras says that there is no falsehood, then he cannot
say that the opposite, the contradiction, of his own doctrine is false.
Protagoras wants to have it both ways — that there is no falsehood but
that the denial of what he says is false — and that is typical of
relativism. And if we say that relativism simply means that whatever I
believe is nobody else’s business, then there is no reason why I should
tell anybody else what I believe, since it is then none of my business
to influence their beliefs.

http://www.friesian.com/relative.htm

Matt: I don’t believe that all points of view are equally valid.

Jan: Why not?

Matt: Because it doesn’t make sense that everything is relative. That
wouldn’t be logical.

Jan: Ah, you see? That is your problem. You are using logic to refute
relativism and you cannot do that. Relativism isn’t based upon logic.
It isn’t the same thing. So you can’t use logic to refute relativism.

Matt: If you say I cannot use logic to refute relativism, then you are
using logic to say this since you give me the logical statement and
conclusion that I cannot use logic to refute relativism because
relativism isn’t based on logic. I hope you can see that you made a
logical case here for not using logic. If that is so, then your
complaint is self contradictory and invalid. Would you want me to
follow a system of thought that is self contradictory?

Jan: I can see why they call you slick. But, the point is that
relativism is true within itself and logic is not a necessary property
of relativism. It can be used within relativism, but it is not superior
to relativism.

Matt: To say that relativism is true within itself is an absolute
statement. Don’t you see that you can’t do that if relativism is true?
You would have to say something like, "Relativism is true some of the
time."

Jan: You are playing word games here.

Matt: I do not see how. I am simply responding to what you said. I
think what you are doing is simply making assertions without proof. You
are saying that it is true because it is true. In essence, you are
telling me an absolute truth that relativism is its own self-existing
truth. This is an absolute statement which again refutes the notion
that relativism is true. Furthermore, if relativism is true then
relativism itself is relative. In other words, if relativism is true,
then relativism may or may not be true in and of itself. If that is
true, then relativism can be false. If relativism can be false, then
relativism can’t be true.

Jan: There you go using logic again. Logic is not the whole means by
which truth is determined. Relativism goes beyond logic to truths that
logic cannot prove.

Matt: Okay, then without using logic, can you tell why relativism is
true?

Jan: It is true because it is true that people believe different things
and that people have different perceptions of reality and what is right
for them.

Matt: I agree that people believe different things, but does believing
different things make them true because they are believed?

Jan: No, of course not. But you must understand that we perceive things
differently, and that these different perceptions are true for
different people.

Matt: I can agree with that, but I am not speaking about things that
really are relative like which side of the bed you should get out of in
the morning. I’m talking about things like lying, cheating, stealing,
etc. If relativism is true and all points of view are equally valid,
then someone’s view that it is okay to steal, is valid.

Jan: Technically, it would be, depending on the circumstances. For
example, if it meant feeding your family or helping someone.

Matt: I see. Okay, give me your money right now. I want to steal it
from you. If I had a gun, I’d point it at you and rob you. Is that
okay?

Jan: Of course not.

Matt: Why not? My view is that in order to win the argument, I must rob
from you to demonstrate the absurdity of your position. Therefore, it
is right for me. You should approve.

Jan: But I cannot, because it isn’t right for me that you steal from
me.

Matt: Oh, so relativism has boundaries? It is true only for the
individual, no one else?

Jan: In that case yes.

Matt: Then relativism isn’t a universal truth is it? If it is only true
for individuals on an individual basis, it may or may not be true or
false or right or wrong or whatever. It is just a kind of "whatever you
want to do and feel" philosophy.

Jan: Sort of, but you can’t harm anyone else.

Matt: Are you saying that it is an absolute that you are not to harm
anyone else?

Jan: There you go again turning this into an argument on absolutes.

Matt: But I am only following your lead. You’re the one who said that
relativism is true because it is true. Correct?

Jan: Yes, I said that, but you have to understand that it is relative
to the individual.

Matt: If relativism is true because it is true, then can I say that it
is false because it is false?

Jan: You could if you wanted to.

Matt: Then would it be false or not?

Jan: It would be false for you.

Matt: But that isn’t what I said. I said it was false…. "because it
is false." I didn’t say it was false for me. I said that it is by
nature false. Don’t you see? You said it was true "because it is true."
You spoke of it as being true "by nature." You implied an absolute
quality to relativism as a real truth. If I can do the same thing in
the opposite direction, then how does my assertion become different in
nature than yours? In other words, "by nature" it is true and "by
nature" it is false. Both cannot be true. Therefore relativism doesn’t
work.

Jan: What you are doing is using logic again. Relativism and logic are
different things. You cannot use one thing to judge another.

Matt: But you just did. You made a statement and drew a conclusion. You
said that relativism and logic are different. Then you said that I
cannot use one to judge the other. In other words, you made a statement
and drew a logical conclusion. Look. If you want to validate relativism
using relativism, then why do you keep using logic to do it?

Jan: You keep going back to these logic games. You have to understand
that they are simply different.

Matt: So then, what you are saying is that I am not allowed to examine
relativism in a logical manner. Correct?

Jan: Correct.

Matt: You want truth, right?

Jan: Of course.

Matt: But, if I must accept that relativism is simply true, how can I
possibly know if it is ever false? What you are saying is that it is
never false. If it is never false, then it is always true. If it is
always true, then it isn’t relative, is it?

Jan: There you go using logic again.

Matt: I’m trying to ask questions. But, it seems that you want me to
avoid thinking and just accept relativism as true. If I were to say
that relativism is true, then it is absolutely true that relativism is
true which would mean that the opposing view that relativism is false,
could not be true…which would mean that relativism is not true since
it states that all views are true. It seems to me that the only way
relativism is true, is if you stop thinking logically and just accept
it on blind faith that it is true.

Jan: This is the problem with the western, Aristotelian logic system.
It teaches you that there are absolutes when there are not.

Matt: But to say there are not absolutes is an absolute statement,
which is self refuting. Again, it seems that the only way to accept
relativism is to not think logically. You have to believe it on faith.

Jan: The nature of relativism is that it is not subject to logic. No
logical reasons are necessary to establish this. Relativism, by its
nature, is not of logic, but beyond logic. The essence of relativism is
that relativism itself, is true.

Matt: Then you are simply stating that relativism is true without

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Metamathematically True or False?

The set expressed by a wff is recursively enumerable iff the set
expressed is the set represented.

1. Is the above assertion true or false of Peano Arithmetic?

2. What simpler conditions (especially frequently used properties of
axiomatic systems e.g. sound, consistent) are necessary or sufficient?

3. Who has discussed or proven it?

Please & Thank You.

C-B

(A wff expresses (represents) the set of numbers that when substituted
for its free variables forms a true (provable) sentence.)

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decidability results for relational logic

hi everyone,

i was reading an article by don knuth which showed that given a binary
relation R, there are at most 10 different relations that can be
derived from R using the transitive closure operation (written as R+)
and the complement operation (written as R-).

he showed that you need to define R over a set with at least 5 elements
to meet the bound of 10.  there are similar bound when you introduce
more operators, such as transpose, unioning identity, etc.

i was wondering if anyone know of general decidability results for
simple identities involving relations?

specifically, i thought one path to deciding these knuth-like problems
may be to  prove a finite model theorem, i.e., derive a bound on the
cardinality of the universe from the structure of the parse tree of the
formula in questions – the identity holds iff it holds in all cases
where the relations are defined over sets whose cardinality is the
bound.

cheers,
adnan

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Adequate sets of n-ary connectives

Have there been results published that give an adequate set of n>2-ary
connectives that is capable of expressing all truth functions? I’m
looking for a general method of determing which sets of connectives are
adequate.

The only way I can think of for determining whether a set of n-ary
connectives is adequate is by writing out all the 2^{2^n} truth tables
of the nth order and then seeing if some adequate set of connectives
(e.g. {~, v}) can be defined in terms of some set of those truth
tables—that set will then be adequate (i.e. the connectives defined
in terms of those truth tables). But this method is obviously
impractical even for small n.

Thanks

Michael

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ILLC Research Reports and Technical Notes 2005

ILLC Scientific Publications
—————————-

This document contains the titles of the reports that were published
by the Institute for Logic, Language and Computation (ILLC) this year.
All ILLC reports are available from the ILLC bureau:

       ILLC Bureau
       University of Amsterdam
       Plantage Muidergracht 24
       NL-1018 TV Amsterdam
       The Netherlands

Many reports are also electronically available,
 by WWW at http://www.illc.uva.nl/Publications and
 or FTP at ftp://ftp.science.uva.nl/pub/theory/illc/researchreports/
The ILLC bureau may be contacted by email, at i…@science.uva.nl

Reports are numbered Series-Year-Number, where `Series’ is one of
  PP = Prepublication Series
  MoL = Master of Logic Thesis

———————————————————————-

Report PP-2005-01
Title: Neural Networks, Penalty Logic and Optimality Theory
Author: Reinhard Blutner

Report PP-2005-02
Title: On the complexity of hybrid logics with binders
Author: Balder ten Cate, Massimo Franceschet

Report PP-2005-03
Title: Minimality, Non-Determinism, and Absent Information in Multi-Context
Systems
Author: Floris Roelofsen

Report PP-2005-04
Title: XpathMark: an XPath benchmark for XMark
Author: Massimo Franceschet

Report PP-2005-05
Title: A Different Story about Indexicals
Author: Isadora Stojanovic

Report PP-2005-06
Title: Open Problems in Logical Dynamics
Author: Johan van Benthem

Report PP-2005-07
Title: Guards, Bounds, and Generalized Semantics
Author: Johan van Benthem

Report PP-2005-08
Title: Modal Frame Correspondence Generalized
Author: Johan van Benthem

Report PP-2005-09
Title: Logics of Communication and Change
Author: Johan van Benthem, Jan van Eijck, Barteld Kooi

Report PP-2005-10
Title: Cognition as Interaction
Author: Johan van Benthem

Report PP-2005-11
Title: An Essay on Sabotage and Obstruction
Author: Johan van Benthem

Report PP-2005-12
Title: From Onions to Broccoli: Generalizing Lewis’s counterfactual logic
Author: Patrick Girard

Report PP-2005-13
Title: What does Game Theory have to do with Plans?
Author: Olivier Roy

Report PP-2005-14
Title: Hybrid Definability in Topological Spaces
Author: Dmitry Sustretov

Report PP-2005-15
Title: The many faces of interpretability
Author: Evan Goris, Joost J. Joosten

Report PP-2005-16
Title: A finitary treatment of the closed fragment of Japaridze’s
provability logic
Author: Lev D. Beklemishev, Joost J. Joosten, Marco Vervoort

Report PP-2005-17
Title: Signalling in IF games: a tricky business
Author: Theo M.V. Janssen, Francien Dechesne

Report PP-2005-18
Title: Mathematical Knowledge is Context Dependent
Author: Benedikt L\"owe, Thomas M\"uller

Report PP-2005-19
Title: A simple inductive measure analysis for cardinals under the Axiom of
Determinacy
Author: Stefan Bold, Benedikt L\"owe

Report PP-2005-20
Title: Epistemic Logic and Epistemology, the state of their affairs
Author: Johan van Benthem

Report PP-2005-21
Title: Logic in Philosophy
Author: Johan van Benthem

Report PP-2005-22
Title: Where is Logic Going, and Should It?
Author: Johan van Benthem

Report PP-2005-23
Title: Issues in Multiagent Resource Allocation
Author: Yann Chevaleyre, Paul E. Dunne, Ulle Endriss, J\’er\^ome Lang,
Michel Lema\^itre, Nicolas Maudet, Julian Padget, Steve Phelps, Juan A.
Rodr\’igues-Aguilar, Paulo Sousa

Report PP-2005-24
Title: Extensions of the Axiom of Blackwell Determinacy
Author: Benedikt L\"owe

Report PP-2005-25
Title: Temporal Logics for Representing Agent Communication Protocols
Author: Ulle Endriss

Report PP-2005-26
Title: The Modal Logic of Forcing
Author: Joel David Hamkins, Benedikt L\"owe

Report PP-2005-27
Title: Brouwer’s incomplete objects
Author: Joop Niekus

Report PP-2005-28
Title: Preference logic, conditionals and solution concepts in games
Author: Johan van Benthem, Sieuwert van Otterloo, Olivier Roy

Report PP-2005-29
Title: Dynamic Logic of Preference Upgrade
Author: Johan van Benthem, Fenrong Liu

Report MoL-2005-01
Title: `binyanim ba’avir’: An investigation of Aspect Semantics in Modern
Hebrew
Author: Reut Tsarfaty

Report MoL-2005-02
Title: The Value of Agreement: a new Boosting Algorithm
Author: Boaz Leskes

Report MoL-2005-03
Title: Algebraizing Hybrid Logic
Author: Evangelos Tzanis

Report MoL-2005-04
Title: Pseudo-Imperatives
Author: Michael Franke

Report MoL-2005-05
Title: Exploring Logical Perspectives on Distributed Information and its
Dynamics
Author: Floris Roelofsen

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Simple yet Profound Metatheorem

Prove ( P = |- Q ) => |- ( P = Q )

(P and Q have the same sets of free variables.)  This simple theorem (I
created 12/1/05) provides the link between Theory of Computation and
Proof Theory (Incompleteness in Logic) that theoreticians such as
myself have been looking for since the 1930′s.  (Each Theory of
Computation theorem becomes an Incompleteness theorem in Logic,
providing almost trivial formal derivation of the exact results of
Godel, Rosser and Smullyan.)

C-B

Hint: Consider the equivalent ( P = |-Q ) => ( P = |- P )

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