Logic — math, philosophy & computational aspects

What is the consistency strength of "Every sigma-1,2 set is Lebesgue
measurable"?

Call for Papers – The Journal of American Science

The international academic journal "The Journal of American
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Please visit http://www.americanscience.org and send your manuscript to
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Announcing ttcnf (Truth Table CNF), a program that computes the truth
tables generated by CNF boolean expressions of one to five variables.
It counts these truth tables in a number of ways. These results may be
useful in understanding CNF expressions.
          http://www.qhull.org/ttcnf/

The number of truth tables for 3-CNF truth tables of three to five
variables is
          256  43,146  120,510,132
This sequence is unlikely to be extended for a while.   Using a 64-bit
computer, the generating program for six variables is easy to write,
but memory and time requirements make it impractical.

A conjecture is that 3-CNF truth tables are incompressible and hence
random.   Randomness may be a pervasive property of the natural
numbers.  The number of 3-CNF truth tables grows substantially slower
than the total number of truth tables
         256  65,536  4,294,967,296

–Brad Barber

Godel’s Incompleteness work depends heavily on the assumption
that the theory T in question be consistent. But how could we know
if T is consistent, for any given general T? It seems like we don’t
have a precision procedure to determine that. So Godel’s results
are _hypothetical_ results: it doesn’t assert that a particular T
is in fact incomplete, or G(T) is in fact true; it only assert
them hypothetically so. In fact, if T later turns out to be
inconsistent, T would be complete for example.

Two questions seem inevitable:

(1) Why would Godel’s work have a huge impact in modern mathematical
     formalism? [Arguably, GIT would be more complicate than "If we know
     a counter example of GC, then ~GC is provable in PA". But the fact
     that both of them are hypothetical means that T might be no more
     factually incomplete than ~GC might be factually provable in PA.]

(2) Is it true then there is *a real danger* that there might exist an
     inconsistent theory T in the sense that for all the theorems that
     we – as human being – could conceivably prove, their negation
     counterparts would have proof lengths that are beyond human capacity
     to comprehend?

–
—————————————————-
Time passes, there is no way we can hold it back.
Why then do thoughts linger, long after everything
else is gone?
                                               Ryokan
—————————————————-

               FINAL CALL FOR PAPERS

                        DEON2006

              Eighth International Workshop on
              Deontic Logic in Computer Science

              Special Topic: Artificial Normative Systems

              Utrecht, The Netherlands
              12, 13, and 14 July 2006

              http://www.cs.uu.nl/deon2006/

Sponsored by SIKS (Dutch Research School of Information and Knowledge
Systems), JURIX (Dutch Foundation for Legal Knowledge and Information
Systems), BNVKI (Belgian-Dutch Association for AI), NWO (Netherlands
Organisation for Scientific Research) and the Department of Information
and Computing Sciences of Utrecht University.

The biennial DEON workshops are designed to promote cooperation among
scholars across disciplines who are interested in deontic logic and its
use in computer science. These workshops traditionally support research
linking the formal-logical study of normative concepts and normative
systems with computer science, artificial intelligence, philosophy,
organisation theory and law. In addition to these general themes,
DEON2006 will encourage a special focus on the topic

      Artificial Normative Systems

There have been seven previous DEON workshops: Amsterdam, December 1991;
Oslo, January 1994; Sesimbra, January 1996; Bologna, January 1998;
Toulouse, January 2000; London, May 2002; Madeira, May 2004. Selected
papers from each of these workshops have been published internationally.
(See the links on the DEON2006 website.)

The Program Committee invites papers concerned with these

             WORKSHOP GENERAL THEMES:

    * the logical study of normative reasoning,
      including formal systems of deontic logic,
      defeasible normative reasoning, the logic
      of action, and other related areas of logic,

    * the formal analysis of normative concepts and
      normative systems,

    * the formal representation of legal knowledge,

    * the formal specification of aspects of norm-
      governed multi-agent systems and autonomous
      agents, including (but not limited to) the
      representation of rights, authorisation,
      delegation, power, responsibility and liability,

    * the formal specification of normative systems
      for the management of bureaucratic processes
      in public or private administration,

    * applications of normative logic to the specification
      of database integrity constraints,

    * applications of normative logic to the specification
      of computer security protocols,

    * normative aspects of protocols for communication,
      negotiation and multi-agent decision making.

And the Committee especially welcomes papers addressing the workshop
specific theme:

             ARTIFICIAL NORMATIVE SYSTEMS

DEON2006 has a special focus on deontic notions in the theory,
specification and implementation of artificial normative systems, such
as electronic institutions, norm-regulated multi-agent systems, and
artificial agent societies more generally. We also invite studies of
hybrid systems, incorporating both human and computer-based agents.
Topics of interest in this special theme include, but are not limited to:

    * normative systems

    * regulated multi-agent systems

    * norms in agent societies

    * normative agents

    * (electronic) institutions

    * virtual organisations

    * contracts, laws, regulations in artificial societies

    * norm violation and punishment

    * norm verification

We welcome both theoretical work (formal models, representations,
specifications, logics, verification) and implementation-oriented work
(architectures, programming languages, design models, simulations,
prototype systems) on these specific topics.

SUBMISSION DETAILS

    Authors are invited to submit an original, previously
    unpublished, research paper pertaining to any of these
    topics. The paper should be in English, and should be
    no longer than 15 pages, or approximately 7500 words.
    The first page should contain the full name and contact
    information for at least one of the authors, and it
    should contain an Abstract of no more than ten lines.
    Authors should submit their papers electronically,
    in either .pdf or .ps format.

    Authors should consult the website http://www.cs.uu.nl/deon2006/
    for instructions for submitting their papers electronically.
    [These instructions will become available shortly.]
    (Anyone who is unable to send the paper electronically
    and wishes to submit hard copies should inquire for
    details from one of the Program Co-Chairs at the
    addresses given below.) Authors are especially
    encouraged to use the Springer LNCS
    styles if possible; these are available at
    http://www.springer.de/comp/lncs/authors.html.
    The deadline for submission is 27 January 2006.

TIMETABLE

     * 27 January 2006: Submission deadline
     * 24 February 2006: Notification of acceptance
     * 24 March 2006: Deadline for final, camera-ready versions.
     * 12-14 July 2006: The Workshop

PUBLICATION

    Copies of the Workshop Proceedings, will be provided
    to all participants. We expect to publish the proceedings
    with Springer in their LNCS series. In addition, we anticipate
    that revised versions of selected papers from the workshop will
    be published in a special issue of the Journal of Applied Logic
    (Elsevier).

INVITED SPEAKERS

    * Jose Carmo (Madeira)
    * Frank Dignum (Utrecht)
    * Paolo Petta (Vienna)

GENERAL & PROGRAM CO-CHAIRS

    * Lou Goble
      Department of Philosophy
      Willamette University
      Salem, Oregon 97301, USA
      lgo…@willamette.edu
      phone: 1-503-370-6002
      fax: 1-503-370-6944

    * John-Jules Ch. Meyer
      Intelligent Systems Group
      Institute of Information and Computing Sciences
      Universiteit Utrecht
      P.O.Box 80.089
      3508 TB Utrecht, The Netherlands
      j…@cs.uu.nl
      phone: +31-(0)30-2534117
      fax: +31-(0)30-2513791

ORGANIZING COMMITTEE CO-CHAIRS

    * Jan Broersen
      Intelligent Systems Group
      Institute of Information and Computing Sciences
      Universiteit Utrecht
      P.O.Box 80.089
      3508 TB Utrecht, The Netherlands
      broer…@cs.uu.nl
      phone: +31-(0)30-2533193
      fax: +31-(0)30-2513791

    * Henry Prakken
      Intelligent Systems Group
      Institute of Information and Computing Sciences
      Universiteit Utrecht
      P.O.Box 80.089
      3508 TB Utrecht, The Netherlands
      he…@cs.uu.nl
      phone: +31-(0)30-2532313
      fax: +31-(0)30-2513791
      also at: Centre for Law & ICT, Faculty of Law, University of
Groningen,
      phone +31-50-3635696.

PROGRAM COMMITTEE

    * Paul Bartha (University of British Columbia)
    * Jan Broersen (Universiteit Utrecht)
    * Mark Brown (Syracuse University)
    * Jose Carmo (University of Madeira)
    * Frederic Cuppens (ENST-Bretagne Rennes)
    * Robert Demolombe (ONERA Toulouse)
    * Frank Dignum (Universiteit Utrecht)
    * Lou Goble (Willamette University, co-chair)
    * Risto Hilpinen (University of Miami)
    * John Horty (University of Maryland)
    * Andrew Jones (King’s College London)
    * Lars Lindahl (University of Lund)
    * Alessio Lomuscio (University College London)
    * Paul McNamara (University of New Hampshire)
    * David Makinson (King’s College London)
    * John-Jules Meyer (Universiteit Utrecht, co-chair)
    * Ron van der Meyden (University of New South Wales / NICTA)
    * Donald Nute (University of Georgia)
    * Rohit Parikh (City University of New York)
    * Henry Prakken (Universiteit Utrecht / University of Groningen)
    * Filipe Santos (ISCTE Portugal)
    * Giovanni Sartor (University of Bologna)
    * Krister Segerberg (Uppsala University)
    * Marek Sergot (Imperial College London)
    * Carles Sierra (IIIA-CSIC)
    * Leon van der Torre (CWI Amsterdam / Delft University of Technology)
    * Lennart Aqvist (Uppsala University)

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      Hello, I have a problem. It seems easy but i couldn’t succeed.
What is the order of magnitute(big Oh) of the below expression,

       sum(a^i* (n^2-i^2)),  i=n, n+1, …..,n   for |a|<1

      here sum refers the sigma notation. Thanks alot.

Babel Science

The Sumerians and Babylonians asked, "What keeps the heavenly bodies in
their places?" Lucretious, Newton and Einstein also asked this question.
Modern Science is in fact based, in varying degree, upon their answers. (1.)

Most modern scientists believe their assessment of the empirical
evidence is correct. (2.) However, "The business of Science is not to
corroborate previous beliefs, but to test them." (3.) This chapter will
show Modern Science is in fact founded upon delusion practiced by the
Sumerian and Babylonian Astrologers.

Before testing beliefs that are the foundation of Modern Science, a
definition of the Logic to be used is in order. There are several
branches of logic. Pythagorean logic is one. Mathematics, Euclidean
Geometry or otherwise–however elegant, is a branch of logic.

It is not possible to determine which mathematical system represents
reality by mathematical methods alone because: (4) the scheme adopted by
Tycho Brahe "was mathematically equivalent to the Copernican system."
And, "Astronomical computations were rendered easier by the Copernican
scheme …but the prediction of planet places was not more accurate."
And, (5) Einstein accounted for the evidence of the rotation of the
earth on its axis by the false assumption that the universe rotates
around the earth. Last, because Pythagoreans have confused the Logical
with the Real, Pythagorean logic will not be used. (6.)

The logic practiced by Modern Philosophers is a combination of the
Dynamism of Boscovich, the Mechanism of Descartes and the Skepticism of
Hume. The Modern Sophists have castrated themselves with the question
"What is Truth," which they cannot answer. (7.) Their methods and
conclusions are therefore without use or value. That form of logic begun
by Aristotle and refined by St. Thomas will be used, since it is,
according to them, possible for Reason to obtain Truth. (8.)

According to Dr. Jerry Bergman, "Science" is a method of obtaining
knowledge by: First, Observation, Second, Classification, Third,
Hypothesis, and Fourth, Tests. (9.) Science is the study of that which
is tangible and measurable by controlled and repeatable experiment. The
inherent nature of Science limits it to things that can be perceived by
human senses (or instruments that amplify them) and to things that it
can confine, control and manipulate in contrived and isolated tests and
experiments.

To know what Science is, is to know what Science is not. If scientists
cannot see or touch an object or get it to cooperate in repeatable
experiments and tests, it cannot be the subject of scientific study. If
scientists cannot demonstrate that a thing has tangible attributes, they
cannot prove its existence. If scientists cannot show tangible evidence
of the non-existence of an object, rather than just a lack of evidence
of its existence, they cannot prove its nonexistence by the scientific
method. Scientists can only demonstrate, in this case, that Science
cannot treat the subject: it is rightfully the property of Philosophy or
Theodicy.

Sir Frances Beacon said, "When philosophy is cut off from its roots in
experience, where it was born, it dies." (10.) Kepler said, "If a
scientist’s hypothesis fit into a certain metaphysical theory, fine; but
if not, then it is the metaphysics which must go." (11.)

According to Webster, Metaphysics is a branch of Philosophy. (12.)
Specifically, Ontology (the science of being) and Cosmology (the science
of the fundamental cause of things) are Metaphysics. Therefore, if the
empirical evidence, rather than Sophists misinterpretation of evidence,
does not support the theories of Uniformatism, Evolution, Big Bang and
Relativity, they must go.

Harlo Shaply (13.) said the origin of Origins is beyond Astronomy in the
realm of the, to us, unknowable. George Gaylord Simpson (14.) said the
source of all physical laws was quite unknown, probably unknowable to
science, and here religion may honorably enter the picture.

Some early Modern Sophists thought by proving the absence of an Absolute
Point of Reference (from which the Prime Mover was thought to view and
control the universe) they could refute the existence of the Supreme
Being. However, to prove God has no place to stand does not disprove His
existence; it proves man’s concept of God is inadequate, and the subject
is not treatable by scientific method. (15.)

The Word of God tells us the soul of man exists separate from the body.
Some scientists say there is no tangible evidence of the soul, thus it
does not exist. Yet scientists proclaim the existence of other physical
dimensions, of which they have no tangible evidence. (16.) Thus, Science
has severed itself from its roots.

Before proceeding, some examples of irrational thought should be
considered. The absolute winner for putting things backwards–with
intent to delude–is the wrong assumption "man created God." However,
let us consider examples of sophistry directly related to the subject.
According to Webster, "Sophism" or "Sophistry" is "an argument designed
to deceive." The argument, "there is no argument to deceive," is an
argument designed to deceive. Can the statement, "there are no true
statements," be a true statement? Can the statement "there are no
absolutes" be absolute? (17.)

Mosses recorded the first argument designed to deceive. Gen. 3:3-5. "If
God had meant you would die, He would call this the Tree of Death,
rather than the Tree of Knowledge. He meant ignorance would die. It will
make you wise, so you won’t die." Knowledge has nothing to do with the
mortality of the body, thus this is a non-sequitur argument. Another
argument like this is, "Cinnabar is far different, so, it can make
people immortal." (18.) Both arguments lead to death. First for Adam and
Eve: Then second for seven Chinese Emperors by mercury poisoning. One
kind of sophistry is that which is based on, or contains, a false
premise. A more subtle argument uses the delicate shades of meaning of
terms, or the confusion of Real and Logical, with intent to deceive. (19.)

As an example of wrong assumption, consider the epitome "there is no
God." Since there is no tangible evidence to prove such a hypothesis,
and thus it is impossible to arrive at this statement by scientific
method, it can only be an assumption. The beliefs of Evolution and "Big
Bang" cannot proceed except they begin at this wrong assumption.

Consider an example of the confusion of Real and Logical. "Physicists
are wont to talk about `space-time co-ordinates’ as if they were real."
(20.) Form (or Shape) does not exist separate from Substance. The
Concept of "curved space-time" exists only in the mind of the Modern
Sophists; yet they would have us believe Space (empty area) is curved. (21.)

For examples of the terms Modern Sophists have designed with intent to
deceive consider some terms used in Evolution theory: "discontinuous
variation" and "punctuated equilibrium." Consider "unlimited finite
space" as used in Relativistic "Big Bang." Sophists intend that
self-contradictory terms lead to wrong conclusions, and this reveals an
utter contempt for Truth. (22.) 2 Thes. 2:10-12.

The conclusion drawn from the Michelson and Morley experiments by
Fitzgerald and others will now be considered. (23.) Fitzgerald advanced
an untested premise. Namely, that the length of a steal rod is
determined solely (an assumption) by the Electra-static equilibrium of
its particles, and the rod, in motion through the Aether, would contract.

If the premise were correct, the application of a magnetic field would
cause a steal rod to contract, regardless of the motion of the rod, the
Earth, or the existence or nonexistence of Aether. In contradiction to
this false premise, a steal rod affected by a magnetic field will expand.

However, if the premise was correct, then it must be demonstrated that
the motion of the rod — or aether — is of sufficient velocity to
induce a measurable contraction in the length of the rod. There may be a
null result to the tests if the Aether consists of "other than Real" (or
neutral) particles incapable of inducing a magnetic field.

However, the results of the tests were not null. "They did not make the
assertion often attributed to them, that the effect was zero [or null].
Their published result says: `Considering the motion of the earth in its
orbit only… the relative motion of the earth and the aether is
probably less than one-sixth the earth’s orbital velocity, and certainly
less than one fourth.’" (24.)

Yet, consider the sophistry that follows. Some scientists, eager to
promote their preconception, jumped to the non sequitur assumption that
an observer in a moving system cannot know the Absolute Velocity of his
system. They believed they could then eliminate concepts such as
Absolute Space, Absolute Time and a Privileged Observer (God). (25.)

If it could be proven that an observer cannot know the Absolute Velocity
of his system, that would not prove the non-existence of an Absolute
Point of Reference, Absolute Space or Time (or God). What is
demonstrated is, the scientific method is inadequate to the task and the
subject belongs in the field of Philosophy or Theodicy. (26.)

The non sequitur conclusion to the Michelson and Morely experiments
marked the severing of Modern Science from its roots, and the beginning
of Satan’s Ideological war (the Strong Delusion) against mankind. 2
Thes. 2:2-12, Rev. 20:7-8.

Having dispensed with an Absolute Point of Reference, Modern Sophists
needed another Absolute to save Science from absolute chaos. In an
effort to replace the absolute point of reference, Albert Einstein made
man, after Nicolus of Cusa, the center of motion. However, the Theory of
Relativity proves there are no Absolutes and thereby falsifies itself.

If there is no absolute point of reference, and it is not possible to
…

read more »

I want to know more
about all the known paradoxes.
Can you address me to a good web source?
Thank you

Hi guys,

This is the problem I don’t get to solve (Maybe is very easy
for you):

At a bank there is a central queue served by four assistants. The
service times of three of the four assistants are exponentially
distributed with a mean 3 minutes, and the service time of the fourth
assistant is exponetially distributed with mean 4 minutes.

A customer enters the bank to find all four assistants busy, but nobody

waiting.

My question is:
Which is the distribution of the time the new customer has to wait
before moving forward for service? and how can I calculate the expected

time?

I know the exponential probability distribution function (pdf) for:
mean=3 minutes is  f(x)=λexp(-λt) ; λ=1/3
mean=4 minutes is  f(x)=λexp(-λt) ; λ=1/4
and their expected time (mean) are 3 and 4 minutes respectively.

But what about the new pdf taking into account both distributions? Do I

need to add both values of λ ? or take into account the probabilities
of both types of assistants? (I know that the answer is 40 seconds for
the expected time)

(I guess that if I’m able to find the new pdf, I just need to integrate

between 0 and infinity this new f(x) * x and I have the expected time.)

Please help !
Thank you very much in advance )

PS/ Does it have any thing to do with a hyperexponential distribution ?

a logic, a model, an isomorphism, an intention
———————————————–

   the logic:
————-

   Following Kalmbach, our terms are the elements
of a term algebra T(X) and are defined by:

           the elements of X are terms;

           if p, q are terms, then p\/q,
           p/\q, ~p are terms.

   Our semantics is the class of orthomodular
lattices OM.  A valuation v is a homomorphism
from T(X) in some L of OM, i.e

           v(p\/q)=v(p)\/v(q),

           v(p/\q)=v(p)/\v(q),

           v(~p)=v(p)’

   The element p of T(X) is a consequence of
a subset S of T(X), written as (S |= p) if, for
all valuations v satisfying v(s)=1 for every
s in S, holds v(p)=1.

   Our syntax consists of a set of axioms and a
rule of modus ponens.  We write pRq for
(p/\q)\/(~p/\~q).  The axioms A are:

A-01   xRx

A-02   ~(xRy)\/(~(yRz)\/(xRz))

A-03   ~(xRy)\/(~xR~y)

A-04   ~(xRy)\/((x/\z)R(y/\z))

A-05   (x/\y)R(y/\x)

A-06   (x/\(y/\z))R((x/\y)/\z)

A-07   (x/\(x\/y))Rx

A-08   (~x/\x)R((~x/\x)/\y)

A-09   xR~~x

A-10   ~(x\/y)R(~x/\~y)

A-11   (x\/(~x/\(x\/y)))R(x\/y)

A-12   (xRy)R(yRx)

A-13   ~(xRy)\/(~x\/y)

   Define the pseudoconnective "/->/" relative
to lattice elements a and b by

       a/->/b = (a’/\b)\/(a’/\b’)\/(a/\(a’\/b))

Then we have the identity between lattice elements
given by

       a/->/(a/->/b) = a’\/b

whence we formulate the two additional axioms for
our logic

A-14   (~x\/y)/->/(x/->/(x/->/y))

A-15   ~(x/->/y)\/(~x\/y)

   Modus ponens in this logic is given by

       p, p/->/q
       ———
           q

   the model:
————-

   The model in which we are interested is the
othomodular lattice freely generated by two
elements.

   the isomorphism:
——————-

   The orthomodular lattice freely generated
by two elements is isomorphic to

       2^4 X MO2

   the intention:
—————–

   Since my posts generally attract flames, I
will try to make this as uncontroversial as
possible.

   Many of my posts in the past had tried to
talk about "the mathematics of truth tables".
Consider the fixed aspect of a truth table
for a moment,

    A  B |
   ——|—–
    T  T |
    T  F |
    F  T |
    F  F |

If one compares this fixed representation with
a typical representation of MO2,

                      1

              /     /   \    \
           /      /       \     \
        /       /           \      \

      a       a’              b      b’

        \       \           /      /
           \      \       /     /
              \     \   /    /

                      0

one can begin to see how the logic given above
might relate to connectivity in classical logic.
That is, consecutively relabel the diagram above
according to the sequence

                      1

              /     /   \    \
           /      /       \     \
        /       /           \      \

      A      ~A               B      ~B

        \       \           /      /
           \      \       /     /
              \     \   /    /

                      0

                      T

              /     /   \    \
           /      /       \     \
        /       /           \      \

     TTFF    FFTT           TFTF   FTFT

        \       \           /      /
           \      \       /     /
              \     \   /    /

                      F

As I have  noted before, it is the two "projection
connectives" and their negations that are invariant
under DeMorgan conjugation.  Since people are
unaccustomed to thinking about DeMorgan conjugation
in this way, I will reproduce what I mean by this
from a previous post:

     A  B | A   L   B       pLq <-> -((-p)L(-q))
    ——|———–
     T  T |     T            T   T  T  FT F FT
     T  F |     T            T   T  T  FT F TF
     F  T |     F            F   T  F  TF T FT
     F  F |     F            F   T  F  TF T TF

     A  B | A   R   B       pRq <-> -((-p)R(-q))
    ——|———–
     T  T |     T            T   T  T  FT F FT
     T  F |     F            F   T  T  FT T TF
     F  T |     T            T   T  F  TF F FT
     F  F |     F            F   T  F  TF T TF

     A  B | A NOT-L B       pNOT-Lq <-> -((-p)NOT-L(-q))
    ——|———–
     T  T |     F              F     T  F  FT   T   FT
     T  F |     F              F     T  F  FT   T   TF
     F  T |     T              T     T  T  TF   F   FT
     F  F |     T              T     T  T  TF   F   FT

     A  B | A NOT-R B       pNOT-Rq <-> -((-p)NOT-R(-q))
    ——|———–
     T  T |     F              F     T  F  FT   T   FT
     T  F |     T              T     T  T  FT   F   TF
     F  T |     F              F     T  F  TF   T   FT
     F  F |     T              T     T  T  TF   F   FT

   The isomorphism of the free orthormodular
lattice on two generators with MO2 x 2^4 is
problematic.  Because the sixteen elements of
the lattice 2^4 can be put in correspondence
with the basic Boolean functions, the product
MO2 x 2^4 seems to be express structural
relationships one sees in the columns of a
truth table–or, perhaps better, the invariance
of the four Boolean functions above.

   Anyone who has seen my posts before knows I
could go on.  But, there is no need.  I have
no desire for this post to be flamed, and, I
am already aware that what I have done to make
sense of this coincidence is intractable to
others.

   This is mostly just a clarification for the more
reasonable people on the newsgroups who were
probably bewildered by my posts.  The village
idiots on these newsgroups who love to flame
never had an original question in their life–or.
for that matter, had to answer their own questions
because the answers could not be found in
a book.