What is Interpretation: Definition and 831 Discussions

An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics.
The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways of presenting an interpretation. In these contexts an interpretation is a function that provides the extension of symbols and strings of symbols of an object language. For example, an interpretation function could take the predicate T (for "tall") and assign it the extension {a} (for "Abraham Lincoln"). Note that all our interpretation does is assign the extension {a} to the non-logical constant T, and does not make a claim about whether T is to stand for tall and 'a' for Abraham Lincoln. Nor does logical interpretation have anything to say about logical connectives like 'and', 'or' and 'not'. Though we may take these symbols to stand for certain things or concepts, this is not determined by the interpretation function.
An interpretation often (but not always) provides a way to determine the truth values of sentences in a language. If a given interpretation assigns the value True to a sentence or theory, the interpretation is called a model of that sentence or theory.

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  1. Doc Al

    Lectures on Interpretation of Quantum Mechanics

    I stumbled across this site quite by accident. I've never heard of the Perimeter Institute for Theoretical Physics, but they know how to party! Earlier this year they hosted a series of lectures on "Interpretation of Quantum Mechanics: Current Status and Future Directions". A top-notch...
  2. M

    Reinterpreting Wave-Particle Duality: A New Perspective on Electrons and Protons

    I don't know where I can post my question that will certainly appear to be a kind of heresy or the proof of my naivity. We all have learned the duality between wave and associated particle (or the way around). Some particles are carrying an electric charge. This means in reality that if the...
  3. wolram

    Exploring a New Interpretation of the Universe's Evolution

    http://arxiv.org/ftp/gr-qc/papers/0506/0506007.pdf Title: A New Interpretation about the Evolution of the Cosmos Authors: Fang-Pei Chen Comments: 16 pages Based on Lorentz and Levi-Civita's conservation laws, it can be shown that the energy of the matter field in the universe might...
  4. SpaceTiger

    Non-Cosmological Interpretation of Redshift

    In order to quell complaints from those members of the board who feel they are being discriminated against in my recent threads, I would like to directly address the issue of a non-cosmological interpretation of redshift. If you're a layman trying to learn about astronomy, I advise you to...
  5. R

    Interpretation Schrödinger's formulae

    Dear Friends, Does anybodi knows the meaning, or anything related to the term: \Psi \nabla \Psi^* or \Psi \nabla \Psi^* - \Psi^* \nabla \Psi Is the representation of something in the reality? Best reggards.
  6. S

    Confidence in traditional interpretation of Compton effect ?

    It appears more and more people are challenging the traditional interpretation of the Compton/Photoelectric Effects. Cramer back in 1986 used the Hanbury-Brown-Twiss effect to show that there is not a 1:1 correspondence between the emitted and dected quanta. You have to combine fractions of...
  7. T

    Many Worlds Interpretation justifies Selfishness

    I wasn't sure where to put this thread because it is about moral philosophy but depends on your understanding of quantum mechanics. I'll try to keep quantum mechanics out of it and just explain what results from the Many Worlds Interpretation (MWI) of what's happening in quantum mechanics (QM)...
  8. Reshma

    Geometrical interpretation of gradient

    I am not completely satisfied with Griffith's explanation for the geometrical interpretation of a gradient. Can someone elaborate on the geometrical meaning of the magnitude and the direction of a gradient?
  9. P

    Interpretation of Kubrick's 2001

    Being a Kubrick fan, I just had to pass this along knowing that someone here would appreciate this. Enjoy! :biggrin: (flash required) http://www.kubrick2001.com/2001.html
  10. Hans de Vries

    Aspect/Innsbruck Interpretation which respects SR locality

    -- -- EPR experiments seem to show a significantly higher correlation rate in the detection of separated photons which are in an entangled state. From the measured correlation we may or may not want to draw very fundamental conclusions. One such a far reaching conclusion would be that...
  11. B

    Many Worlds Interpretation of SR

    Special Relativity predicts that moving clocks run slow, mass and length are variable and simultaneity is relative. These are 'real' phenomena and leads me to think that the reality of one observer (the passing of time, all physical properties and space-time events) can be regarded as 'his...
  12. S

    Physical Interpretation ~Quantum Numbers

    :rofl: 1.Can anyone explain the physical interpretation of the Quantum numbers? 2. How they are vectors? 3.Are they known before solving the hydrogen atom problem? 4. Are there quantum numbers for protons and neutrons also?
  13. M

    Question about the Many Worlds Interpretation

    I was learning about the "Many Worlds" interpretation of QM, and it got me to thinking. In some ways, doesn't it contradict the laws of thermodynamics? I came up with the following thought experiment: Suppose that you had a gas containing nitrogen and oxygen in a homogeneous mixture, in a...
  14. M

    Physical interpretation of Feynman path integral

    so I herd that atpms are actuall blob like particles insted of hard crystal orb like things but are quarks the same way? are quarks like blobs too?
  15. B

    Interpretation of the uncertainty principle

    I have a fundamental question regarding the uncertainty principle (position and momentum). This principle states that it is impossible simultaneously to know both position and momentum with arbitrarily good precision - even in principle. Now, what does "know" mean? No one can prevent you from...
  16. E

    Help with a geometric interpretation of the following

    When I use d, I am referring to a partial derivative here. So where w(z)=u(x,y) + iv(x,y), and the derivative of w(z) exists, I have shown that (du/dx)(du/dy) + (dv/dx)(dv/dy) = 0 But I have to give a geometric interpretation of this which is somewhat confusing to me. I am not sure what...
  17. C

    Physical interpretation of Reluctance

    Hi, I would like to know what is the physical interpretation of magnetic reluctance. Also, I would like to know why should the magnetic flux in a magnetic circuit composed of different magnetic materials and subject to a magnetomotor force should be the same? Thank you.
  18. C

    Physical interpretation of Reluctance

    Hi, I would like to know what is the physical interpretation of magnetic reluctance. Also I would like to know why the magnetic flux in a magnetic circuit composed of different magnetic materials should be the same? Thank you.
  19. C

    Question About Many Worlds Interpretation

    After having researched on many different Websites the Many Worlds Interpretation of Quantum Mechanics, it seems to me as if there are two positions defended by physicists: Position 1: All the outcomes of a system actually happen in reality. That is, every time a choice is made all possible...
  20. humanino

    Interpretation of GR: Change in Einstein's Understanding

    Please take a look at http://xxx.lanl.gov/abs/physics/0204044 and post your comments/opinions.
  21. humanino

    Interpretation of GR: Einstein vs. Contemporary Physicists

    Please take a look at http://xxx.lanl.gov/abs/physics/0204044 and post your comments/opinions.
  22. G

    Is block time an inevitable consequence of relativity?

    Hi, I posted this question in Astronomy & Cosmology but by advice of some users I post it here as it has some philosophycal side too: It seems to me that block time is an unavoidable consequence of Relativity. The fact that events that still lie in our future must have already been observed...
  23. D

    Anyone know a logical expression of Copenhagen Interpretation

    hiya! Does anyone know of any logical expressions of the Copenhagen Interpretation. I've read about it, I can summarize it, but I've never really seen anything other than discussions of it in pop-science books. I'd really like to break it down if I could.
  24. G

    Exploring the Implications of Block Time in General Relativity

    It seems to me that block time is an unavoidable consequence of GR. The fact that events that still lie in our future must have already been observed by other (hypotetical) observers seems to leave no room for escaping the fact that (at least some of) the events in our future "have already...
  25. F

    Transactional Interpretation question

    In the transactional interpretation of quantum events, can the absorber and the emiter correspond to the same particle? Could an electron at time t1 for example, transfer a virtual photon to itself at time t2? If this is the case, could this provide an explanation of why an electron does not...
  26. Z

    Interpretation of integral as area?

    I know the definite integral of a function can be thought of as the area between the function and y=0 and between the lower and upper bounds of integration, so long as the function is positive in that region. However, I also know that: \int_{a}^{b} f(x) ~dx = -\int_{b}^{a} f(x) ~dx And...
  27. F

    Physical interpretation of Feynman path integral

    Hi What is the physical interpretation of Feynman path integral? Thanks :smile:
  28. U

    Correct Interpretation of Simple Expression ?

    (3p^2 q)^3 \div 9 p q^2 The above is a simple algebra expression. The question concerns the correct interpretation of the divisor in the above example. Strictly speaking I would have thought that only “9” is the divisor here and if you wanted the whole “9pq^2” as the divisor then you should...
  29. P

    Will u guys give some comments on the transactional interpretation?

    recently,i am having a report on the issue concerning the quantum interpretation,somehow,i choosed to read the transactional interpretation by prof cramer.i have complete about 60% of the studying,however,the deadline is coming closer(march 13th).as a result,the alternatives interpretations...
  30. B

    Interpretation of a picture

    http://www.frozenwinds.com/Portal/pic_display.asp?id=55 What do you think, when you see this picture ? What do you feel ? Sadness or do you want to sing a song about frogs :wink: ? Note: Hope I posted this in the right forum. Sry if it's the wrong one :smile:
  31. Kerrie

    Is interpretation of the bible meant to be symbolic?

    Just wondering if you all believe if the bible should be interpreted as symbolic or literal...
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