Interpretation Definition and 834 Threads

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. P

    Geometric interpretation of a given Alexandrov compactification

    What is the Alexandrov compactification of the following set and give the geometric interpretation of it: [(x,y): x^2-y^2>=1, x>0] that is, the right part of the hyperbola along with the point in it. This is a question from my todays exam in topology. I wrote that the given set is...
  2. R

    Questions re Cramer's Transactional Interpretation?

    Hello Forum Users, I am currently writing up a general discussion of John Cramer's Transactional Interpretation (TI) , intended to address questions, confusions, or concerns about TI. I have noticed occasional comments here and there regarding TI on this forum, both pro and con...
  3. S

    How Do IR Spectra Differ Between 4-Methylcyclohexene and 4-Methylcyclohexanol?

    1. Compare and interpret the infared spectra of 4-methylcyclohexene and 4-methylcyclohexanol. 2. Identify the C-H out-of-plane bending vibrations in the infared spectrum of 4-methylcyclohexene. What structural information can be obtained from these bands?
  4. N

    Sigma Interpretation: f(x)=X^2, j=1, n=4

    I just need a quick clarification on how to read this function f(x) = sigma of X^2, starting at j=1, and n so does that mean that f(3) would equal to 36, if n=4?
  5. D

    Help with geometric interpretation of 1-form

    I am currently reading the special relativity section in Goldstein's Classical, and there is an optional section on 1-Forms and tensors. However i am having a lot of trouble understanding the geometric interpretation of a 1-form. Here is what I do understand: You take a regular vector...
  6. K

    Interpretation of the randomness in statistical mechanics?

    One postulate of sta mech is all accessible microstates are equally probable in thermal equilibrium, while according to classical mechanics this postulate is not true. But the postulate is still applicable in the real world. I remember that I read one interpretation before: 1. any particle in a...
  7. G

    Meaning of velocity in Bohm interpretation

    In the Bohm interpretation particles have a definite position and also a velocity? How is this velocity related to velocities and momenta in the Copenhagen interpretation of QM?
  8. S

    How Do You Interpret the Integral \int_0^a dxf(x) in Calculus?

    Homework Statement I recently came across a simple type of integral that I did not know how to evaluate. Generally speaking how would one interpet \int_0^a dxf(x)? Homework Equations The Attempt at a Solution At a glance, I thought to integrate with respect to 1, but then noticed...
  9. S

    Relational Quantum Mechanics Interpretation

    In Young's double slit experiment, any act of observation to determine which slit the particle passes through destroys the interference pattern. Whenever I asked my physics professors why this was, their response was always either "Your question is physically meaningless", or, "There is no...
  10. F

    On the many-worlds interpretation

    I've read mostly non-mathematical accounts of this interpretation so forgive me if I'm not making any sense. I have the impression that a many worlds theory is an application of our laws of the universe, to the multiverse. To make a simple analogy, it would be conceivable (?) that in one...
  11. J

    Interpretation of box-percentile plots

    Hi everybody, anybody can provide me with some guidelines to interpret box-percentile plots? I am so confused :(. thank you! jo
  12. J

    A little help with Poynting's theorem interpretation?

    hi, I am doing some exam preparation and I am having trouble understanding what Poynting's theorem is all about. After much messing around with Maxwell's equations, it turns out that \frac{\partial U}{\partial t} + \nabla \cdot \vec{S} + \vec{E} \cdot \vec{J} = 0 where the Poynting...
  13. R

    Stairstep Interpretation of Catalan Numbers

    How does one go about proving that C_n (Catalan number) is the number of ways to tile a stairstep shape of height n with n rectangles? :rolleyes:
  14. H

    Physical interpretation of unitary transformation

    what actually happens physically ...when we make transpose of a matrix...and in unitary transformation we transpose the matrix and take the conjugate...physically what type of change happens in it.
  15. L

    Consciousness and the Interpretation of Quantum Mechanics

    Dear participants and visitors of a forum ! By the present moment, very many publications on a subject "Consciousness and the Interpretation of Quantum Mechanics" have collected. It, first of all, concerns to "Many-worlds interpretation" and "Bohmian interpretation" ...
  16. T

    Root mean square interpretation

    i am working in control theory problem where at the end i get error signals and i am trying to classify this signals, i choosed easy implementation because of limitaion of microcontroller which i will program later. the easiiest way was to calculate the Root mean square of the random signals...
  17. Schrodinger's Dog

    Which interpretation is your favourite?

  18. Fredrik

    Does anyone actually use the term ensemble interpretation ?

    Does anyone actually use the term "ensemble interpretation"? People have been asking questions about the "ensemble interpretation" here lately. It's mentioned on the Wikipedia page "interpretations of quantum mechanics" and has its own page. But is that term actually used in books and articles...
  19. rrw4rusty

    Questions on Many Worlds Interpretation

    Hi! I've seen videos depicting the ‘Many Worlds Interpretation’ of quantum physics which show T-Rex stomping through your living room because the K2 Event didn’t take place in that parallel universe, you know the hype you see on the MWI. While probably, no one ‘really’ thinks this is...
  20. P

    Double slit interpretation - what is the mainstream view?

    Can someone summarise what is the currently accepted interpretation of how measurement affects the interference pattern in a double slit experiment? (Answers which say things like 'the electron knows if it is being observed' are not acceptable - :-) ) To quote from the PF rules, I'm looking for...
  21. B

    Physical interpretation of Lorentz invariant fermion field product?

    Hey all! Just a very short question: May I interpret the Lorenz invariant quantity \bar\psi\psi as being the probability density of a fermion field? Thanks! Blue2script
  22. D

    Geometric Interpretation for Virtual Velocity

    Hello, I am having hard time giving a geometric interpretation for the virtual velocity in classical mechanics, defined as: \delta \dot{x} = \frac{d}{dt} \delta x where \delta is the virtual differential operator, and \delta \dot{x} denotes the virtual velocity of x. I think having a...
  23. S

    Can someone elaborate on the ensemble interpretation for me?

    My understanding of this interpretation is that (in the context of the electron double slit experiment) the experiment is one particular outcome of an ensemble of equally prepared experiments. This explains the statistical nature of QM. But how does this explain the interference pattern...
  24. G

    Everett Interpretation in English; correct or flawed?

    I came across this document http://www.hedweb.com/manworld.htm#faq containing a plain english explanation of the Everett interpretation. While it is clear that the author is very much in favor of this interpretation and has objections to others, is there any thing here that is fundamentally...
  25. G

    What Is the Stochastic Interpretation of Quantum Mechanics?

    Would anyone have any resources on the stochastic interpretation of quantum mechanics? It appears to be a relatively new interpretation, proposed this year by Roumen Teskov, based on John Wheeler's "quantum foam." That's really the extent of the information I have, and I'm curious to find...
  26. M

    Photon energy threshold for γ+p→p+π, question *interpretation*

    Homework Statement Calculate the photon energy threshold for the reaction γ + p → p + π. Assume that the initial state proton is stationary. <thats really it> Homework Equations < unknown, but suspects include: standard special relativity equations > -- other useful relations: proton rest...
  27. J

    How to Prove Points in an Open Interval are of a Certain Form?

    Homework Statement Prove the points of the open interval (a,b) are those of the form a + t(b-a) for 0 < t < 1. Homework Equations The Attempt at a Solution I'm interpreting this as asking me to prove that if x is in (a,b), then x can be written as a + t(b-a) for some 0 < t <...
  28. O

    Interpretation of random variable

    Homework Statement The probability mass function of a random variable X is: P(X=k) = (r+k-1 C r-1)pr(1-p)k Give an interpretation of X. Homework Equations The Attempt at a Solution The PMF looks like the setup for a binomial random variable. The first combination looks like you...
  29. J

    Proving b = a^{-1} = a^2 = a + 1 in Field F_4 with 1 + 1 = 0

    Homework Statement Let F_4 = {0,1,a,b} be a field containing four elements. Assume that 1 + 1 = 0. Prove that b = a^{-1} = a^2 = a + 1 . Homework Equations The Attempt at a Solution Do I assume that 0, 1, a, and b are al distinct elements? If so, then I can prove the question.
  30. S

    Is this interpretation of 2nd law of Thermodynamics correct?

    Suppose A box represents the universe. It also has a battery and a propellor inside it. The propellor is supposed to increase the temperature of the whole universe including itself and the battery. If this hypothetical universe is initially at 25 degrees C, then we incresed this temp to 27...
  31. Y

    Rotational Kinematics Problem Interpretation

    Homework Statement If you step on your car's brakes hard, the wheels stop turning (i.e., the wheels "lock") after 2.0 revolution. Part A. At the same constant acceleration, how many revolutions do the wheels make before stopping if your initial speed is twice as high? Homework...
  32. I

    Interpretation of Interaction in Boosts in QFT

    Question concerns the existence of the interaction in boost operator in the instant form of relativistic dynamics. (referring to "Relativistic quantum dynamics" after E.V.Stefanovich, http://arxiv.org/abs/physics/0504062) From the existence of interactions in boosts (e.g., in instant form...
  33. C

    Acceleration and velocity: Newtonian versus relativistic interpretation.

    In another thread a discussion arose about the interpretation of derivatives. For example acceleration is the time derivative of velocity. Obviously, in the strictly mathematical sense: in relativistic physics and classical physics alike acceleration is the time derivative of velocity...
  34. Q

    Questions about the de-Broglie Bohm interpretation

    These questions were originally asked to one of PF.com's member, but he wanted me to post it publically so more people could benefit from the answers: Also if anyone else got enough knowledge about this interpretation to answer these too, go ahead. #1 In dBB (deBroglieBohm), what does...
  35. Demystifier

    There is no Copenhagen interpretation of QM

    Many physicists say that they prefer the "Copenhagen" interpretation of QM, but it does not mean that all these physicists prefer the same (or even a very similar) interpretation. There are at least 4 very different interpretations that are sometimes referred to as "Copenhagen": 1. Shut up...
  36. V

    Is the Speed of Light Decreasing Due to a New Interpretation of Ether?

    Here I try to explain what I read somewhere- that the speed of light has decreased over the last couple of centuries. If it is reported that the speed of sound is decreasing in a solid, you may say thatdue to continued vibrations and deformations of the solid, its modulus of elasticity has...
  37. F

    Physical interpretation of circulation

    Can the circulation about some closed (rigid) path in a force field be interpreted as the work done by the force field on the path over an infinitesimal time?
  38. Д

    Geometrical interpretation of dot product (trying to prove)

    Hi! I am trying to find out where: cos\theta=\frac{a \cdot b}{|a||b|} came from. Here is mine geometrical interpretation of scalar projection: Now, (pr means projection) pr_{\overrightarrow{A}} \overrightarrow{B} = p\overrightarrow{B_0} and...
  39. T

    Popper/Lande interpretation of QM

    Karl Popper, the highly influential philosopher of science was unusual in that, as a philosopher, he had a large impact on science itself. He was actually listened to by physicists! He's best known, of course, for his falsifiability criterion for theories to be considered scientific, which has...
  40. A

    Relational Interpretation of QM

    I have started to read about Rovelli's Relational interpretation in Wikipedia. http://en.wikipedia.org/wiki/Relational_quantum_mechanics#All_systems_are_quantum_systems In the section labeled "All systems are Quantum Systems" in the article it says: In the above paragraph it is assumed...
  41. W

    Interpretation of Flamm Paraboloid

    In the Schwarzschild Metric, the curvature of space around the gravitating mass can be described by the Flamm Paraboloid: w(r) = 2 \sqrt{r_{s} (r - r_{s})} Unlike the Newtonian depiction of Gravitational Potential Wells (U = - G M / r) which decrease inwards, the Flamm Paraboloid increases...
  42. K

    MCNP output file interpretation

    I am running (a very basic) simulation of the proposed LIFE concept reactor at LLNL as part of my MSc thesis. What I hope to achieve is to calculate the fission energy gain from a fissile blanket surrounding a source of fusion neutrons (ie D-T pellet blasted by lasers) The problem summary...
  43. K

    Mass warping time, question/ interpretation

    Does mass warp time because there is no time contained within the mass itself? (making a gradient like hot flows to cold sort of thing, except its time flowing to mass) My assumption is that gravity is the measurement of the warping of time, and as you get closer to the mass, gravity is...
  44. Dale

    Resulting state vector interpretation

    If we have an operator A which operates on some state described by vector x the result is a new vector y A |x> = |y> My question is: is the new vector y considered to be a different state vector in the same vector space as x or is it considered to be a vector in an entirely different vector...
  45. Z

    Spectral interpretation of Primes

    the idea is is there a Linear operator L so L | \phi _n > =p_n |\phi_n > with p_n being the nth prime and L a linear operator , is it possible to have an spectral interpretation for prime numbers ?
  46. S

    Is this interpretation on Hubble's Law/Constant right ?

    Is this interpretation on "Hubble's Law/Constant" right ? I referred to this page http://en.wikipedia.org/wiki/Hubble's_law The hubbles constant 'H0' is anywhere between 72 to 78 kms per second per megaparsec. My doubts :- 1) Let us consider a rod (made of streatchable light weight...
  47. S

    The ensemble interpretation of QM

    The ensemble interpretation of QM essentially ignores the wave function collapse, and apparently decoherence as well, by stating that only the statistical distributions within ensembles of systems matter (each system being in just one state). My questions are: Does the preparation of...
  48. T

    Interpretation of symmetries in physics

    Hi all. I was wondering about symmetries in physics, and have a couple of questions. The symmetries of space/time translation and rotation are often explained in terms of doing an experiment e.g. 10m away instead of right here and getting the same result, as long as we are in the same...
  49. C

    Medical Why newly born baby weeps?(psychology interpretation)

    hi guys , I want to ask every intellectual persons , a question? A newly born baby which just got from mothers stomach,what is in its concept that makes it weep(please psychological interpretation)
  50. B

    Physical interpretation of charges and casimirs for SU(2) and SU(3)

    For SU(2) rotational invariance there is a clear interpretation of what all the generators mean. They correspond to operators whose eigenvalues are some observable. The noether charges correspond to the x,y and z components of angular momentum. The casimir is just the total angular momentum...
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