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. H

    Interpretation of a wave function collapse

    Suppose the system is in a state of superposition of two determinate states (of an observable) and has equal probability of getting each determinate state, when observed. An observation forces the collapse of the wave function to either one of the determinate state (say, states A and B). Since...
  2. kostoglotov

    Insight into determinants and certain line integrals

    I just did this following exercise in my text If C is the line segment connecting the point (x_1,y_1) to (x_2,y_2), show that \int_C xdy - ydx = x_1y_2 - x_2y_1 I did, and I also noticed that if we put those points into a matrix with the first column (x_1,y_1) and the second column (x_2,y_2)...
  3. Feeble Wonk

    Particles in dBB Interpretation

    I was recently reading a PF thread that was questioning the meaning of zero dimensional fundamental "point" particles and virtual particles, and it raised a question in my mind. It's been my impression from previous discussions that most physicists don't really think of fundamental particles...
  4. SpiderET

    Interpretation of double bending / deflection

    Probably the most famous experiment confirming GR is bending of light by Sun. Here are the best explanations to this topic what I have found: http://www.mathpages.com/rr/s8-09/8-09.htm http://mathpages.com/rr/s6-03/6-03.htm Especially the graph of GR double bending vs Newtonian bending is...
  5. S

    Interpretation of the Heisenberg picture in QM

    I was always a bit puzzled by the Heisenberg picture (not mathematically, I'm fine with that, but conceptually) - if a "state" describes a system, how can it not be time-dependent, if the system changes? I just found an alternative way of looking at it which seems to make sense to me, but I'm...
  6. Feeble Wonk

    QP Interpretation Hierarchy and Subclasses

    As an interested reader of the work done by you professional physicists, it sometimes seems a little murky to me as to where some subcategories of QP interpretation schools of thought belong in the theoretical hierarchy. I'm curious if it's possible to definitively delineate these theoretical...
  7. L

    Interpretation of a before $\gamma^{5}$ in J$_{\alpha}$

    Could you explain what's the interpretation of a before \gamma^{5} in this current: J_{\alpha}=\bar{\psi_{e}}\gamma^{\alpha}\left(1-a\gamma^{5}\right)\psi_{\nu_{e}} +\bar{\psi_{\mu}}\gamma^{\alpha}\left(1-a\gamma^{5}\right)\psi_{\nu_{\mu}}? And will this factor complicate calculations of decay...
  8. R

    Interpretation of Bremsstrahlung diagram

    This is what we have been given in class: I'm a little confused as the electron seems to emit two gamma rays? I understand that the process can't occur if there isn't interaction with a nucleus due to conservation of momentum. Please could someone confirm that the top gamma is the initial...
  9. D

    Interpretation of the Michelson-Morley experiment

    Dear Sirs, I have a question regarding the interpretation of the Michelson-Morley experiment. As I understand it, the special relativity theory implies that, say, if I were to watch another person in a n inertial reference frame (say a vehicle) moving relative to me send a light beam towards...
  10. S

    Intuitive interpretation of some vector-dif-calc identities

    Dear All, I am studying electrodynamics and I am trying hard to clearly understand each and every formula. By "understand" I mean that I can "truly see its meaning in front of my eyes". Generally, I am not satisfied only by being able to prove or derive certain formula algebraically; I want to...
  11. C

    Interpretation of Accelerometer Measurements

    I have performed an impact test on different football shin guards to assess their performance. I am however confused with the readings measured by the accelerometer I have used. The sensor was attached to a striking mass of 4.3 kg which was dropped at different heights. The graph I have attached...
  12. beer

    Graphical interpretation of a double integral?

    Hello, I was helping my friend prepare for a calculus exam today - more or less acting as a tutor. He had the following question on his exam review: ∫∫R y2 dA Where R is bounded by the lines x = 2, y = 2x + 4, y = -x - 2I explained to him that R is a triangle formed by all three of those...
  13. MexChemE

    Energy balance -- Physical interpretation of Q

    Hello PF! I have a simple question on energy balances. Suppose you have an isothermal reactor where you want to have an exothermic reaction happening at 450 °C. The simplified energy balance for the reactor is Q = ΔH. Supposing ΔH = -150 kcal, then Q = -150 kcal. Does this mean that, a) in order...
  14. A

    Intuitive Interpretation of Rest Energy

    Hi there, I'm trying to get a better intuitive handle on the concept of rest mass and rest energy - the energy term associated with rest mass. Introductory Physics textbooks often give statements along the lines of "mass is a form of energy" or "mass can be converted to energy" to explain...
  15. Rodrigo Cesar

    Many Worlds Interpretation and act of measuring

    "We can’t make a measurement without influencing what we measure. before we look, there are only probabilities. When we open the box, they give way to a single actuality" It would be more like this, all the time, Until we look...
  16. M

    Scaling Interpretation for 2-D Continuity PDE: What Does UH/L Represent?

    Hi PF! I'm doing some scaling over a PDE and I understand the math side of things but I do not understand the physical side of what we are finding. For example, suppose we have some PDE, say 2-D continuity for it's simplicity ##u_x + v_y = 0##. Let ##L## be the length of a side of a flowing...
  17. M

    Interpretation of differentiation results

    Homework Statement Please see the attached file. I am trying to understand the sensitivity of two related variables - Y and K - to an independent variable M. a. Is my differentiation of equation 2 correct? b. I can see that, based on eq. 4, K is more senstive to M than Y is, however I am not...
  18. nomadreid

    What is the correct interpretation of a qubit with v= 0.6|0> + 0.8|1>?

    This is undoubtedly one of the more basic (not to say stupid) questions ever to appear in this rubric. But here goes: Suppose you have v= 0.6|0> + 0.8|1>. This means that there is 36% chance of measuring |0> and 64% chance of measuring |1>. Otherwise put, given a million particles in this...
  19. F

    Reflectance or reflectivity spectrum interpretation

    Hello forum, The reflectance spectrum has % on the vertical axis and wavelength on the horizontal axis. A red object is red because it reflects all the red light and absorbs all the other wavelengths of the white incident light. If the read object was ideal, would its reflectance spectrum be...
  20. S

    Time dilation in the field interpretation of GR

    IIUC, there are two different interpretations of GR - either as curvature of space time (as in Misner Thorne Wheeler) or as a (spin-2)field that influences all matter (as in the books by Weinberg or in the Feynman Lectures on Gravitation) and that leads to the underlying Minkowski metric being...
  21. P

    Binney's interpretation of Violation of Bell Inequalities

    Although he is primarily an astrophysicist, Dirac medal-winning Oxford Professor James Binney has taught a Quantum Physics course to second-year students at the university for years. A series of 27 of his lectures for the course is featured on the university's official website. Binney's take on...
  22. Q

    Evidence for retrocausal interpretation of QM?

    This article about a recent experiment was just published the other day: http://phys.org/news/2015-02-hindsight-foresight-accurately-quantum-state.html I can't help but think that this is at least weak evidence in favour of the retrocausal interpretation. Of course other interpretations aren't...
  23. Tyrannosaurus_

    Is my interpretation good? simple Kinetic E problem

    Homework Statement A cat is chasing a mouse in a straight line. The cat's mass, mc, = 5.0kg. The mouse's mass, mm, is 0.035kg. Problem 1. If the kinetic energy of the cat is 100 times the kinetic energy of the mouse can the cat catch the mouse? Problem 2. If the cat and the mouse have the...
  24. Shackleford

    What is geometric interpretation of this equality?

    Homework Statement Prove that for any a, b ∈ ℂ, |a - b|2 + |a + b|2 = 2(|a|2 + |b|2). Homework Equations |a|2 = aa* (a - b)* = (a* - b*) (a + b)* = (a* + b*) * = complex conjugate The Attempt at a Solution I've already shown that the relation is true. I'm not quite sure what the...
  25. L

    Interpretation of Relativity of Simultaneity

    If relative simultaneity implies that one event that could be already measured w.r.t. one reference frame not yet measured w.r.t. another reference frame: then could one find an reference frame at which none of the events were measured? If such reference frame exists, could one observe the...
  26. A

    Physical interpretation of Neumann-Dirichlet conditions

    I am working on a PDE problem like this: Consider the wave equation with homogeneous Neumann-Dirichlet boundary conditions: ##\begin{align} u_{tt} &= c^2U_{xx}, &&0<x<\mathscr l, t > 0\\ u_x(0, t) &=u(\mathscr l, t) = 0, &&t > 0\\ u(x, 0) &=f(x), &&0<x< \mathscr l\\ u_t(x, 0) &=g(x), &&0<x<...
  27. P

    Are observables like position emergent properties?

    Title basically says it all. I'm a physics undergrad trying to wrap my head around quantum physics, and I was hoping people here could help. My question comes from something in one of my textbooks. It tries to explain particle-wave duality through a piece of string, which I'll quickly go over as...
  28. C

    Mutual inductance interpretation

    How to explain mutual inductance with the image I attached? There are two conducting frames, one has a source of DC and a variable resistor, the other just a galvanometer. What I should conclude from this picture that the flux is F1=alpha*I and F2=c*F1, and Ein=-M*dI/dt. How? Is the current I...
  29. D

    Interpreting E=hf: Particle, Wave & Planck's Constant

    I know what the letters mean, E = Energy of the photon, h = Planck's constant, f = frequency of the photon. But what does it mean for a particle to have a frequency, something that I'd associate with a wave. And what can you think Planck's constant is representing? Any replies would be much...
  30. D

    Fizeau's Experiment interpretation

    Hi all,In Einstein's book, "Relativity: The Special and General Theory", he uses the Fizeau experiment to show how the Lorentz Transform correctly predicts the addition of velocities. I have some difficulty understanding the interpretation of the results, however. Suppose that liquid M is in...
  31. C

    Penrose Diagram for the Kerr Black Hole

    Hey Guys, so i was reading Hawking&Ellis a bit and still encounter always problems with the Penrose-Diagrams. Looking at the Penrose-Diagram for the rotating Kerr-Black hole (just one illustrating picture at the end) i come up the following question: Why are there TWO regions III and III ? In...
  32. N

    Question about copenhagen interpretation

    Does the Copenhagen interpretation allow for particles(electrons) to be in more than once place at the same time. I am not talking about quantum superposition here. I'm asking if it allows for electrons to be in many places at once like the many worlds interpretation does.
  33. N

    Physical interpretation of divergence

    I'm trying to figure out what the physical meaning of divergence is for a vector field. My textbook offered the following example: if v = <u, v, w> represents the velocity field of a fluid flow, then div(v) evaluated at P = (x, y, z) represents the net rate of the change of mass of the fluid...
  34. M

    Many World Interpretation and Personal Choice

    So I've heard of the many worlds interpretation - something about any event that could have happened in the past, really did happen in some parallel universe. What I want to know is - how does this translate into personal choice? Like, say I am considering some decision. Tonight for dinner I...
  35. D

    Interpretation of the maximum value of a CDF

    I was watching a youtube video from MIT's open courseware series on probability. A scenario was proposed: Al is waiting for a bus. The probability that the bus arrives in x minutes is described by the random variable X, which is uniformly distributed on the interval [0,10] (in minutes). I...
  36. P

    Interpretation for continuity equation with complex potential.

    For the potential V(x)=V1(x)+iV2(x) the continuity equation yields: ∇⋅j=-∂ρ/∂t + 2*ρ*V2/ħ (unless I am mistaken). What is the interpretation of this result?
  37. S

    Physical interpretation of the stress energy momentum tensor

    First, I'd like to thank everyone that has helped me thus far in deriving the general relativistic tensors for the Morris-Thorne wormhole metric in an orthonormal basis. I have finally done it and grasped that concept. Now that I have done that, my new stress energy momentum tensor for this...
  38. J

    Living Opponents of the Copenhagen Interpretation

    I was wondering if anyone could tell me who are considered the leading opponents of the Copenhagen Interpretation who are alive today?--and even what would be the best way to get myself some formal physics education under such individuals? I would love to learn more about physics, although I...
  39. Mogarrr

    Contingency Table Interpretation

    Homework Statement 10.24 Is there any relationship between the type of treatment and the response? What form does the relationship take? Here's that data (column variables are responses): \newcommand\T{\Rule{0pt}{1em}{.3em}} \begin{array}{|c|c|c|c|c|} \hline Treatment & +Smear &...
  40. B

    Linear Momentum Algebraic interpretation

    Homework Statement A light object and a heavy object have the same kinetic energy. Which has more momentum? Homework Equations I am trying to prove this through algebra. I don't understand how to show this any help? The Attempt at a Solution 1/2m1v1^2 = 1/2m2v2^2 when m1 > m2 v1 = v2...
  41. D

    Physics interpretation of integrals of differential forms

    Be a vector field \vec{F}=(f_1,f_2,f_3) and \omega^k_{\vec{F}} the k-form associated with it , i know if i do \int \omega^1_{\vec{F}} is the same of a line integral and \int \omega^2_{\vec{F}} i obtain the same result of \int \int_S \vec{F}\cdot d\vec{S}, which is the flux of a vector field in a...
  42. T

    Results from TLE & SGP4 propagation - don't seem right & with interpretation

    Greetings all ! I have this problem with SGP4 propagation, that I hope someone can help me out with. I acquired a TLE of the ISS from internet and used the C++ SGP4 propagator to compute future position and velocity vectors of the Station. I am unsure about some aspects of results though and...
  43. S

    Interpretation of chromatogram

    1. In my polychemistry laboratory , the task was to determine the Number Average Molecular Weight and the Weight Average Molecular weight of two samples , one a polystyrene sample prepared by radical polymerization , and the other a polystyrene-block-isoprene polymer prepared by anionic...
  44. bhobba

    What is De-Broglie's interpretation and how does it relate to DBB theory?

    This thread is in response to another thread where the issue of what De-Broglie's interpretation says came up. For reference here is a paper that details it: http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf It was posted that theory contains a singularity at the particle. But, as the...
  45. G

    Physical interpretation of Force=power/velocity

    I understand the derivation of the equation Force=power/velocity, but I'm not sure I quite understand the physical interpretation of this. If you had a constant force acting on a particle in a vacuum, then it would gain velocity and as it did so the power would have to go down for the force to...
  46. 1

    Enthelpy's physical interpretation

    Hi I'm new to this site, so I'm not sure where to post this question but chemistry seemed fitting. I'm current taking 2 thermo classes, engineering and chemistry, and I'm having trouble with the concept of enthalpy. This is what I believe I understand. I Hope the following is all correct if...
  47. noir1993

    Books on Interpretations of Quantum Mechanics

    What are some good textbooks dealing with various Interpretations of Quantum Mechanics? I am not asking for popular science books. I have a book called 'Understanding Quantum Mechanics' by Ronald Omens on the consistent histories approach and I am looking for something like that.
  48. B

    Interpretation of induction in terms of symmetry transformations

    It just occurred to me that induction can be seen as a statement quite analogous to that of "a function whose derivative is 0 on an interval is constant on that interval". Suppose there is a property P about the natural numbers that we want to prove. Then let P: N -> {0, 1} be a function for...
  49. M

    Physical Interpretation of Coordinates in GR

    What is the relationship between the differentiable manifold that is space-time and the physical space around us? How does one relate the three seemingly Cartesian coordinates around us, those which we can measure out with a ruler, to the coordinates of the Lorentzian manifold? If i say, measure...
  50. Telemachus

    Continuum mechanics, physical interpretation of terms in balance eq.

    Hi there. I'm reading Gurtin's 'the mechanics and thermodynamics of continua', and working some exercises of his book. In the section 21: 'The first law: balance of energy', after the derivation of the balance equation, he uses an identity to rewrite the balance of energy. The balance of energy...
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