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. N

    B GR interpretation of a scenario

    Imagine three marbles A, B & C with each with 2 small lasers attached. All in the same rest frame, separated from each other by a light year, and forming an isosceles triangle (where AB and AC are the same length, and the centre of BC is a kilometre from A), and that the lasers of each pointed...
  2. G

    B Boltzmann factor interpretation

    Hi community, trying to get my head around the Boltzmann factor... e^(-E/kT) It states in a book I'm reading that this is linked to the probability of a particle moving from its current energy state to an energy state E above it? So if you were looking at an energy jump of 4kT that the...
  3. N

    I Problem of quantum tunneling and Many Worlds interpretation?

    On wikipedia it says that MWI doesn't explain quantum tunneling well. "A tunnelling particle would have more energy than what is actually measured in experiments." What do you guys think?
  4. N

    A Many worlds interpretation incompatible with quantum gravity

    On wikipedia, I found one of the objections to MWI. "We cannot be sure that the universe is a quantum multiverse until we have a theory of everything and, in particular, a successful theory of quantum gravity.[73] If the final theory of everything is non-linear with respect to wavefunctions then...
  5. C

    I Visual interpretation of Fundamental Theorem of Calculus

    Hi, this is a newbee question. Does the Fundamental Theorem of Calculus supply a visual (graphical) way of linking a function (F(x)) with its derivative (f(x))? That is, the two-dimensional area under a curve in [a,b] for f(x) is always equals to the one-dimensional distance F(b)-F(a)? If...
  6. L

    A Interpretation of Derivative of Metric = 0 in GR - Learning from Wald

    I am trying to learn GR, primarily from Wald. I understand that, given a metric, a unique covariant derivative is picked out which preserves inner products of vectors which are parallel transported. What I don't understand is the interpretation of the fact that, using this definition of the...
  7. V

    Physical interpretation of the "total potential energy"

    The principle of minimum total potential energy is frequently used in solid mechanics as an elegant way of deriving the equilibrium equations for an elastic body under conservative forces. This method states that out of all the possible displacement fields that fulfill the boundary conditions...
  8. Dopplershift

    I Schrodinger's Interpretation of the Wave Function?

    Schrodinger developed his famous wave equation which describes how the quantum state of a system changes over time. But, what was Schrodinger trying to initially prove with his equation?I assume that it has to do with Debrogile's hypothesis. I know from my classes that we use the Schrodinger...
  9. hsdrop

    Does the Copenhagen interpretation require consciousness for the same outcome?

    does it matter if a person or a computer looks at the result I guess I'm asking if something needs consciousness to have the same outcome in the case that I'm not making any sense please ask and I will try to seaplane in more detail and thank you for anyone that respons
  10. I

    Is anything possible in the many worlds interpretation?

    In the many worlds interpretation of Qm, is there one universe in which I am a horrible murderer, for example?
  11. G

    I Universe thermodynamic equilibrium & Transactional Interpretation

    Hello, for those who don't know me I'm layman with some knowledge at popular science level. Discussing with a friend we came to the following point and I would like to ask it here because we had doubts about our reasoning. Cramer's Transactional Interpretation proposes that, in a sense, a...
  12. S

    A Physical interpretation of Pauli-Lubanski pseudo-vector

    ##P^{\mu}## generates translations and extracts the four-momentum of a particle when it acts on the momentum eigenstate of a particle. ##J^{\mu\nu}## generates rotations and measures the spin angular momentum along the ##i##-direction of a particle when it acts on the ##i##-th direction spin...
  13. Mayan Fung

    Physical interpretation of Schrodinger equation

    Schrodinger Equation is the very first step when we start learning QM. However, I never learned about the physical meaning of it. I have read a number of articles and discussion online. Regarding the ones I understand, there are generally two points of view. 1. Fundamental physical laws are not...
  14. P

    A Did Einstein Disbelieve in General Relativity Geometry?

    I have read this paper http://www.sciencedirect.com/science/article/pii/S1355219813000695 that the author try to said that einstein not believe that gravity is not cause the space time curvature. I want to know that this is true or not. Because when I have read about general relativity I always...
  15. S

    Physical interpretation of free body force diagram

    Homework Statement Free body force diagram question, where I have selected the best answer but the diagram doesn't ring completely true (see diagram uploaded). I think mathematically the diagram is sufficient but it doesn't properly represent the situation. Do you agree? Homework EquationsThe...
  16. S

    A Physical interpretation of Mandelstam variables

    In ##2-2## scattering, the Mandelstam variables ##s##, ##t## and ##u## encode the energy, momentum, and angles of particles in a scattering process in a Lorentz-invariant fashion. ##s=(p_{1}+p_{2})^{2}=(p_{3}+p_{4})^{2}## ##t=(p_{1}-p_{3})^{2}=(p_{2}-p_{4})^{2}##...
  17. M

    FEA Results Interpretation for a Pin Support

    Greetings to all, I am doing FEA analysis of a jib crane. I am using Autodesk Inventor. The results show that the max Von Mises stress in the support pin is 773 MPa. This value exceeds the yield strength of the Carbon Steel. Does this mean that the Pin will fail under load ?
  18. wololo

    Is Person A a Knight or a Knave on the Island?

    Homework Statement A person can either be a knight (always tells the truth) or a knave (always tells a lie). On an island with three persons (A, B and C), A tells "If I am a knight, then at least one of us is a knave". Homework Equations Truth tables, logic rules. The Attempt at a Solution...
  19. A. Neumaier

    I Entangled particles in the thermal interpretation

    Ah. It was skepticism about publishing, not about giving a comprehensive account! Yes, I am preparing a book on quantum mechanics, which will contain an account of the thermal interpretation - but primarily to macroscopic, nonrelativistic reality, where it is obvious that it gives the correct...
  20. A

    I What is physicial interpretation of deviatoric strain rate

    How these properties are related to velocity fluid. The https://postimg.org/image/674a6sw4t/ https://postimg.org/image/674a6sw4t/ figure shows an area of Earth's mantle where upwelling of hot semi-liquid mantle is occurring in middle and then two downwelling currents on two sides (forming...
  21. J

    I What's the geometric interpretation of the trace of a matrix

    Hello, I was just wondering if there is a geometric interpretation of the trace in the same way that the determinant is the volume of the vectors that make up a parallelepiped. Thanks!
  22. R

    Hi, how to find the magnitude of a rotating vector?

    i get stuck in how to find the magnitude of rotating vector . why say that |dA/dt|=A(dθ/dt) but who we can derive it or interpret this fact
  23. R

    Interpretation of ODE Question

    Hi Could someone please help me to understand what questions a) and b) here are asking for?
  24. martinbandung

    I Pca and eigenvalue interpretation

    hello, i have a reasearch to analyse the movement of human walking using pca. i did it like this 1. i dibide the body into some part (thigh, foot, hand, etc) 2. i film it so i can track the x position of the parts 3. i get the x to t graph for every part 4. i make a matrix which column is the...
  25. F

    A Physical interpretation of correlator

    Consider the 2-point correlator of a real scalar field ##\hat{\phi}(t,\mathbf{x})##, $$\langle\hat{\phi}(t,\mathbf{x})\hat{\phi}(t,\mathbf{y})\rangle$$ How does one interpret this quantity physically? Is it quantifying the probability amplitude for a particle to be created at space-time point...
  26. G

    I Is the Transactional Interpretation deterministic?

    Hi, This is a question about the Transactional Interpretation of quantum physics proposed by John G. Cramer. As you surely know this interpretation proposes that interactions only happen when the emitter has some sort of 'confirmation of receipt' by an absorber. In a sketch way we might say...
  27. I

    I Interpretation of direct product of Hilbert spaces

    Dear all, I know how to interpret a vector, inner product etcetera in one Hilbert space. However, I can not get my head around how the direct product of two (or more) Hilbert spaces can be interpreted. For instance, the Hilbert space ##W## of a larger system is spanned by the direct product of...
  28. Srv44

    Dye doped spectroscopy interpretation

    Hello all, I am working on a dye doping project and got a photospectrometry result as show in a picture for my thin film. Can anyone please help me interpret the physical meaning of the graph below? Thanks!
  29. Victor Alencar

    A Geometrical interpretation of Ricci and Riemann tensors?

    I do not get the conceptual difference between Riemann and Ricci tensors. It's obvious for me that Riemann have more information that Ricci, but what information? The Riemann tensor contains all the informations about your space. Riemann tensor appears when you compare the change of the sabe...
  30. E

    I Fermi distribution interpretation

    Hello! Let E_1, E_2, \ldots, E_n be n allowed energy levels for a system of electrons. This system can be described by the Fermi-Dirac distribution f(E). Each of those levels can be occupied by two electrons if they have opposite spins. Suppose that E_1, E_2, \ldots, E_n are such that...
  31. entropy1

    Is there any interpretation covering this?

    I was wondering if it is possible that not only the past influences (or causes) the future, but also the converse, that the future influences the past. I imagine waves of probability propagating from the future into the past as well as from the past into the future, thereby influencing each...
  32. entropy1

    Interpretation of entanglement

    Once I heard a fellow-layman on QM say that he imagined two entangled particles never been separated in the conceptual sense, that is: the two particles are conceptually 'one', only they connect two parts of spacetime, and are so able to exhibit correlations over spacetime with respect to the...
  33. J

    I Questions on exact details of the many worlds interpretation

    I have hard time thinking the many worlds interpretation is correct. I also find its description imprecise. Here are some questions I would like someone to answer about the interpretation. 1. When a wave form photon hits a screen and become a particle form photon, this event splits the world...
  34. L

    Age table interpretation problem

    Homework Statement calculate for men and women each, the probability at which... the lifespan left, of a forty-year-old is 20-40 years. Homework Equations 3. The Attempt at a Solution [/B] That's a mouthful of a sentence. It looks like if the lifespan is exactly 20 years... there could be...
  35. G

    A FFT phase result interpretation?

    I have a complex signal eg: cos(wt + phase1) + i*cos(wt + phase2) the frequency of both the waves is same. When i have a look at the phase spectrum of the above signal, i am not able to interpret the phase values. They are making no sense. I tried to determine phase shift for real signals and...
  36. Seeker3

    DSC Polymer Characterisation interpretation help

    Hi respected peers, Firstly, i must apologise in advance for any error i may make within this forum, I'm a new member here. The question i wish to ask is with regards to observing a glass transition and crystallisation peak upon cooling, however without observing the obvious melt of a polymer...
  37. F

    I Quantum superposition and its physical interpretation

    I understand that if we have a quantum mechanical system, then its state at some given time ##t## is fully described by a state vector ##\lvert\psi(t)\rangle## in a corresponding Hilbert space. This state vector containing all possible information about the distributions (of all possible values)...
  38. M

    A Interpretation of [itex]\partial_\nu T^{\mu \nu}[/itex]

    I am working on Sean Carroll's problem 1.8. If \partial_\nu T^{\mu \nu}=Q^\mu, what physically does the spatial vector Q^i represent? Use the dust energy momentum tensor to make your case. The dust energy momentum tensor is T^{\mu \nu}= \rho U^\mu U^\nu, where U is the four-velocity and \rho...
  39. D

    A Interpretation of the EM tensor as a rotation matrix

    In special relativity, the electromagnetic field is represented by the tensor $$F^{\mu\nu} = \begin{pmatrix}0 & -E_{x} & -E_{y} & -E_{z}\\ E_{x} & 0 & -B_{z} & B_{y}\\ E_{y} & B_{z} & 0 & -B_{x}\\ E_{z} & -B_{y} & B_{x} & 0 \end{pmatrix}$$ which is an anti-symmetric matrix. Recalling the...
  40. michael879

    A Hidden Measurements Interpretation

    I've been reading up on HMI, and the claims its proponents make are pretty impressive. I'm struggling to understand some details though, so I'm hoping someone here is more familiar with it. In http://www.vub.ac.be/CLEA/aerts/publications/1998Berlin.pdf, the authors describe a "macroscopic...
  41. ShayanJ

    A Measurement problem in the Ensemble interpretation

    The ensemble interpretation asserts that QM is only applicable to an ensemble of similarly prepared systems and has nothing to say about an individual system and in this way, it seems, it can prevent the need for introducing the concept of wave-function collapse and so it may seem that there is...
  42. ChrisVer

    A Signal strength parameter (interpretation)

    How can in general the signal strength parameter ##\mu## be interpreted? I am talking for the parameter defined in Eq.1 here and plots like the Fig.1 here: http://arxiv.org/abs/1507.04548 It says that it's the ratio of the i->H->f of the observed over what's expected by the SM... is the last...
  43. R

    Interpretation of a signal (sound) spectrum - hydrophones

    ooops so obvious sorry! please delete
  44. entropy1

    Interpretation of polarisation experiment

    Consider a fully entangled pair of polarized photons, A and B, fired at two detectors with polarisation filters in front of them. I have to get a little philosophical to understand the way the interpretations of this experiment play out. My knowledge is still very basic but I'm working on it...
  45. A. Neumaier

    B Is classical mechanics philosophically sound?

    They are subjective even in the classical, nonrelativistic mechanics of a pendulum, since the notions appear when you try to relate the theory to a real pendulum. In classical, nonrelativistic mechanics, the interpretation of the words ''observation'', ''experiment'' and ''measurement'' needed...
  46. Einstein's Cat

    Can Quantum Physics Confirm the Correct Interpretation of GHZ and GRW?

    Could physics ever be able to confirm that a certain interpretation of quantum mechanics is correct or is the matter entirely philosophical and thus doomed to the depths of subjectivity?
  47. Markus Hanke

    I Geometric Interpretation of Einstein Tensor

    Is there a simple geometric interpretation of the Einstein tensor ? I know about its algebraic definitions ( i.e. via contraction of Riemann's double dual, as a combination of Ricci tensor and Ricci scalar etc etc ), but I am finding it hard to actually understand it geometrically...
  48. FallArk

    C/C++ What is the Functionality of this C++ Code?

    The way the classes and functions are named confuses me. What is the program trying to do? class Y { long y; public: Y() { y = 4; } long get(long yy) { long ret = yy * y; y = yy; return ret; } }; class X { long x; Y y; public: X() { x = 7; } void Xx(long xx) { x += y.get(xx); } int get() {...
  49. S

    Interpretation of kinetic energy

    While studying energy on Sears & Zemansky's University Physics, I came up with a doubt on the meaning of kinetic energy. The book gives two possible physical interpretations of this quantity. I'm okay with the first meaning of KE but I don't understand completely the second one. I don't...
  50. J

    The Higgs Mass and the Many worlds interpretation

    I have a question about the Many worlds interpretation. Does the observed mass of the Higgs boson suggest that the many worlds interpretation is incorrect, as the mass falls smack in the middle of the predicted values of both supersymmetry and multiverse interpretations of the standard model of...
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