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. F

    Help with Shapiro-Wilk Test interpretation.

    Hi everyone, I need to make sure that I'm interpreting the Shapiro WIlk test correctly. This is how I'm doing the interpretations: Set 1 CI = 95% n = 15 Shapiro W = .92 p = .171 I think this set is distributed normally because p is the probability that it is not normal, so the...
  2. M

    Interpretation of spacetime diagrams.

    Hello all I have been at ease with spacetime diagrams of the usual sort where the y and z dimensions are suppressed until I came across this passage from the following book. Problems of Space and Time. A reader edited and with an introduction by J.J.C.Smart. Page 293 of the chapter...
  3. jambaugh

    Measurements and The Copenhagen Interpretation

    I started this thread to continue the following discussion from the thread: https://www.physicsforums.com/showthread.php?p=2203566#post2203566" But you and Weinberg are both making a mistake in assuming ontological status to both the collapse of the wave function and to entanglement...
  4. S

    Colloidal chemistry - interpretation of lecture notes

    How do you interpret this?
  5. U

    Postulates of many worlds interpretation of QM

    I am interested to see a clear enumeration of the postulates of this interpretation. There seem to be something fuzzy about how MWI describes what we call "reality". It might be a problem with the theory or, more probable, a misunderstanding of my part. Here is a list I found on Google...
  6. M

    Interpretation of the field operator

    Hi, I've just finished a 2 semester course on Quantum Mechanics and I am now eager to learn some Quantum Field Theory. I started to read some books on my own, but I have some problems understanding a few concepts. My main problem is this: In the Canonical Quantization procedure, we take...
  7. J

    Bohmian Interpretation: Equivalent or not to Standard QM

    (My previous thread on Bohm Interpretation quickly became 4 pages of mostly unrelated discussion. So I'm restarting here with more precise questions.) Okay, I've read some references on the Bohm Interpretation and I am still confused. As one paper mentioned, some extensions have stochastic...
  8. J

    Explaining Bohmian Mechanics: Wavefunction, Pilot Wave & Particles

    I do not understand why (apparrently) so many people on this board prefer the Bohm interpretation. To have more meaningful discussion, I tried to refresh my memory on the details and read some about it. Unfortunately, Bell's "unspeakable in quantum mechanics" book was not very helpful to me...
  9. K

    Can you point out physical interpretation of the complex permittivity?

    Hi, Can u point out physical interpretation of the complex permittivity? (ie. what can u expect from a material with \epsilon' = x and \epsilon'' = y ? what happens if y is very large etc. \epsilon = \epsilon' -j \epsilon'' thanks Krindik
  10. A

    Statistical Mechanical interpretation of work and heat

    According to my thermal physics book , from classical thermodynamics for a reversible change : dU = dQ - dW From stat mech , dU = \sum_i \epsilon _i dn_i + \sum_i n_i d \epsilon _i Then by drawing some arguments from quantum mechanics the writer relates the change in volume and...
  11. K

    Transformers Coursework- Interpretation?

    did an investigation on Transformers- something I thought would be a good idea. The aim was to find out how the amount of resistance put onto the transformer affects the power loss. By having a step-up transformer 300 turns on the primary and 600 turns on the secondary, then by connecting a...
  12. B

    Physical interpretation of V and A couplings

    Hi, I'm trying to remind myself of exactly what, physically, is the difference between V and A couplings. Now, a vector coupling is of the form \bar{\psi}\gamma^\mu\psi, and axial coupling of the form \bar{\psi}\gamma^\mu\gamma^5\psi. Thinking in terms of a chiral fermion expanded as: f...
  13. N

    Stress energy tensor interpretation

    I'd appreciate any explanations of the physical interpretations of Einstein's stress energy tensor...for general relativity...maybe a favorite explanatory/expository online source. Wikipedia is not very satisfying on this nor on the electromagnetic stress energy tensor. For example all involve...
  14. N

    Bohm Interpretation and Bell Theorem

    I recently read about the pilot wave theory and the Bohm interpretation, and I must say I really like the idea. The only of my confusions it leaves unchanged are those concerning the EPR paradox. The Bohm interpretation does not seem to answer the question of the dreaded spokhafte Fernwirkung...
  15. C

    Feynman diagram interpretation - 2 electrons in and 2 electrons out

    Homework Statement Hello :smile: The question is from "Advanced Physics" by Adams and Allday. It is from section 9 "The Physics of Particles", "Practice Exam Questions". It is question 11, part c. The level of this study is between school and University. Figure 9.5 represents a simple...
  16. A

    How to make another interpretation of curl ?

    How to make another interpretation of "curl"? Recently,I've tried hard to find the physical interpretation of "curl". But , most of what I found were the same ,that is,"fluid flow"! I'm now wondering whether there's another annotation so that I can learn more about vecor calculus...
  17. M

    Can We Identify Every Distribution with a Smooth Function in C_0^\infty?

    Since C_0^\infty (the space of smooth functions with compact support) is reflexive, we should, in theory, be able to identify every distribution (object that lives in the dual space C_0^{\infty '}) with a corresponding actual function in C_0^\infty. Is it all interesting or useful to do so...
  18. D

    Does the Many Worlds Interpretation Affect the Original Universe?

    According to the Many Worlds Interpretation the universe supposedly splits off into two realities when a quantum event has more than one possible outcome(Schrodinger's cat for example). One in which Schrodinger will find his cat dead, and another in which his cat lives. But what happens for the...
  19. C

    Interpretation of probability which includes complex number

    Hi everybody! I'm trying to find the probability at time t of finding the state pointing in the positive x-direction of an initial system which points in the negative x-direction. I'm not sure if the result is correct, but I get the probability is sin^2(iwt). Can this be understood as the...
  20. B

    Probability Interpretation of QM

    What is it that motivated Max Born to interpret psi in Schrodinger's equation as a probability amplitude? It seems a very strange thing to do - first of all what made him think that the elementary properties of particles should be of a statistical nature, and second why did he interpret it as a...
  21. O

    Simple intuitive/graphical interpretation of the Gauss-Seidel method

    Hi, I am currently studying the application of Gauss Seidel iterative method for solving systems of linear equations and am having trouble understanding the principle behind it. Can some1 provide any graphical or intuitive interpretation?? thank you
  22. G

    [Q]Different interpretation of same wavefucntion.

    Hi Is it possible that same wavefuction described by math can be interpreted to different aspect? For instance, Some wrote wave function as same as momentum eigenstate which is normalized But he seemed claim that it is not momentum eigenstate even mathmetical formula is same...
  23. B

    Probabilistic interpretation of wave function

    Homework Statement a particle moving in one dimension between rigid walls separated by a distance L has the wave function \Psi(x)=Asin(\Pix/L), since the particle must remain between the walls, what must be the value of A? Homework Equations The Attempt at a Solution Ok so I'm...
  24. S

    Coordinate Systems in Modern Interpretation of Relativity

    Hello, I've really been enjoying reading these forums the last couple of weeks, and finally decided to register to ask a question. This is an earnest question about what the modern interpretation is, and how I and another student of relativity can learn more about the modern understanding...
  25. A

    Physical interpretation of spacetime curvature?

    Folks, I'm in the process of trying to understand spacetime curvature in general relativity. My question might sound odd, but I'm wondering how to best conceptualize spacetime distortions due to a moving mass. If there is a large mass, e.g. a planet, moving through spacetime, the curvature...
  26. K

    Interpretation of the Tanabe Sugano diagram

    We can estimate the value of Δ and B from Tanabe Sugano diagram. For example Ni2+ which is has the electronic configuration of d8. So, by referring the d8 Tanabe Sugano diagram, we can can noticed that there are 3 types of transition. The transitions are observed as V1=8500cm-1, V2=13800cm-1...
  27. E

    Basis of the Copenhagen Interpretation

    Bohr believed that the observer effected the outcome of an experiment at the subatomic level, and it wasn't necessarily the photons used to measure the particle like in Hesienberg's Uncertainty Principle that effected the outcome. What was the basis of this idea if the only way to measure...
  28. D

    What is the intuition behind using eigenvectors of AA^T and A^T A in the SVD?

    In the SVD, we use the eigenvectors of AA^T and A^T A as the input and output bases for the matrix. Does anyone have any intuition about these matrices? ie. if I multiply a vector x by AA^T, what space (in terms of the column space, etc. of A) will it bring x to? Thanks, Dave
  29. D

    What is the Geometric Interpretation of the Final Step in SVD?

    Ax = U \Sigma V^T x (A is an m by n matrix) I understand the first two steps, 1) V^T takes x and expresses it in a new basis in R^n (since x is already in R^n, this is simply a rotation) 2) \Sigma takes the result of (1) and stretches it The third step is where I'm a bit...
  30. B

    Radioactivity problem - Interpretation

    Hi! I should solve this exercise (quite important for me, because related to an important test I should sit next week) but I'm having some trouble with the right interpretation of the problem statement. Homework Statement In which one of the radioactive series do you think the presence...
  31. M

    Need advices about my GP - Sketch Interpretation and Simulation tool

    Hi, I am a computer science student in my final year, and preparing myself for my graduation project (GP). Please check this video: http://www.youtube.com/watch?v=d7eGypGOlOc" This program is from MIT and it is called "A Shrewd Sketch Interpretation and Simulation Tool". I am planning...
  32. Y

    What Is The Most Accepted Interpretation Of Quantum Mechanics?

    I know there are a lot of interpretation's but what is the one that mostly top's the chart's?
  33. jal

    Copenhagen interpretation QGsquared

    The Copenhagen interpretation, (the wavefunction collapse) is not what caught the interest and imagination of the scientific community. It was the Schrödinger's Cat. Is the cat alive or dead? “QGsquared” will not catch the imagination of the 10’s of thousands of interested people by saying...
  34. Saladsamurai

    Understanding Column Vectors: A Physical Interpretation

    Column Vectors? Alrighty. I have a silly question about column Vectors. I first learned about the concept of a vector in Physics, i.e. position, velocity, acceleration, etc. so I easily understand the premise of a row vector. For example the matrix \left[\begin{array}{ccc}1 & 2 &...
  35. A

    A quote regarding entanglement, looking for an interpretation.

    I'll reserve my opinion, but I'd appreciate yours.
  36. E

    The Interpretation of Quantum Mechanics

    Hello Everyone, This time I want to share with you my experience with the book the Interpretation of Quantum mechanics by Erwin Schrodinger. Just let me point out some of his most remarkable points in my humble opinion. In his first chapter, JULY 1952 COLLOQUIUM, he wrote: Let me say at...
  37. S

    Interpretation of Trig Expression

    [SOLVED] Interpretation of Trig Expression Homework Statement Question: Sin xy = y, find dy/dx. This was given as Homework. I did the question as Sin (xy) = y, whereas my teacher took the question as (Sin x)y = y and made a joke out of me in the class for thinking otherwise. All I want to know...
  38. G

    Probability interpretation of QM

    What proof is there that Born's probability interpretation of the QM wavefunction is correct? Born published two papers in 1926 that supposedly shed light on this subject. Does anyone know where I can find english translated versions of these works? Does anyone know of any accessible research...
  39. J

    ?Strange? interpretation of Time-Dilation and it's implications

    First of all, I'm an electrical engineer, I had to take a class on modern physics, so answers don't need to be "dumbed down" so let me START with the question: Can anyone see a flaw in my logic/interpretation of what's happening? My goal is to gain a more accurate conceptual (not mathematical)...
  40. S

    Which interpretation best explains the classical limit?

    Trying decide, apropos that famous Feynman quote, whether there is a 'real problem' with quantum physics. My own rather inexpert view is that if there is, the it's something to do with the classical limit. (The measurement problem being an interesting special case of this.) In particular...
  41. V

    Help with question interpretation

    Homework Statement Give an example of a function f for which the following assertion is false: If |f(x)-l|<\epsilon when 0<|x-a|<\delta, then |f(x)-l|<\epsilon/2, when 0<|x-a|<\delta/2 The Attempt at a Solution I am really not quite sure what I am looking for here. I think i want...
  42. S

    Linear Algebra: Geometric Interpretation of Self-Adjoint Operators

    Homework Statement I'm not interested in the proof of this statement, just its geometric meaning (if it has one): Suppose T \in L(V) is self-adjoint, \lambda \in F, and \epsilon > 0. If there exists v \in V such that ||v|| = 1 and || Tv - \lambda v || < \epsilon, then T has an...
  43. A

    Kernel &quot;stable under&quot;: is my interpretation correct?

    [SOLVED] Kernel &quot;stable under&quot;: is my interpretation correct? Homework Statement A1, A2, A3,..., Ar are endomorphisms. W is the kernel of Ar - lambda*I, where lambda is the eigenvalue of Ar. W is stable under A1, A2, A3,..., Ar-1. Question: does "stable under" equal "closed under"...
  44. N

    Structure and Interpretation of Classical Mechanics

    This is an unusual book which uses the Scheme programming language to functionally describe the various components of classical mechanics. I would say it is at the level of a graduate mechanics course (think Goldstein), however students with a strong programming background will find it easier...
  45. H

    Delayed choice in the Copenhagen interpretation

    Could someone explain to me how the delayed choice experiment is described within the framework of the Copenhagen interpretation? (Double slit experiment with two slits open but a late decission to measure the path of the particle). I do not understand how the deterministic evolution of the...
  46. B

    Coupling fermions to a scalar field: Interpretation problem

    Hi all, I have a little problem concerning the coupling of a fermion to CP^N (or better a 2D scalar O(3) model). Its not a mathematical type of problem. I just read on "The coupling of fermions to the three-dimensional noncommutative $CP^{N-1}$ model: minimal and supersymmetric extensions"...
  47. B

    IQ 195 Genius Challenges the Many Worlds Interpretation

    Earlier today, I saw a show that had the smartest man in America with an IQ of 195 who is working on a Cognitive - Theoretic Model of the Universe. He attacks the MWI with: What do Many-Worlders think about a statement such as this coming from an intelligent person?
  48. B

    Questions on the Copenhagen Interpretation

    Just had four quick questions on the Copenhagen Interpretation (CI). 1. Where is the boundary between realm (classical) space and quantum space. I understand that there is no solid definition for this boundary, but where would we begin to see quantum events occur and see classical events...
  49. C

    Bohmian interpretation and schroedingers cat

    What happens to the cat in the Bohm interpretation? If I've got it right: In MWI it splits, dead in one universe, alive in another. In CI it's not decided until observed. In TI both these absurd concepts are escaped and it's just either dead or alive(I cannot remember the details) but in...
  50. S

    VERY simple Velocity vs time graph interpretation

    Wow, I'm extremely frustrated with this one. Homework Statement http://img262.imageshack.us/img262/4616/probre1.jpg I forgot to label the axis's. The X is time and the Y is Velocity The Attempt at a Solution Iv done a few things on this one: First, I figured I would just count the area...
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