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. J

    A Hardy's Paradox and lorentz invariant realist interpretation

    Does Hardy's paradox show that all realist interpretations cannot be made lorentz invariant? Or is it just realist hidden variable theories?
  2. J

    I Can the Many Worlds interpretation state the Born Rule as a postulate?

    Every derivation from the MWI of the born rule is circular. http://fmoldove.blogspot.com/search?q=MWI So my question is, can the MWI state the born rule as a postulate (without deriving) and still be a coherent interpretation of probability? The most famous argument against this notion is by...
  3. F

    I Normalized source function: physical interpretation

    Hello, In physical radiative processes, I am studying the solution of the following equation : ##S=(1-\epsilon) J + \epsilon B## with : 1) S the source function 2) J the mean intensity ( ##J=\dfrac{1}{2}\int_{-1}^{1} I_{\nu}\text{d}\tau_{\nu}##) 3) B the Boltzmann distribution 4)...
  4. M

    Interpretation of a memristor's hysterisis loop

    Hi forums, Following is the hysteresis loop of a standard memristor: Please note that, the red one is for lowest frequency and black for highest frequency. From the graph, one can take the following observations: 1> As frequency increases, area of graph decreases 2> With increase in frequency...
  5. K

    A Hardy's approach to quantum gravity and QM interpretation

    Work in quantum foundations is partly considered important because of the hope that the way we think about QM may point to a road to quantum gravity. Lucien Hardy, who is well-known in quantum foundations for his reformulation of QM in terms of five "reasonable" axioms, is one of the people who...
  6. prakhargupta3301

    Is this interpretation correct? (diagrams of Carbon Monoxide and Carbon Dioxide)

    *SORRY FOR BAD DIAGRAM* Is this correct for C(triple bond)O ie Carbon Monoxide This is for CO2. Please check both. ALso check everything ie hybridized orbitals, bondings etc. I'm trying to clear concepts. (Note: red= unhybridized, black= hybridized) Thank you.
  7. rude man

    Insights A New Interpretation of Dr. Walter Lewin's Paradox - Comments

    Greg Bernhardt submitted a new PF Insights post A New Interpretation of Dr. Walter Lewin's Paradox Continue reading the Original PF Insights Post.
  8. P

    Multiple processes interpretation

    Hi pf, there was an article in the Stanford encyclopedia about QM that was rewritten. it quoted a "multiprocess" interpretation differing from Everett's one which could be related to Bohm's interpretation. it is no more there. i am wondering if there are interpretatins where different results...
  9. Islam Hassan

    I Physical Interpretation of Compactified Dimensions?

    Do string theory’s compactified dimensions have a predicted physical interpretation? Do they for example represent the space/planes/domains in which a string ‘lives’? That is, the local permissible evolution space of a given string?IH
  10. P

    I Autocorrelation Error Interpretation

    Hello, I have a question on Autocorrelation of OLS model. So I encountered a autocorrelation error, and use Cochrane - Orcutt Two-step Procedure(CORC) to fix it. And my OLS became GLS. And I have no idea how to interpret the coefficient on my initial X and Y with the new model. I mean something...
  11. K

    Interpretation of electronic bands in a solid

    Homework Statement The exercise asks many questions about the following E(k) diagram, but I'm more interested in understanding some basic things about it, from which I'm sure i'll be able to find the answers I'm requested. 1) What do the bands actually correspond to? Is the lowest band...
  12. Demystifier

    A Is there a local interpretation of Reeh-Schlieder theorem?

    Non-philosophically inclined experts in relativistic QFT often insist that QFT is a local theory. They are not impressed much by arguments that quantum theory is non-local because such arguments typically rest on philosophical notions such as ontology, reality, hidden variables, or the...
  13. Jakub

    I Small Reduced Chi Squared interpretation

    Hello everyone, I would be happy if someone explained the small reduced chi squared value to me. I have fitted a set of measured data with an exponential function, which I need for some sw calculations. The fit seams great, the origin sw also provides the reduced chi squared, but it is very...
  14. J

    I Interpretation of the Fourier Transform of a Cauchy Distribution

    Hi, I'm struggling with a conceptual problem involving the Fourier transform of distributions. This could possibly have gone in Physics but I suspect what I'm not understanding is mathematical. The inverse Fourier transform of a Cauchy distribution, or Lorentian function, is an exponentially...
  15. Pushoam

    A Physical interpretation of virtual displacement

    From the above description of Virtual displacement, what I understood is: virtual displacement is another name for ## dx_i ## when dt = 0. I didn’t understand its physical interpretation. Could anyone please put some more light upon it?
  16. P

    A Interpretation of covariant derivative of a vector field

    On Riemannian manifolds ##\mathcal{M}## the covariant derivative can be used for parallel transport by using the Levi-Civita connection. That is Let ##\gamma(s)## be a smooth curve, and ##l_0 \in T_p\mathcal{M}## the tangent vector at ##\gamma(s_0)=p##. Then we can parallel transport ##l_0##...
  17. ezfzx

    A Interpreting Chi Squared .... backward

    OK, so, I've forgotten more statistics than my students will ever know, and I'm not too proud to ask for help, because I'm just blanking out on this. I would appreciate it if someone could patiently follow along and let me know what I've got right or wrong please. My understanding of the...
  18. W

    Mach-Zehnder Interferometer interpretation

    Hi all, I have a problem trying to interpret the mathematics of this experiment and would like some help. I think it's best I write out all my ideas (and misconceptions) so that I can be corrected. An illustration of the setup is below. Thanks in advance for any assistance! Let the following...
  19. C

    I Is there a geometric interpretation of orthogonal functions?

    Hi all. So to start I'll say I'm just dealing with functions of a real variable. In my linear algebra courses one thing was drilled into my head: "Algebraic invariants are geometric objects" So with that in mind, is there any geometric connection between two orthoganal functions on some...
  20. S

    I Unclear on interpretation of equation - oscillation maybe?

    Equation: angular acceleration = 3 (angular displacement) - 100 At start, when displacement is 0, the initial angular velocity is 20 rad per second clockwise. I expect that the (-100) term will cause the angular velocity to decrease to 0 but since displacement is increasing during this process...
  21. Mzzed

    I Interpretation of spatially dependent convective derivative

    <Moderator's note: Moved from the homework forum.> Homework Statement The following equation is one of a few equations that describe a plasma model. The left hand side is the part I am having trouble with in that I can't seem to visualise what (V dot delV) actually does. My physics teacher has...
  22. ISamson

    Theoretical interpretation to understand chemical recations

    Isn't this a breakthrough? Well, a base for a breakthrough? I have always wondered if a complete theory or accurate prediction of the formation of bonds and molecules is possible... I tried to think about this myself... :) What do you think...
  23. A

    I Physical interpretation of a Hamiltonian with a constraint

    Dear physics forums, What is the physical interpretation of imposing the following constrain on a Hamiltonian: Tr(\hat H^2)=2\omega ^2 where \omega is a given constant. I am not very familiar with why is the trace of the hamiltonian there. Thanks in advance, Alex
  24. S

    Standing Waves (Instruments) & Interference interpretation?

    Hi, I'm trying to solve two problems related to standing waves and wave interference; while I'm not having difficulty with the actual solving portion, I don't know if I'm interpreting the questions correctly. Question 1: "A violin string is tuned to 460 Hz (fundamental frequency). When playing...
  25. M

    I Interpretation of complex wave number

    Dear forum members, I'm wondering about the physical meaning of the imaginary part of a complex wave number (e.g., the context of fluid dynamics or acoustics). It is obvious that w = \hat{w} \mathrm{e}^{i k_z z} describes an undamped wave if k_z = \Re(k_z) and an evanescent wave if k_z =...
  26. N

    The Simulation Interpretation of Quantum Mechanics

    It seems like every argument in favor of the Simulation Hypothesis revolves around the strangeness of Quantum Mechanics. So can the Simulation Interpretation be just as valid of an interpretation as Copenhagen or Many Worlds? If not why not?
  27. lahanadar

    Interpretation of the system response to a unit impulse

    Hi, I want to understand the meaning of unit impulse response when time flows. An example is given below: In the example the left signal depicts a δ[n] function value of which is 1 only at n=0. The LHS signal is response of the system to the unit impulse. I want to understand how to...
  28. J

    Heisenberg's indetermination principle and Ccopenhagen interpretation

    Ive been doing some researches about QM and I am in a condition where i can't differ Heisenbergs indetermination principle from copenhagen interp. Can somebody please explain simply or advancedly(?) (in an understandable way) are there any differences between them. If there are, what are those...
  29. L

    Acceleration, Displacement, Graph Interpretation

    Hello, I was working on a worksheet. It gave a graph that was velocity vs. time. I was asked to find the acceleration rate for the given (specific) time in seconds. My first question is if the line on the graph for example is from 1-3 seconds, in that 1-3 second range, is acceleration constant...
  30. Ken G

    A Interpretation of a state in quantum entanglement

    I have never heard a challenge by quantum entanglement to the concept that a state is a "property" of a particle, which I don't understand. I cannot see any way someone can interpret a state as a property of a system, rather than as a means of treating information about the system, given how...
  31. N

    I Many Worlds Interpretation existence

    I have a few questions about the Many Worlds Interpretation. I read the article https://plato.stanford.edu/entries/qm-manyworlds/ but was having trouble understanding what the "measure of existence" is supposed to represent in the theory, and why a believer in the idea should adhere to either...
  32. zonde

    I Is quantum collapse an interpretation?

    A have seen here on forum statements that quantum collapse is interpretation dependent, for example: So I would like to ask for explanation that does not relay on quantum collapse for this phenomena: We have unpolarized beam of light. It goes trough two orthogonally oriented polarizers...
  33. T

    I Interpretation of photons having zero spin

    What is the interpretation of the fact that photons have spin zero? Does it has do to with the fact that their proper time variation is zero? Or let's go a bit deeper into the math. If it's possible to write down an eigenvalue equation for photons as it is possible for electrons, then we should...
  34. ohwilleke

    I Geometry of GR v. Spin-2 Massless Graviton Interpretation

    In classical general relativity, gravity is simply a curvature of space-time. But, a quantum field theory for a massless spin-2 graviton has as its classical limit, general relativity. My question is about the topology of space-time in the hypothetical quantum field theory of a massless spin-2...
  35. Cota

    Accelerometer data interpretation

    Hello, this is my first experience in this forum. :) I was wondering if someone can help me understanding my accelerometer data installed in a project consisting in an object that is dropped in the air from an altitude of approximately 1000 meters. The descent is controlled by a parachute...
  36. S

    I Interpretation of probability density in QFT

    Hello! I am a bit confused about the interpretation of probability density in QFT. Let's say we have the Klein-Gordon equation. I understand that this is the field equation for a spin-0 charged particle. So if we find a solution ##\phi(x)## of the Klein-Gordon equation, as far as I understand...
  37. A

    A Interpretation of the Weinberg-Witten theorem

    The Weinberg-Witten theorem (https://en.wikipedia.org/wiki/Weinberg–Witten_theorem) states that A ##3 + 1##D QFT quantum field theory with a conserved ##4##-vector current ##J^\mu## which is Poincaré covariant does not admit massless particles with helicity ##|h| > 1/2##. A ##3 + 1##D QFT...
  38. B

    I Geometrical interpretation of gradient

    In 'Introduction to Electrodynamics' by Griffiths, in the section of explaining the Gradient operator, it is stated a theorem of partial derivatives is: $$ dT = (\delta T / \delta x) \delta x + (\delta T / \delta y) \delta y + (\delta T / \delta z) \delta z $$ Further he goes onto say: $$ dT =...
  39. LyleJr

    Admissions How Do Graduate Schools Evaluate Multiple Degrees with Varying GPAs?

    Hello all, I just wanted to hear what the collected wisdom makes of my particular situation. I am an undergraduate student in the United States who intends on applying for admissions to graduate school this coming year. In 2005 I went to University for the 1st time right out of high school at...
  40. W

    Geometric interpretation of complex equation

    Homework Statement $$z^2 + z|z| + |z|^2=0$$ The locus of ##z## represents- a) Circle b) Ellipse c) Pair of Straight Lines d) None of these Homework Equations ##z\bar{z} = |z|^2## The Attempt at a Solution Let ##z = r(cosx + isinx)## Using this in the given equation ##r^2(cos2x + isin2x) +...
  41. durant35

    I Can entropy drop in the Copenhagen interpretation?

    I've been reading some speculative articles about the possible quantum arrow of time which emerges through collapse and irreversibility. My question is: does collapse in the Copenhagen interpretation (or perhaps in a objective-collapse model) allow the spontaneous decrease of entropy where an...
  42. Demystifier

    A Value of observable in statistical ensemble interpretation

    The statistical ensemble interpretation (SEI) is supposed to be a minimal interpretation of QM with the smallest amount of philosophy, vagueness and controversy. Yet it turns out not to be the case. For instance Ballentine, the inventor of SEI, interprets Bell theorem as a strong evidence of...
  43. tom.stoer

    I Interpretation of the photoelectric effect

    The photoelectric effect is usually presented as an example disproving classical electromagnetism as viable model for interaction of light with matter and as evidence of quantization of energy in the electromagnetic field, i.e. the existence of photons. I would like to discuss a thought based on...
  44. thenewmans

    Retrocausality interpretations for fermions

    This question is about experiments involving entangled electrons or any other fermion for that matter. I’ll get to that in a sec. I’ve been interested in understanding interpretations that have retrocausality. (TIQM by Cramer, Wheeler–Feynman absorber, time symmetric by Price) It’s easy to...
  45. Ma Xie Er

    A Logistic Regression Interpretation

    I was trying to find an easy interpretation of the predicted probabilities of a logistic regression model, when one of my coworkers claimed that the logistic regression model is a likelihood. Now, I know that maximum likelihood estimation is used to estimate the parameters, but I didn't think...
  46. thenewmans

    B What’s the difference between TIQM and Time Symmetric QM? (a

    I have a few questions about interpretations that use retrocausality. I only know of 2. 1. TIQM - Transactional Interpretation of QM by John Cramer 1986 https://en.wikipedia.org/wiki/Transactional_interpretation 2. TSQM - Time Symmetric QM by Huw Price...
  47. D

    B An Interpretation of the Geometry of Space-Time Inside a BH

    Assume an eternal, static black hole which has an event horizon, a spherical surface at which any object passes a point of no return and is condemned to move toward a mathematical singularity. One of the predictions of being inside a black hole is that every spatial direction points towards the...
  48. M

    MHB What is a geometric interpretation of all these information?

    Hey! :o We have the tableau $\begin{pmatrix} \left.\begin{matrix} 1 & 0 & \alpha \\ 0 & 1 & \beta \\ 0 & 0 & 0 \end{matrix}\right|\begin{matrix} c\\ d\\ 0 \end{matrix} \end{pmatrix}$ Since there is a zero-row, we conclude that the column vectors are linearly dependent. The number...
  49. CynicusRex

    Improbability of the Many-Worlds Interpretation?

    If the MWI would be true, wouldn't there be at least one reality where human civilization advanced much faster than we did and therefore: contacted all other universes; destroyed all the universes; colonized all other universes; etc. Since, as far as we know, this has not happened, doesn't this...
  50. EternusVia

    I Interpretation of the Reynolds Transport Theorem?

    Background: I am taking an undergraduate fluid mechanics class. I seem to have a misunderstanding with my interpretation of Reynolds Transport theorem (RTT), which I have written below: $$\frac{DB_{sys}}{Dt} = \frac{\partial}{\partial t}\int_{CV}\rho bd V +\int_{CS}\rho b \vec{V}\cdot...
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