Logic Definition and 1000 Threads

Logic (from Greek: λογική, logikḗ, 'possessed of reason, intellectual, dialectical, argumentative') is the systematic study of valid rules of inference, i.e. the relations that lead to the acceptance of one proposition (the conclusion) on the basis of a set of other propositions (premises). More broadly, logic is the analysis and appraisal of arguments.There is no universal agreement as to the exact definition or boundaries of logic (see § Rival conceptions). However, the scope of logic (broadly construed) includes:

The classification of arguments.
The systematic analysis of logical forms.
The systematic study of the validity of deductive inferences.
The strength of inductive inferences.
The study of faulty arguments, such as fallacies.
The study of logical paradoxes.
The study of syntax and semantics of formal languages.
The study of the concepts of meaning, denotation and truth.Historically, logic has been studied mainly in philosophy (since Antiquity), mathematics (since mid-19th century), and computer science (since mid-20th century). More recently, logic has also been studied in linguistics and in cognitive science. Overall, logic remains a strongly interdisciplinary area of study.

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  1. N

    Quantum logic gate measurement?

    Do quantum logic gates perform measurements? (collapse the wavefunction) For example: If I apply a cNOT gate to a pair of cubits with wavefunction 1/\sqrt{2} |10> + 1/\sqrt{2} |00> what would I expect as the result? 1/\sqrt{2} |11> + 1/\sqrt{2} |00> ? or 1|11> or 1|00> or...
  2. J

    Help with logic proof (this should be really basic)

    help with logic proof (this "should" be really basic) Hey I am new to logic (I've just started a masters) I can't for the life of me prove this using only the natural deduction inference rules: A --> B |- ¬A v B I can do it easily in the other direction but I cannot do it in the above...
  3. S

    Multiple Choice question about Proposition Logic

    The question is here: http://dl.getdropbox.com/u/175564/logic.png The correct answer is D. My attempt to the problem: Let the beginnings of the sentences be A. In a, A is B -/-> C is D. In b, A is B -/-> C is D. These first two do not make sense. in c and d, the word "only" suggests...
  4. R

    Set Theory Book Reviews: Halmos Edition

    I'm looking for a book on Set Theory, currently. I've found one by Halmos which looks good, but I'd like some input on it.
  5. K

    Who Started Logic: Plato or Aristotle?

    Was it Plato or Aristotle? I don't need to be told that logic was an evolution that was merely advanced by these two Greeks. But who really gave us the rules of the game? I've read some of Plato. Not much, but from his dialogues I gather more ethics and "what does what mean" sort of...
  6. D

    What is Hennessy-Milner Logic and Where Can I Find References?

    Homework Statement What is Hennessy-Milner logic? I need references asap. Wikipedia is empty. Homework Equations The Attempt at a Solution
  7. M

    Does a Valid Rule of Inference Always Lead to a True Conclusion?

    Must a valid rule of inference always lead to a true conclusion?
  8. R

    Digital Logic Fundamentals help

    I have recently started my second year at Uni and one of the areas I am studying is Digital Logic Fundamentals. However due to a mixup with my timetable I missed the first few weeks of the course. I am trying to catch up but have become stuck on part of the course that wasn't explained well in...
  9. S

    Second-Order Logic: Understanding the Basics

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  10. S

    How can I simplify this circuit using boolean algebra for XOR and XNOR gates?

    I want to simplfy M'(A'B'C+ABC')+M(AB'C'+A'BC) to as simple a circuit as possible. I don't know the boolean algebra to simplfy the ABC terms. Help please, Speck
  11. A

    How can changing the value of m affect the percentage p?

    Easy to understand problem (please read; I promise you'll understand): I've created my own financial spreadsheet. One of its functions is to allow me to automatically determine how much money I need to save every month m in order to accumulate x dollars in y amount of time. Normally...
  12. H

    How Do AND/OR Logic Gates Work with Diodes?

    http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/diodgate.html Could someone please explain to me why these circuit arrangements act as AND/OR gates, can't find a decent explanation in any of my books
  13. H

    Solving Predicate Logic Proof Problem with Resolution Refutation

    I have a question on my assignment that I'm having a great deal of trouble with. In this question we will consider a simplified model of the “People you may know” application in Facebook. The basic idea is that if two people have a common friend, then they may know each other. We will also...
  14. iamhumble

    Correct Combination Thought Logic Being Followed

    For fun this semester I decided to take a probability class and doing a lot of the random problems from the book to learn the material. I am finding that sometimes I am over complicating some of these problems. Here is a problem I came across. When I punched in the numbers it didn't seemed...
  15. N

    What is the correct answer to this simple maths problem?

    http://img372.imageshack.us/img372/2057/timezy9.jpg See image above. The answer is D - 88, however I can only find 84! Please can someone let me know what I am missing: 20-7= 13 13*6 + 1 = 79 = total upto 2030 + 2045 bus = 80 + 4 buses (two in 21st hr, two in 22nd hr) = 84 Thanks
  16. M

    The logic behind the cross product with units

    The cross product equals to the area of the parallelogram defined by the two vectors (at least in R^3). So if working on vectors which units v_1 = (1,2,3)m v_2 = (3,4,5)m it correctly returns the according area. However, if used to get a vector perpendicular to each of the vectors the...
  17. D

    Who is the tallest, the smallest of the tallest or the tallest of the smallest?

    Hi, I am a french Student in pures sciences. so its a bit hard for me to express myself in english, but I will do my best. Homework Statement Three hundred (300) persons are placed in thirty (3) rows and ten (10) columns. We choose the tallest person of each ROW. Then, we take the...
  18. J

    Basic vending machine logic circuit, with visual

    1. Homework Statement Design a logic circuit to simulate the circuitry that might exist in a vending machine. the vending machine accepts inputs of nickels, dimes, and quarters but only one of each. It dispenses water and beer. Use three logic switches to simulate the coin detectors one each...
  19. J

    Engineering Basic Logic Circuit for a vending machine

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  20. Q

    Need someone to verify my logic

    Homework Statement Find the supremum and infimum of the following sets and test whether these sets have a maximum or minimum: (a) { |x|/(1+|x|) s.t. x is in R} (b) { x/ (1+x) s.t. x > -1}  Homework Equations Order Axioms and Field Axioms for the real numbers; infimum and...
  21. A

    Decidability of -1<1/0<1 using the ordered field axioms and first order logic

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  22. C

    Logic Gates: Basics & Uses for O-Level Students

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  23. D

    India 450,000"Calculating India's Population: Logic & Facts

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  24. V

    Digital logic circuits material

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  25. Gib Z

    What Are Some Typical Logic Problems Faced by Beginners?

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  26. G

    Programs Searching for Interdisciplinary PhD Program on Logic

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  27. R

    Logical Riddle: How Many Cars Do I Have?

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  28. A

    Quantum Physics, Causality, and Logic

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  29. P

    Valid and Invalid Logic Arguments: Explained

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  30. T

    Learning Logic to Master Math Proofs

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  31. J

    Is my logic correct? - L. Algebra question

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  32. C

    Uncertainty Principle logic help

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  33. Fra

    Logic of E-H action, ricci scalar, cosmological constant?

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  34. N

    Solving Propositional Logic and Quantifier Expressions

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  35. Fra

    Is Smolin's Approach to Quantum Gravity Logic Revolutionary?

    I finally started to read Smolin's Three roads to Quantum Gravity and only read the first two chapters so far. It doesn't contain any math, but it does seem to present a particular choice of reasoning on howto make progress on the matter, which I think is interesting in it's own because it may...
  36. N

    Can Fuzzy Logic Effectively Control Air Flow?

    i want application on fuzzy logic, from internet easy to understand
  37. T

    2nd order logic and mathematics?

    Does most of mathematics use 2nd order logic? If so would studying the foundations of mathematics involve mostly using 2nd order logic?
  38. N

    Understanding Fuzzy Logic for Exam Preparation

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  39. D

    Symbolic logic, with truth table definition

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  40. T

    A question about the logic of certain transformations

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  41. L

    Help with Translating English to Predicate Logic

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  42. M

    How to Solve a Logic Problem with Numbers Using Equations?

    Homework Statement given a number of four ciphers ABCD and another four cipher number CDAB get the values of A,B,C,D if we know that 2x (ABCD)=CDAB-5 Homework Equations 2X (ABCD)=CDAB-5 The Attempt at a Solution no idea.. i have try by brute force but got no results only...
  43. A

    Can someone check my logic? simple harmonic motion.

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  44. V

    Example exercises and answers for predicate logic inference (+ FOL in general)

    I'm battling with first order predicate logic (no identity, no extensions) and currently esp. inference using the so called "natural reasoning" rules for inference. Now, the textbook we use, is very ambiguously defined, even I have spotted several 'errors' in it, the lecturer even more. This...
  45. W

    Is logic ultimately constructed on faith?

    To me, there is no doubt that logic cannot be constructed if it isn't initiated by a set of unprovable 'rules', axioms, to be more precise. For example, I can't prove that a statement is either true or false under any circumstances, but I do assume this is consistently true - if a statement is...
  46. E

    Can u make if A>=B then output=1 Else output=0 using these logic gates?

    [SOLVED] can u make "if A>=B then output=1 Else output=0" using these logic gates? Homework Statement this is not quite a homework problem. I am designing a device and I need to use A>=B comparator. The challenge is I need to do this using only NAND, AND, NOR, OR and ExclusiveOR gates...
  47. J

    Deduction theorem for first order logic

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  48. R

    Diode Logic Gates circuit analysis?

    I need to understand how diode-resistor gates work. I've read a lot about what's supposed to happen based on inputs, but I need to see some numbers & analysis to understand what's going on. Where do you start in terms of trying to analyze the following AND gate...
  49. P

    Engineering ECE - logic circuit for a 4 bit input which counts 1s in input

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  50. S

    Negation of All Participants Being IT and Math Majors: Using Basic Logic Laws

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