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.

View More On Wikipedia.org
Recent contents Top users
  1. F

    What are the steps for using natural deduction in logic?

    Logic: Natural Deduction Can anyone lead me off here? I've broken down the three premises using 'for all' elimination, now I need to start a subderivation with an assumption, but I'm not sure what! Right now I'm unsure of the strategy I need to use to get to the conclusion, what do I...
  2. Femme_physics

    What is the Simplification of a Boolean Function Using Karnaugh Maps?

    Homework Statement Given the function: http://img26.imageshack.us/img26/9718/elel0.jpg A) Write the truth table of the function F (A, B, C, D) B) Present the function F (A, B, C, D) via Karnaugh Map C) Express the function F as the sum of multiplications with minimum literals...
  3. S

    Did any of my classmates cheat on their homework?

    I'm having some troubles about some exercises regarding my first year logic course. 1) Deriving (P -> Q) \/ (Q -> R) and showing that this statement is a tautology without using truth tables or venn diagrams. So far I have no clue on how to start this question. From what I remember in...
  4. K

    What does possibly necessary mean in modal logic [crazy question actually]

    Suppose the following X is not necessarily not Y. If X is Y then X necessarily cannot be Z. Does that mean X cannot be Z? I probably screwed up stating that... To clarify The first line is meant to be a solipsistic statement - I may be all there is. The second line is meant to state...
  5. S

    Logic gates, inverting output without increasing transistor count

    Homework Statement Hello all, I have the following logic gates: (A'.(B+C))' which I had reduced to A+B'.C'. I then want use a NAND gate connected to a NOR gate, then connected to an inverted. However, I have been informed that I need not to use ten transistors, and that 8 can get the job...
  6. B

    Becoming proficient in Symbolic Logic

    Homework Statement I'm not sure where this goes, but I'll post it here, as it seems to be a quasi-mathematical subject. Anyway, I was doing derivations from conclusions using implication rules, and I was quite confused to say the least. The rules of implication are: Modus Ponens...
  7. A

    Mathematical Logic, Interpretation, Satisfiable, Consequence relation

    Theorem : let A be a set of formulas, a be a formula For all A and all a, Every interpretation which is a model of A is also a model of a iff not (Sat A) U {~a} Proof Every interpretation which is a model of A is also a model of a iff(1) there is no interpretation which is a model of A but...
  8. L

    Translating a statement to logic.

    Homework Statement Translate the following sentences into propositional or predicate logic. Use the shorthand symbols (e.g. \vee) and define the meaning of each of your predicates and propositional variables. Be sure to include a domain (aka replacement set) for each quantified variable...
  9. @

    Solve Predicate Logic Homework Equations

    Homework Statement 1) (∀xεℝ)((x≠0)→((∃yεℝ)(xy=1) 2) (∃yεℝ)(∀xεℝ)((x≠0)→(xy=1)) Homework Equations ∃ - there exists ∀ - for all → implication The Attempt at a Solution The brackets and implication are throwing me for a loop 1) for all real numbers, there exist...
  10. A

    Cubic Spline what is the logic in constructing it?

    Cubic Spline...what is the logic in constructing it? Hey guys, I am not trying to directly code a cubic spline computation, but I am writing a sub routine in VBA that takes input data, and outputs it to a text file in Maple syntax. Anywho, my cubic spline actually produces LINEAR splines! I...
  11. F

    To derive arithmatic from logic

    I guess it was Whitehead and Russell who tried to prove that all of math could be derived from the principles of basic logic. Where is that effort today? I'd rather not read a 3 volume set to understand how 1+1=2 can be derived from logic. Is there a more modern text on the subect? Is it still...
  12. F

    Universal restriction in description logic

    I am struggling to understand how a universal restriction works in description logic. I can understand the extistential restriction but not the universal. the definition is I have two examples with answers for this. For the first one (B AND A) is easy enough to work out...
  13. S

    Proving ∃x(P(x) → ∀y(P(y))): An Exercise in Logic

    Homework Statement Prove ∃x(P(x) → ∀y(P(y))). Homework Equations The Attempt at a Solution ∃x(P(x) → ∀y(P(y))) is equivalent to ∃x(¬P(x) ∨ ∀y(P(y))). This exercise is found in a section on "proofs involving disjunctions." I have tried many different ways to solve this and...
  14. J

    Implication (Discrete math logic)

    The truth table for implication looks like this p|q| p -> q ------------ T|T | T T|F | F F|T | T <----I'm trying to make sense of this one. My prof warned us that its strange. F|F | T I that implication means: "If p, then q" "q is necessary for p" "p is sufficient for q" "p, only...
  15. B

    Is the Arthur Beiser Logic in Concepts of Modern Physics Appropriate?

    In his book 'Concepts of MODERN PHYSICS', Chapter 1, Section 1.7, page# 22to 24, Arthur Beiser tries to derive an equation for relativistic momentum, which he finally does. But I found the situation considered by him inappropriate so is with the way he deals with it. Can anyone please tell me...
  16. A

    Exploring Math Beyond Formal Logic

    Using the formal logical structure of the original theorem, the converse, the curious inverse, and the all important contrapositive, mathematics is at a standstill. I am trying to get to this very particular coordinate without using formal logic.
  17. P

    Solving a Logic Problem: Prove ~(A * F)

    Hey everyone I'm new to the forums and I came here because I completely stumped. This is basic logic but for some reason I'm having trouble with this one. Homework Statement 1) ~(A * G) 2) ~(A * E) 3) G v E / prove ~(A * F) As I go through and show each step I have to give...
  18. T

    Logic question (conjunction of implications)

    hi all, I'm no logician but am interested in sorting out this problem. Say you've shown that 1. x implies y and 2. z implies w what steps/assumptions are required, in classical logic, to get from 1&2 to: 3. x&z implies y&w Do the steps require some sort of separability...
  19. S

    Which Logic Translation Correctly Expresses Everyone Likes Mary, Except Mary?

    Homework Statement I am going back and reviewing some elementary material in logic/set theory. Among the problems in the quantifier section is the following english sentence to logic sentence translation: Everyone likes Mary, except Mary herself. Now, my attempt was: (∀x)[(x≠m →...
  20. C

    Complexity of SAT in First-order logic

    I have been thinking about this question for weeks and can't figure it out! I reckon it's decidable and in EXPTIME, but not sure how to prove this! Any help would be reallllly appreciated! (Note: the question is in the attachment) -Peter
  21. I

    The Logic of Believing in Free Will

    The Logic of Believing in Free Will Please Be Aware: My “proof” here is by no means complete. In all honesty, although I have spent countless sleepless nights pondering this in my head, my thirst for knowledge and truth in the matter has only just begun. With that in mind, I kindly request...
  22. L

    Please help construct a proof (propositional logic)

    This is a two part question my book gives as practice problem. I, however am struggling to construct logical proofs and the book does not have a key. Thanks in Advance! 2a. Construct a proof, using any method (or rules) you want, that the following argument is valid: Premises (3): –...
  23. M

    LOGIC: A Request for Clarification of definitions

    With the study of logic, lots of words get thrown around that I don't really understand their complete meaning. With a deductive argument the conclusion is true if the premises are true, and an argument is valid if all the inferences (and the conclusion) follow logically from the axioms. These...
  24. K

    Why Am I Getting an Extra Area in My Karnaugh Map Simplification?

    Hi, I'm new to this forum. My problem led me here. Homework Statement I need to solve this, using simplifying rules. ∫ = Ʃ(0,5,6,7,13) But I always get one extra area when checking with Karnaugh map, which isn't necessary. Homework Equations ∫() = a' b' c' d' + a' b c' d +...
  25. G

    Triplet paradox: where's the error in my logic?

    Consider the following scenario: There is a triplet of persons A, B and C. Person A stays on earth, while person B and C both go onto two different space missions, the directions parallel to each other. Person B travels at 0.45*c, person C at 0.9*c. The space missions are both set to take...
  26. G

    Are there any good books on logic and plane geometry?

    Hello, After reading both How to Prove It: A Structured Approach - By Daniel J Velleman, and one of the Lost Feynman Lectures on Planetary Orbits, I'm wondering if anyone could suggest to me any good books they've read (or heard about) pertaining to logic (paired with analysis), or plane...
  27. N

    Logic Statements: Understanding F(x) & \forall y (F(y)

    Hello! 1) \forall x (F(x) \rightarrow \forall y (F(y) \rightarrow y=x)) 2) \exists x (F(x) \rightarrow \forall y (F(y) \rightarrow y=x)) 3) \forall x (F(x) \land \forall y (F(y) \rightarrow y=x)) 4) \exists x (F(x) \land \forall y (F(y) \rightarrow y=x)) If 1) is true then 2) is true...
  28. M

    Digital Logic; 4 inputs if and only if

    Homework Statement Using a truth table and a karnaugh map, build a minimized circuit (using only AND and OR gates) to have an output if and only if any two inputs A,B,C,D are true (let true = 1, false = 0). Homework Equations karnaugh maps. The Attempt at a Solution My only...
  29. A

    Exploring Logic and Implications: Vacuous Truths

    I don't understand the concept (or need for) of vacuous truths/implications. Why is it that if say a statement a is false then we can conclude that any implication a => b is 'true'? Ive been reading online on this but everything has been vague so far, the most sensible explanation I've seen...
  30. L

    Predicate logic and one point rule using Z notation

    Hello all, I'm in the process of simplifying the following equation using one-point rule and other predicate logic. But I’m a bit stuck with where to start or which inference rule to use first. Please help or any pointers would be much appreciated. Thanks
  31. S

    How to Translate and Prove a Complex Predicate Logic Statement?

    Homework Statement No matter what positive real number x we choose, there exists some positive real number y such that yz2 > xz + 10 for every positive integer z. Translate the above statement to predicate logic and prove it using a direct approach. Homework Equations I don't...
  32. S

    Apostol 1.19 - Understanding where my logic went wrong (Sets, sup, inf)

    Okay, so I'm struggling with understanding where I went wrong. The instructor feels like I don't understand the material and when she presented my explanation to a colleague, he too agreed with her. I would really appreciate if someone could tell me the first part of where I went wrong in my...
  33. M

    Intro to Logic: Answers to Your Questions

    I want A book which gives an introduction to logic , so it answer my questions like that I have posted https://www.physicsforums.com/showthread.php?t=541777 THanks
  34. M

    Can Contradiction Prove a Real Number Equals Zero?

    Propositional logic urgent help please Homework Statement for every a in ℝ+: for every ε>0 : a<ε Homework Equations prove that a=0 The Attempt at a Solution is it possible to use contradiction to solve that problem, if not how can I. Urgently need help.
  35. H

    Logic Gates and CPUs: Basic Design Structure of Computer Processors

    I would like to know the basic design structure of computer processors. My concept of a processor is that it reads some binary data from memory, performs operations on it (according to a set of instructions, which it also reads in), and then writes the result to memory somewhere. (Is this...
  36. B

    Using a 8-1 MUX only (no external gates) to perform digital logic

    Homework Statement Assuming the existence of 6 digital inputs and 1 digital output, design a schematic circuit diagram using any number of 8-1 muxs (i.e. no external gates) to satisfy the following requirements:  The output is true (1) when (inputs 1 and 2 are not the same) and at least 2...
  37. T

    Symbolic Logic Homework Questions

    Hi! I was kind of struggling with a couple of the problems on my symbolic logic homework, and any help/hints/etc. would be very much appreciated! The same symbolizations are used as in Klenk's "Understanding Symbolic Logic" book: • = dot, meaning "and", as in p • q v = wedge, meaning...
  38. S

    Implementing a Logic Circuit with NAND & NOR Gates

    Homework Statement Given the above circuit, implement the logic circuit with only NAND gates, and then one with only NOR gates.Homework Equations N/A The Attempt at a Solution I made a truth table but I'm pretty sure its wrong because I'm confused on how to implement the 'g' part of the...
  39. W

    What is the role of logic in philosophy, mathematics, and other disciplines?

    I will try to make my OP based on the rules this sub-forum subscribes to, if not please inform me. Sorry. My question is about logic. How did we acquire it? Was it evolutionary? How is it that Japanese logicians do very much the same work as white American ones do. I am asking because logic...
  40. K

    Can someone explain what Bertrand Russell is saying on Aristotle's logic?

    http://books.google.com/books?id=Ey94E3sOMA0C&lpg=PP1&pg=PA190#v=onepage&q&f=false" Aristotle's Logic I want to know whether I have understood this right. We shouldn't be saying , "All Greeks are men,all greeks are white,therefore some men are white". So we should be saying "there are...
  41. H

    Simple Logic Question of Converting or to and

    Simple Logic Question of Converting "or" to "and" Homework Statement As the title would have you believe it's really just a basic question. I have to write (¬q <---> r) /\ (¬p \/ ¬r) ---> (p \/ ¬q) just using "¬'s" and "/\'s" i know how to change everything else, but i cannot, for the life of...
  42. S

    Engineering Logic circuits for boolean functions

    Homework Statement Draw a logic circuit for the boolean function ((p+qr)')(pq+r) do not simplify the function first The Attempt at a Solution I got this: http://screencast.com/t/BC4akgo9J but I'm pretty sure it's wrong because of the first part how the bar goes over the whole...
  43. N

    Wrong answer using correct logic

    Homework Statement A plane has the equation aX + bY + cZ + d = 0. A line L goes from (0,0,0) and crosses the plane at some point. L and plane are orthogonal. express the coordinates of the crossing point P by: a, b, c and d. Homework Equations |d|/sqrt(a^2 + b^2 + c^2) is the distance between...
  44. K

    What are some recommended books on mathematical logic and set theory?

    Hello, I would like to know about a good introductory book on mathematical logic. It should start from set theory , include ZFC axioms and also touch on Godel's theorems.
  45. S

    Logic gates in excitonic single-quantum-dot qubits

    I am searching for physical realizations of universal logic operations (phase rotation, CNOT, Hadamard) in single-dot excitionic qubits. Phase rotations are easy to implement with sinusoidal electric fields but my literature search for CNOT and Hadamard gates runs dry. I can find them in spin...
  46. J

    Tell if this Argument is valid (Propositional Logic)?

    Tell if this Argument is valid (Propositional Logic)? P = If a man is bachelor he is unhappy Q= if a man is unhappy he dies young C = so the conclusion will be Bachelors die young is his right ? This we have to write this in this form is this correct ----> means implies Q ---> Q Q...
  47. H

    How to Simplify Complex Logical Statements?

    Homework Statement Simplify the following compound statements (give a smallest formula equivalent to each of them). State which logical identities you used at each step (a) (p→q)↔(q→p) (b) ¬(p∧q)→(q→(p∨q)) Homework Equations n/a The Attempt at a Solution (a) ( p → q ) ↔ ( q...
  48. S

    Logic gates in excitonic single quantum dot qubits

    I am searching for physical realizations of universal logic operations (phase rotation, CNOT, Hadamard) in single-dot excitionic qubits. Phase rotations are easy to implement with sinusoidal electric fields but my literature search for CNOT and Hadamard gates runs dry. I can find them in spin...
  49. Dembadon

    Logic: Logical Status of Statement Forms

    The professor for my symbolic logic course requires us to be extremely precise with our explanations. Given the subject, I understand his reasoning and appreciate his rigor. I am studying for our first exam by doing some of the exercises at the end of the sections on which we're going to be...
  50. B

    Compactness in Topology and in Logic

    Hi, All: I am trying to understand better the similarity between the compactness theorem in logic--every first-order sentence is satisfiable (has a model) iff every finite subset of sentences is satisfiable, and the property of compactness : a topological space X is said...
Back
Top