Program Equilibrium in the Prisoner`s Dilemma via Löb`s Theorem
... footing is the model-checking result of van der Hoek, Witteveen, and Wooldridge (2011), which seeks “fixed points” of strategies that condition their actions on their opponents’ output. However, in many interesting cases there are several fixed points, or none at all, and so this approach does not c ...
... footing is the model-checking result of van der Hoek, Witteveen, and Wooldridge (2011), which seeks “fixed points” of strategies that condition their actions on their opponents’ output. However, in many interesting cases there are several fixed points, or none at all, and so this approach does not c ...
Lecture notes from 5860
... These notes summarize ideas discussed up to and including Lecture 14. This material is related to Chapter 6 of the textbook by Thompson. In particular the idea of extracting a program from a proof is examined. The ideas discussed here take us deeper into the issues behind the design of constructive ...
... These notes summarize ideas discussed up to and including Lecture 14. This material is related to Chapter 6 of the textbook by Thompson. In particular the idea of extracting a program from a proof is examined. The ideas discussed here take us deeper into the issues behind the design of constructive ...
Full text
... consecutive ones, exactly ks at least k, and so on). Collectively, these kinds of problems might be labelled fc-in-a-row problems, and they have a number of interpretations and applications (a few of which are discussed in §4): combinatorics (menage problems), statistics (runs problems), probability ...
... consecutive ones, exactly ks at least k, and so on). Collectively, these kinds of problems might be labelled fc-in-a-row problems, and they have a number of interpretations and applications (a few of which are discussed in §4): combinatorics (menage problems), statistics (runs problems), probability ...
Algebra 1 Secondary Education MAFS.912.N
... The value of the area of the rectangle, in square feet, is an irrational number. The number that represents the width of the rectangle must be ? Select the best answer to fill in the blank. A. A whole number. B. A rational number. C. An irrational number. D. A non-real complex number ...
... The value of the area of the rectangle, in square feet, is an irrational number. The number that represents the width of the rectangle must be ? Select the best answer to fill in the blank. A. A whole number. B. A rational number. C. An irrational number. D. A non-real complex number ...
On the paradoxes of set theory
... crisis in the foundations of mathematics created and because of the profound effect that it had not only on the theory itself but with the other subjects in mathematics, that these paradoxes are presented. SinDe the discovery of paradoxes in set theory, a great deal of literature has appeared offeri ...
... crisis in the foundations of mathematics created and because of the profound effect that it had not only on the theory itself but with the other subjects in mathematics, that these paradoxes are presented. SinDe the discovery of paradoxes in set theory, a great deal of literature has appeared offeri ...
(pdf)
... This concludes the exposition of first order logic. While the reader might feel like the next section is quite disconnected with the previous one, both are essential in constructing the basic framework of non-standard analysis. 2. Filters, Ultrafilters, Ultraproducts and Ultrapowers Filters are a wa ...
... This concludes the exposition of first order logic. While the reader might feel like the next section is quite disconnected with the previous one, both are essential in constructing the basic framework of non-standard analysis. 2. Filters, Ultrafilters, Ultraproducts and Ultrapowers Filters are a wa ...
page 139 MINIMIZING AMBIGUITY AND
... understandable). We should also take into account that the required precision is dependent on the actual text or theory we are dealing with. The classical view is right in that the formalization of our premises could be more precise. For instance: if we formalize the word “chair”, we should make use ...
... understandable). We should also take into account that the required precision is dependent on the actual text or theory we are dealing with. The classical view is right in that the formalization of our premises could be more precise. For instance: if we formalize the word “chair”, we should make use ...
![arXiv:math/0408107v1 [math.NT] 9 Aug 2004](http://s1.studyres.com/store/data/015366745_1-b96e81e8ee635380ae70d20316f65919-300x300.png)
The Complete Proof Theory of Hybrid Systems
... ensure soundness by checking it locally per proof rule. More intriguingly, however, our logical setting also enables us to ask the converse: is the proof calculus complete, i.e., can it prove all that is true? A corollary to Gödel’s incompleteness theorem shows that hybrid systems do not have a sou ...
... ensure soundness by checking it locally per proof rule. More intriguingly, however, our logical setting also enables us to ask the converse: is the proof calculus complete, i.e., can it prove all that is true? A corollary to Gödel’s incompleteness theorem shows that hybrid systems do not have a sou ...
Introductory Mathematics
... proved by J. Lagrange in the 18th century; (ii) is a false statement: the odd number 5777 cannot be written as p + 2a2 with p prime; (iii) is not currently (2004) known to be true or false — it is called “Goldbach’s Conjecture” and although most mathematicians think it’s true, one cannot be certain ...
... proved by J. Lagrange in the 18th century; (ii) is a false statement: the odd number 5777 cannot be written as p + 2a2 with p prime; (iii) is not currently (2004) known to be true or false — it is called “Goldbach’s Conjecture” and although most mathematicians think it’s true, one cannot be certain ...
CPSC 411 Design and Analysis of Algorithms
... Big Theta Notation Let S be a subset of the real numbers (for instance, we can choose S to be the set of natural numbers). If f and g are functions from S to the real numbers, then we write g (f) if and only if there exists some real number n0 and positive real constants C and C’ such that C|f(n ...
... Big Theta Notation Let S be a subset of the real numbers (for instance, we can choose S to be the set of natural numbers). If f and g are functions from S to the real numbers, then we write g (f) if and only if there exists some real number n0 and positive real constants C and C’ such that C|f(n ...
Mathematical proof
In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms. Proofs are examples of deductive reasoning and are distinguished from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproved proposition that is believed true is known as a conjecture.Proofs employ logic but usually include some amount of natural language which usually admits some ambiguity. In fact, the vast majority of proofs in written mathematics can be considered as applications of rigorous informal logic. Purely formal proofs, written in symbolic language instead of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics (in both senses of that term). The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.