Intuitionistic Logic
... the general claim. So, this would be an elusive truth. Why is this a problem? We are trained in the use of our language. We learn meanings by way of use. Elusive sentences can’t be mastered, for we can’t use them appropriately or inappropriately; there are no circumstances of either kind. We must ta ...
... the general claim. So, this would be an elusive truth. Why is this a problem? We are trained in the use of our language. We learn meanings by way of use. Elusive sentences can’t be mastered, for we can’t use them appropriately or inappropriately; there are no circumstances of either kind. We must ta ...
A mathematical sentence is a sentence that states a fact or contains
... p : There are 31 days in January. (True) ~p : There are not 31 days in January. (False) ...
... p : There are 31 days in January. (True) ~p : There are not 31 days in January. (False) ...
Overview of proposition and predicate logic Introduction
... have no meaning by themselves, semantics can only be given to expressions by a function which maps syntactical objects to objects in some real world. A world consists of – a universe U of objects, – a collection P of predicates on U, i.e., subsets of (ordered n-tuples of) objects of U, – a collectio ...
... have no meaning by themselves, semantics can only be given to expressions by a function which maps syntactical objects to objects in some real world. A world consists of – a universe U of objects, – a collection P of predicates on U, i.e., subsets of (ordered n-tuples of) objects of U, – a collectio ...
24.241 Logic I Problem set 04 solutions
... Γ and the conclusion of α is P (I’m using ‘α’ so you don’t confuse it with a sentence letter of SL, but you can use whatever you like). 1. α is valid in SD iff there is an SD derivation that has the members of Γ as primary assumptions and P in the scope of those assumptions only (by definition of ‘va ...
... Γ and the conclusion of α is P (I’m using ‘α’ so you don’t confuse it with a sentence letter of SL, but you can use whatever you like). 1. α is valid in SD iff there is an SD derivation that has the members of Γ as primary assumptions and P in the scope of those assumptions only (by definition of ‘va ...
Document
... Standard 3: Students will learn and apply geometric concepts. Objectives: Use symbolic notation to represent logical statements. Form conclusions by applying the laws of logic to true statements, such as statements about a trip to Alabama. ...
... Standard 3: Students will learn and apply geometric concepts. Objectives: Use symbolic notation to represent logical statements. Form conclusions by applying the laws of logic to true statements, such as statements about a trip to Alabama. ...
HW-04 due 02/10
... (,), represent in predicate logic the following sentences, write the negation of the predicate expression and translate back to English a. Some classes are difficult and boring. b. Difficult classes are not boring. c. No classes are difficult and boring ...
... (,), represent in predicate logic the following sentences, write the negation of the predicate expression and translate back to English a. Some classes are difficult and boring. b. Difficult classes are not boring. c. No classes are difficult and boring ...
Omit Needless Words and Use Definite, Specific, Concrete Language
... If those who have studied the art of writing are in accord on any one point, it is this: the surest way to arouse and hold the readers attention is by being specific, definite, and concrete. The greatest writers — Homer, Dante, Shakespeare — are effective largely because they deal in particulars and ...
... If those who have studied the art of writing are in accord on any one point, it is this: the surest way to arouse and hold the readers attention is by being specific, definite, and concrete. The greatest writers — Homer, Dante, Shakespeare — are effective largely because they deal in particulars and ...
4 slides/page
... • epistemic logic: for reasoning about knowledge The simplest logic (on which all the rest are based) is propositional logic. It is intended to capture features of arguments such as the following: Borogroves are mimsy whenever it is brillig. It is now brillig and this thing is a borogrove. Hence thi ...
... • epistemic logic: for reasoning about knowledge The simplest logic (on which all the rest are based) is propositional logic. It is intended to capture features of arguments such as the following: Borogroves are mimsy whenever it is brillig. It is now brillig and this thing is a borogrove. Hence thi ...
Variations on a Montagovian Theme
... terminology. A numerical relation R is called recursive if there is a mechanical algorithm to check, for any given numbers, whether they stand in this relation to one another or not. R is recursively enumerable if there is an algorithm for listing all and only the numbers that stand in the relation ...
... terminology. A numerical relation R is called recursive if there is a mechanical algorithm to check, for any given numbers, whether they stand in this relation to one another or not. R is recursively enumerable if there is an algorithm for listing all and only the numbers that stand in the relation ...
ch1_1
... 1. Assume p is true and q is false 2. Show that ~p is also true. 3. Then we have that p ^ (~p) is true. 4. But this is impossible, since the statement p ^ (~p) is always false. There is a contradiction! 5. So, q cannot be false and therefore it is true. ...
... 1. Assume p is true and q is false 2. Show that ~p is also true. 3. Then we have that p ^ (~p) is true. 4. But this is impossible, since the statement p ^ (~p) is always false. There is a contradiction! 5. So, q cannot be false and therefore it is true. ...
Logic and proof
... To maybe get an idea of why we do it this way, suppose we want to prove “If n is an even integer greater than 2, then n is not prime”. We could write that as “if p(n) then ¬q(n)”, where p(n) means “n is an even integer greater than 2” q(n) means “n is prime”. Note that for a fixed n, p(n) and q(n) a ...
... To maybe get an idea of why we do it this way, suppose we want to prove “If n is an even integer greater than 2, then n is not prime”. We could write that as “if p(n) then ¬q(n)”, where p(n) means “n is an even integer greater than 2” q(n) means “n is prime”. Note that for a fixed n, p(n) and q(n) a ...
Propositional Logic - University of San Francisco
... Model: A model is an assignment of values to each of the variables of interest in our state. A model for the fox-and-chickens world would indicate the values taken on by nfoxesLeft, nfoxesRight, nchickensLeft, nchickensRight, and boatPos. We’ll often be interested in finding models that make a sente ...
... Model: A model is an assignment of values to each of the variables of interest in our state. A model for the fox-and-chickens world would indicate the values taken on by nfoxesLeft, nfoxesRight, nchickensLeft, nchickensRight, and boatPos. We’ll often be interested in finding models that make a sente ...