ch1_Logic_and_proofs
... 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. ...
A(x)
... Formula A is true in interpretation I, |=I A, if for all possible valuations v holds that |=I A[v]. Model of formula A is interpretation I, in which is A true (that means for all valuations of free variables). Formula A is satisfiable, if there is interpretation I, in which A is satisfied (i.e., if ...
... Formula A is true in interpretation I, |=I A, if for all possible valuations v holds that |=I A[v]. Model of formula A is interpretation I, in which is A true (that means for all valuations of free variables). Formula A is satisfiable, if there is interpretation I, in which A is satisfied (i.e., if ...
Partial Correctness Specification
... A proof in Floyd-Hoare logic is a sequence of lines, each of which is either an axiom of the logic or follows from earlier lines by a rule of inference of the logic u ...
... A proof in Floyd-Hoare logic is a sequence of lines, each of which is either an axiom of the logic or follows from earlier lines by a rule of inference of the logic u ...
Palo Alto 2016 - Stanford Introduction to Logic
... properly, we can create another variable called index that only increments when the satisfied.add(i) command is run. This would eliminate the need for the second for loop and make the program have an efficiency of O(n). As a result of this exercise, the students were able to draw connections to diff ...
... properly, we can create another variable called index that only increments when the satisfied.add(i) command is run. This would eliminate the need for the second for loop and make the program have an efficiency of O(n). As a result of this exercise, the students were able to draw connections to diff ...
Sentential Logic 2 - Michael Johnson's Homepage
... they are all either true or false. There are two truth-values: true and false. So, for example, the sentence “My name is Michael” is true, and the sentence “Today is Wednesday” is false. Since a translation of a sentence is true when the original sentence is true and false when it is false, “M” is t ...
... they are all either true or false. There are two truth-values: true and false. So, for example, the sentence “My name is Michael” is true, and the sentence “Today is Wednesday” is false. Since a translation of a sentence is true when the original sentence is true and false when it is false, “M” is t ...
Logic and Automata - Cheriton School of Computer Science
... Theorem. A set of integers is definable in Th(N, +, Vk ) if and only if its characteristic sequence is k-automatic. Proof. First we show how to construct a finite automaton Mϕ corresponding to any formula ϕ of Th(N, +, Vk ). The idea again is that Mϕ will accept the base-k representations of all n-t ...
... Theorem. A set of integers is definable in Th(N, +, Vk ) if and only if its characteristic sequence is k-automatic. Proof. First we show how to construct a finite automaton Mϕ corresponding to any formula ϕ of Th(N, +, Vk ). The idea again is that Mϕ will accept the base-k representations of all n-t ...
Notes and exercises on First Order Logic
... Examples of relational structures are partially ordered sets and graphs. On the other hand groups, rings, fields, lattices and Boolean algebras are examples of algebras. We are aiming of course to establish when a formula is true in a structure U. The next example shows that the truth value of a for ...
... Examples of relational structures are partially ordered sets and graphs. On the other hand groups, rings, fields, lattices and Boolean algebras are examples of algebras. We are aiming of course to establish when a formula is true in a structure U. The next example shows that the truth value of a for ...
PHIL12A Section answers, 9 February 2011
... 2. How many different ternary sentential connectives are there? How did you arrive at this number? You should not try to list them all! We calculate the number of ternary connectives in the same way as we calculated the number of binary connectives in the last question. A truth table for a ternary ...
... 2. How many different ternary sentential connectives are there? How did you arrive at this number? You should not try to list them all! We calculate the number of ternary connectives in the same way as we calculated the number of binary connectives in the last question. A truth table for a ternary ...
Introduction to Theoretical Computer Science, lesson 3
... An argument is valid iff the conclusion is true in every model of the set of the premises. But the set of models can be infinite! And, of course, we cannot examine an infinite number of models; but we can verify the ‘logical form’ of the argument, and check whether the models of premises do satisfy ...
... An argument is valid iff the conclusion is true in every model of the set of the premises. But the set of models can be infinite! And, of course, we cannot examine an infinite number of models; but we can verify the ‘logical form’ of the argument, and check whether the models of premises do satisfy ...
