2 Lab 2 – October 10th, 2016
... U is the set of real numbers, P is interpreted as the property “to be a square root of −1”. Since no real number has the property I(P ), our sentence is true in hU, [[−]]i. On the other hand, consider the interpretation: U 0 is the set of natural numbers, P is interpreted as the property “to be even ...
... U is the set of real numbers, P is interpreted as the property “to be a square root of −1”. Since no real number has the property I(P ), our sentence is true in hU, [[−]]i. On the other hand, consider the interpretation: U 0 is the set of natural numbers, P is interpreted as the property “to be even ...
Document
... • P : it-is-raining-here-now • since this is either a true or false statement about the world, the value of P is either true or false ...
... • P : it-is-raining-here-now • since this is either a true or false statement about the world, the value of P is either true or false ...
Modal_Logics_Eyal_Ariel_151107
... It means that A knows that if B doesn’t knows whether his forehead is muddy then A knows that it is possible in B’s knowledge that A’s forehead is muddy! Remember that: [i]A A ...
... It means that A knows that if B doesn’t knows whether his forehead is muddy then A knows that it is possible in B’s knowledge that A’s forehead is muddy! Remember that: [i]A A ...
STEPS for INDIRECT PROOF - Fairfield Public Schools
... triangle theorem that states all angles of an equilateral triangle are congruent.) 3) Write a ‘therefore’ statement as a conclusion that the PROVE must be TRUE. For example, “Therefore , since our assumption lead to a CONTRADICTION (or absurd statement) , then our assumption must be FALSE, and _____ ...
... triangle theorem that states all angles of an equilateral triangle are congruent.) 3) Write a ‘therefore’ statement as a conclusion that the PROVE must be TRUE. For example, “Therefore , since our assumption lead to a CONTRADICTION (or absurd statement) , then our assumption must be FALSE, and _____ ...
Exam #2 Wednesday, April 6
... There are no further clauses to be obtained from these by resolution. If we use the Davis-Putnam Procedure, first eliminating P to get {Q} and then Q to get no clauses, we also see that the original formula is not valid. 3. (P -> Q) -> ( (P -> R ) -> (Q -> R)) The negation of the formula in CNF is: ...
... There are no further clauses to be obtained from these by resolution. If we use the Davis-Putnam Procedure, first eliminating P to get {Q} and then Q to get no clauses, we also see that the original formula is not valid. 3. (P -> Q) -> ( (P -> R ) -> (Q -> R)) The negation of the formula in CNF is: ...
Notes Predicate Logic
... domain, then the statement that follows is true. Propositional logic doesn’t work as well with existential quantification. Example: To say some real number is irrational, we write ∃ x ∈ R, x ∈ / Q. Comment: In propositional logic, we could write ¬( x ∈ R ⇒ x ∈ Q), or in ...
... domain, then the statement that follows is true. Propositional logic doesn’t work as well with existential quantification. Example: To say some real number is irrational, we write ∃ x ∈ R, x ∈ / Q. Comment: In propositional logic, we could write ¬( x ∈ R ⇒ x ∈ Q), or in ...
Slides - UCSD CSE
... If A and B are wffs, then: – (A ! B) is a wff – (A " B) is a wff – (A !B) is a wff B) is a wff – (A ...
... If A and B are wffs, then: – (A ! B) is a wff – (A " B) is a wff – (A !B) is a wff B) is a wff – (A ...
Bound and Free Variables Theorems and Proofs
... Modern database query language date back to SQL (structured query language), and are all based on first-order logic. • The idea goes back to Ted Codd, who invented the notion of relational databases. Suppose you’re a travel agent and want to query the airline database about whether there are flights ...
... Modern database query language date back to SQL (structured query language), and are all based on first-order logic. • The idea goes back to Ted Codd, who invented the notion of relational databases. Suppose you’re a travel agent and want to query the airline database about whether there are flights ...
An Introduction to Lower Bounds on Formula
... properties of Kripke frames and models. To put things in perspective, I am going to start by giving an informal overview of some techniques used for proving lower bounds on the size of Boolean formulae and then I am going to show how to extend and apply them in the modal case where we have obtained ...
... properties of Kripke frames and models. To put things in perspective, I am going to start by giving an informal overview of some techniques used for proving lower bounds on the size of Boolean formulae and then I am going to show how to extend and apply them in the modal case where we have obtained ...
Language of Logic 1-2B - Winterrowd-math
... What counterexamples to Alice’s logic were given by the Mad Hatter, the March Hare, and the Dormouse? What is the difference between “I mean what I say” and “I say what I mean”? If you had attended the tea party, what counterexample to Alice’s logic could you have added to the conversation? ...
... What counterexamples to Alice’s logic were given by the Mad Hatter, the March Hare, and the Dormouse? What is the difference between “I mean what I say” and “I say what I mean”? If you had attended the tea party, what counterexample to Alice’s logic could you have added to the conversation? ...
Modal Logic
... (i) Every tautology of propositional logic is valid. (ii) ❏(❏❏ (iii) Suppose that is valid. Then, ❏must also be valid. ...
... (i) Every tautology of propositional logic is valid. (ii) ❏(❏❏ (iii) Suppose that is valid. Then, ❏must also be valid. ...
POSSIBLE WORLDS AND MANY TRUTH VALUES
... each j exactly one qij holds, and let α∗ be γ ⇒ β. Then α∗ is a formula of K valid on exactly the same frames as α, as required. Formal systems in K are assumed to have just the usual rules (Substitution, Detachment, Necessitation), and at least the axioms of the system K. If M is standard, then for ...
... each j exactly one qij holds, and let α∗ be γ ⇒ β. Then α∗ is a formula of K valid on exactly the same frames as α, as required. Formal systems in K are assumed to have just the usual rules (Substitution, Detachment, Necessitation), and at least the axioms of the system K. If M is standard, then for ...
