CS243, Logic and Computation Propositional Logic 1 Propositions
... truth value for z is obtained by “plugging in” the truth values for t into the definition of z: t(z) = orf(t(p), notf(t(q))) = orf(false, notf(false)) = orf(false,true) = true Boolean satisfiability. A propositional formula is satisfiable if there is some truth assignment that makes its truth value ...
... truth value for z is obtained by “plugging in” the truth values for t into the definition of z: t(z) = orf(t(p), notf(t(q))) = orf(false, notf(false)) = orf(false,true) = true Boolean satisfiability. A propositional formula is satisfiable if there is some truth assignment that makes its truth value ...
Decomposing Specifications of Concurrent Systems
... 3.1.1. Review of the syntax and semantics A state is an assignment of values to variables. (Technically, our variables are the “flexible” variables of temporal logic that correspond to the variables of programming languages; they are distinct from the variables of first-order logic.) A behavior is an ...
... 3.1.1. Review of the syntax and semantics A state is an assignment of values to variables. (Technically, our variables are the “flexible” variables of temporal logic that correspond to the variables of programming languages; they are distinct from the variables of first-order logic.) A behavior is an ...
Complexity of Existential Positive First-Order Logic
... The output of T can be viewed as an instance of CSP(Γ ), since it can be transformed to a primitive positive sentence (by moving all existential quantifiers to the front). It is clear that T has polynomial running time, and that Φ is true in Γ if and only if there exists a computation of T on Φ that ...
... The output of T can be viewed as an instance of CSP(Γ ), since it can be transformed to a primitive positive sentence (by moving all existential quantifiers to the front). It is clear that T has polynomial running time, and that Φ is true in Γ if and only if there exists a computation of T on Φ that ...
class notes
... Step 1 Locate the variable you are asked to solve for in the equation. Step 2 Identify the operations on this variable and the order in which they are applied. Step 3 Use inverse operations to undo operations and isolate the variable. ...
... Step 1 Locate the variable you are asked to solve for in the equation. Step 2 Identify the operations on this variable and the order in which they are applied. Step 3 Use inverse operations to undo operations and isolate the variable. ...
Introduction to algebra and equations
... Language of Algebra Variables – variables are letters that are used to represent an unknown quantity. In the car example above, the price of the Astra is represented by the variable a, because the price is unknown and can vary depending on the supplier. Another name for variable is pronumeral , indi ...
... Language of Algebra Variables – variables are letters that are used to represent an unknown quantity. In the car example above, the price of the Astra is represented by the variable a, because the price is unknown and can vary depending on the supplier. Another name for variable is pronumeral , indi ...
Chapter 5 - Computer Science | SIU
... 2. if no end borrow occurs, then M>= N, and the result is nonnegative and correct. 3. If an end borrow occurs, then N > M, and the difference, M – N + 2n, is subtracted from 2n, and a minus sign is appended to the result. See Example 5-1 and Figure 5-7 ...
... 2. if no end borrow occurs, then M>= N, and the result is nonnegative and correct. 3. If an end borrow occurs, then N > M, and the difference, M – N + 2n, is subtracted from 2n, and a minus sign is appended to the result. See Example 5-1 and Figure 5-7 ...
10_2InverseJointVari..
... Direct, Inverse and Joint Variation Direct Variation is a linear function. For example d = r • t If time is constant, as rate goes up, distance goes up. We can say, distance varies directly with rate... Direct variation equations can be written as y = kx where k is the constant of variation. Exampl ...
... Direct, Inverse and Joint Variation Direct Variation is a linear function. For example d = r • t If time is constant, as rate goes up, distance goes up. We can say, distance varies directly with rate... Direct variation equations can be written as y = kx where k is the constant of variation. Exampl ...
Chapter 9: Quantified Formulas
... Since we create a new clause from each pair of the two types of clauses, this results in O(m2 ) new clauses, while we erase the m old clauses that contain n x. Repeating this process n times results in O(m2 ) clauses. This seems to imply that the complexity of projection with binary resolution is do ...
... Since we create a new clause from each pair of the two types of clauses, this results in O(m2 ) new clauses, while we erase the m old clauses that contain n x. Repeating this process n times results in O(m2 ) clauses. This seems to imply that the complexity of projection with binary resolution is do ...
1A. Propositional Logic
... e. Finally, when several operators of equal precedence occur in the absence of parentheses, they are evaluated from left to right. i. p ∧ q ∧ r is equivalent to (p ∧ q) ∧ r [although in this case, it doesn’t matter because ∧ is an associative operation, more on this later.] f. Suppose we want to ver ...
... e. Finally, when several operators of equal precedence occur in the absence of parentheses, they are evaluated from left to right. i. p ∧ q ∧ r is equivalent to (p ∧ q) ∧ r [although in this case, it doesn’t matter because ∧ is an associative operation, more on this later.] f. Suppose we want to ver ...
DecModelingBooleanAlgebraSpreadSheets FAS2015 3/20
... In order to use simple mathematical operations to model logic. In order for X*X to equal X, he used the values zero (0) and one (1) for false and true. (Boole, George, Investigation of the Laws of Thought, Chapter 3. pp. 39-51) ...
... In order to use simple mathematical operations to model logic. In order for X*X to equal X, he used the values zero (0) and one (1) for false and true. (Boole, George, Investigation of the Laws of Thought, Chapter 3. pp. 39-51) ...
First-order logic syntax and semantics
... If there exists an isomorphism from are said to be isomorphic, denoted ...
... If there exists an isomorphism from are said to be isomorphic, denoted ...
Lesson 3
... Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjunction in which each symbol (element of S) occurs just once: Ex.: p q Disjunctive normal form (DNF) of a formula F is a formula F’ such that F’ is equivalent to F and F’ has the form o ...
... Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjunction in which each symbol (element of S) occurs just once: Ex.: p q Disjunctive normal form (DNF) of a formula F is a formula F’ such that F’ is equivalent to F and F’ has the form o ...
(p q r) (p q r) (p q r) (p q r) ( p q r)
... Ex.: p q Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjunction in which each symbol (element of S) occurs just once: Ex.: p q Disjunctive normal form (DNF) of a formula F is a formula F’ such that F’ is equivalent to F and F’ ha ...
... Ex.: p q Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjunction in which each symbol (element of S) occurs just once: Ex.: p q Disjunctive normal form (DNF) of a formula F is a formula F’ such that F’ is equivalent to F and F’ ha ...
Notes and exercises on First Order Logic
... order logic from higher order logics. In second order logic there are variables that range over function symbols and predicate symbols.) The concept of a structure is quite common in mathematics, though usually not explicit. The natural numbers N, the integers Z, the rationals Q, the reals R and the ...
... order logic from higher order logics. In second order logic there are variables that range over function symbols and predicate symbols.) The concept of a structure is quite common in mathematics, though usually not explicit. The natural numbers N, the integers Z, the rationals Q, the reals R and the ...
pdf
... successively assigning truth values to the junction and simple points in terms of the truth values already assigned to their successors, in accordance with the truth table rules.] Oddly enough, the standard recursive procedure can be thought of in this way. Let’s write down that recursive procedure. ...
... successively assigning truth values to the junction and simple points in terms of the truth values already assigned to their successors, in accordance with the truth table rules.] Oddly enough, the standard recursive procedure can be thought of in this way. Let’s write down that recursive procedure. ...
Precedence - cs.csustan.edu
... http://www.java-tips.org/java-se-tips/java.lang/what-is-java-operator-precedence.html Java operator precedence is how Java determines which operator to evaluate first. In this chart, operator precedence is displayed from highest precedence to lowest precedence. Java has lots of operators. I colored ...
... http://www.java-tips.org/java-se-tips/java.lang/what-is-java-operator-precedence.html Java operator precedence is how Java determines which operator to evaluate first. In this chart, operator precedence is displayed from highest precedence to lowest precedence. Java has lots of operators. I colored ...
Recall... Venn Diagrams Disjunctive normal form Disjunctive normal
... of a logic table (equivalently: given an interpretation for all possible assignments). This begs the question: ...
... of a logic table (equivalently: given an interpretation for all possible assignments). This begs the question: ...
Lecture_Notes (original)
... Note that a directed edge in the graph from x to y means that if x is true in the formula then y must be true. This idea is the key to the reduction. For example (x + -y) (y + -w) (-x + -y) (z + y) (-z + w) is not satisfiable and will result in a graph with a cycle including y and –y. Note how much ...
... Note that a directed edge in the graph from x to y means that if x is true in the formula then y must be true. This idea is the key to the reduction. For example (x + -y) (y + -w) (-x + -y) (z + y) (-z + w) is not satisfiable and will result in a graph with a cycle including y and –y. Note how much ...
Worksheet Boolean Algebra
... A house alarm has a sensor on the door (A) and a pressure pad inside the house (B). The logical values of the sensors are A = 1 means the door is closed, A = 0 means the door is open B = 1 means someone is on the pressure pad, B = 0 means no-one is on the pressure pad The alarm sounds when the door ...
... A house alarm has a sensor on the door (A) and a pressure pad inside the house (B). The logical values of the sensors are A = 1 means the door is closed, A = 0 means the door is open B = 1 means someone is on the pressure pad, B = 0 means no-one is on the pressure pad The alarm sounds when the door ...