Chapter 1
... These assumptions are call axioms. From axioms we deduce, logically, other properties and connections. Hence, a requirement for being able to write a mathematical proof is an understanding of logic. While we will not delve into the foundations of logic here, we will clean up and make more precise ou ...
... These assumptions are call axioms. From axioms we deduce, logically, other properties and connections. Hence, a requirement for being able to write a mathematical proof is an understanding of logic. While we will not delve into the foundations of logic here, we will clean up and make more precise ou ...
Partial Correctness Specification
... These specifications are ‘partial’ because for {P } C {Q} to be true it is not necessary for the execution of C to terminate when started in a state satisfying P It is only required that if the execution terminates, then Q holds {X = 1} WHILE T DO X := X {Y = 2} – this specification is true! ...
... These specifications are ‘partial’ because for {P } C {Q} to be true it is not necessary for the execution of C to terminate when started in a state satisfying P It is only required that if the execution terminates, then Q holds {X = 1} WHILE T DO X := X {Y = 2} – this specification is true! ...
Philosophy as Logical Analysis of Science: Carnap, Schlick, Gödel
... conditions gives one information about meaning. For surely, if ‘S’ is true were apriori equivalent to, or made the same statement as, S, then ‘S’ is true iff S would be apriori equivalent to, or make the same statement as S iff S. But then since knowledge that the earth is round iff the earth ...
... conditions gives one information about meaning. For surely, if ‘S’ is true were apriori equivalent to, or made the same statement as, S, then ‘S’ is true iff S would be apriori equivalent to, or make the same statement as S iff S. But then since knowledge that the earth is round iff the earth ...
Math 2534 Test 1B Solutions
... which fulfills the definition of a rational number which states that all rational numbers b can be expressed as a ratio of integers , c ≠ 0 . Therefore all integers are rational. c ...
... which fulfills the definition of a rational number which states that all rational numbers b can be expressed as a ratio of integers , c ≠ 0 . Therefore all integers are rational. c ...
• Use mathematical deduction to derive new knowledge. • Predicate
... If the unicorn is mythical, then it is immortal, but if it is not mythical then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical if it is horned. Q: Is the unicorn mythical? Magical? Horned? ...
... If the unicorn is mythical, then it is immortal, but if it is not mythical then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical if it is horned. Q: Is the unicorn mythical? Magical? Horned? ...
THE ABUNDANCE OF THE FUTURE A Paraconsistent Approach to
... “utility” of this logical approach in the worst case. In order to defeat criticisms of the second kind one should give a possible application, or at least a natural interpretation of this logic. Abundance has at least some intuitive grounding in our linguistic use: most of the times, when we say “ ...
... “utility” of this logical approach in the worst case. In order to defeat criticisms of the second kind one should give a possible application, or at least a natural interpretation of this logic. Abundance has at least some intuitive grounding in our linguistic use: most of the times, when we say “ ...
ppt
... • Problem solving agents cannot infer unobserved information. • We want an algorithm that reasons in a way that resembles reasoning in humans. ...
... • Problem solving agents cannot infer unobserved information. • We want an algorithm that reasons in a way that resembles reasoning in humans. ...
True
... • Problem solving agents cannot infer unobserved information. • We want an algorithm that reasons in a way that resembles reasoning in humans. ...
... • Problem solving agents cannot infer unobserved information. • We want an algorithm that reasons in a way that resembles reasoning in humans. ...
Predicate Logic - Teaching-WIKI
... • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat i ...
... • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat i ...
An Introduction to SOFL
... The use of parenthesis An expression is interpreted by applying the operator priority order unless parenthesis is used. For example: the expression not p and q or r <=> p => q and r is equivalent to the expression: (((not p) and q) or r) <=> (p => (q and r)) Parenthesis can be used to change the pr ...
... The use of parenthesis An expression is interpreted by applying the operator priority order unless parenthesis is used. For example: the expression not p and q or r <=> p => q and r is equivalent to the expression: (((not p) and q) or r) <=> (p => (q and r)) Parenthesis can be used to change the pr ...
The Foundations: Logic and Proofs
... raining.” then p →q denotes “If I am at home then it is raining.” In p →q , p is the hypothesis (antecedent or premise) and q is the conclusion (or consequence). ...
... raining.” then p →q denotes “If I am at home then it is raining.” In p →q , p is the hypothesis (antecedent or premise) and q is the conclusion (or consequence). ...
ppt
... If the unicorn is mythical, then it is immortal, but if it is not mythical then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical if it is horned. Q: Is the unicorn mythical? Magical? Horned? ...
... If the unicorn is mythical, then it is immortal, but if it is not mythical then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical if it is horned. Q: Is the unicorn mythical? Magical? Horned? ...
Chapter 1 Logic and Set Theory
... The relation between intuition and formal rigor is not a trivial matter. Intuition tells us what is important, what might be true, and what mathematical tools may be used to prove it. Rigorous proofs are used to verify that a given statement that appears intuitively true is indeed true. Ultimately, ...
... The relation between intuition and formal rigor is not a trivial matter. Intuition tells us what is important, what might be true, and what mathematical tools may be used to prove it. Rigorous proofs are used to verify that a given statement that appears intuitively true is indeed true. Ultimately, ...
Modus Ponens Defended
... It is commonly thought that logically valid arguments play some kind of special normative role in our epistemic practices. From the first-person standpoint of deliberation and the related second-person standpoint of advice—which is an attempt to aid in another’s deliberation—logically valid argument ...
... It is commonly thought that logically valid arguments play some kind of special normative role in our epistemic practices. From the first-person standpoint of deliberation and the related second-person standpoint of advice—which is an attempt to aid in another’s deliberation—logically valid argument ...
Beginning Logic - University of Notre Dame
... IV. Analysis of arguments We will apply all three of the tools above to analyze arguments. We will translate our argument into an appropriate language and then use proof and/or truth analysis to determine whether the argument is valid. For an argument that translates successfully into propositional ...
... IV. Analysis of arguments We will apply all three of the tools above to analyze arguments. We will translate our argument into an appropriate language and then use proof and/or truth analysis to determine whether the argument is valid. For an argument that translates successfully into propositional ...
Sections 1.7 and 1.8
... Biconditional-if a conditional statement and its converse are both true, the statement is said to be biconditional. ...
... Biconditional-if a conditional statement and its converse are both true, the statement is said to be biconditional. ...
Propositional logic - Computing Science
... [Q] How to formalize/validate our arguments? Argument = premises (proposition or statement) + conclusion To have confidence in the conclusion in your argument, the premises should be acceptable on their own merits or follow from other statements that are known to be true. [Q] Any logical forms for v ...
... [Q] How to formalize/validate our arguments? Argument = premises (proposition or statement) + conclusion To have confidence in the conclusion in your argument, the premises should be acceptable on their own merits or follow from other statements that are known to be true. [Q] Any logical forms for v ...
Flowchart Thinking
... So far, you have been writing explanations as paragraph proofs. Example A in your book is an example. Read this example and make sure you understand the proof. When a logical argument is complex or includes many steps, a paragraph proof may not be the clearest way to present the steps. In such cases ...
... So far, you have been writing explanations as paragraph proofs. Example A in your book is an example. Read this example and make sure you understand the proof. When a logical argument is complex or includes many steps, a paragraph proof may not be the clearest way to present the steps. In such cases ...
Chapter 1 Logic and Set Theory
... The relation between intuition and formal rigor is not a trivial matter. Intuition tells us what is important, what might be true, and what mathematical tools may be used to prove it. Rigorous proofs are used to verify that a given statement that appears intuitively true is indeed true. Ultimately, ...
... The relation between intuition and formal rigor is not a trivial matter. Intuition tells us what is important, what might be true, and what mathematical tools may be used to prove it. Rigorous proofs are used to verify that a given statement that appears intuitively true is indeed true. Ultimately, ...
Diagrams in logic and mathematics - CFCUL
... “the laws of logic are not sculpted in stone, eternal and immutable. A realistic look at the development of mathematics shows that the reasons for a theorem are found only after digging deep and focusing upon the possibility of a theorem. The discovery of such hidden reasons is the work of the mathe ...
... “the laws of logic are not sculpted in stone, eternal and immutable. A realistic look at the development of mathematics shows that the reasons for a theorem are found only after digging deep and focusing upon the possibility of a theorem. The discovery of such hidden reasons is the work of the mathe ...
Basics in Mathematical Logic 1 Assertions
... An interesting mathematical statement (= assertion) is usually called a theorem or a proposition. A lemma is a statement which is itself not that important, but is useful to prove a theorem or a proposition. Statements typically have the form "A ) B"; where A is a - possibly combined - statement (th ...
... An interesting mathematical statement (= assertion) is usually called a theorem or a proposition. A lemma is a statement which is itself not that important, but is useful to prove a theorem or a proposition. Statements typically have the form "A ) B"; where A is a - possibly combined - statement (th ...
Lecture 11 Artificial Intelligence Predicate Logic
... • Representing knowledge using logic is appealing because you can derive new knowledge from old mathematical deduction. • In this formalism you can conclude that a new statement is true if by proving that it follows from the statement that are already known. • It provides a way of deducing new state ...
... • Representing knowledge using logic is appealing because you can derive new knowledge from old mathematical deduction. • In this formalism you can conclude that a new statement is true if by proving that it follows from the statement that are already known. • It provides a way of deducing new state ...
Lecture 4 - Michael De
... Assume that instead of interpreting i as a gap, we interpret it as a glut. But then taking the value i means being both true and false, and hence true, and hence designated. So we need to add i to D. The resulting logic is called LP, or the Logic of Paradox, as Priest originally called it. It is the ...
... Assume that instead of interpreting i as a gap, we interpret it as a glut. But then taking the value i means being both true and false, and hence true, and hence designated. So we need to add i to D. The resulting logic is called LP, or the Logic of Paradox, as Priest originally called it. It is the ...
2.2 Conditional Statements
... you will get the job” It is vacuously true if you do not show up for work Monday morning. In general, when the “if” part of an if-then statement is false, the statement as a whole is said to be true, regardless of whether the conclusion is true or false. ...
... you will get the job” It is vacuously true if you do not show up for work Monday morning. In general, when the “if” part of an if-then statement is false, the statement as a whole is said to be true, regardless of whether the conclusion is true or false. ...
Homework 1
... (that is, if x12 = 8, x13 = 3, x22 = 6 and so on), then x11 = 9. Proof: Suppose x11 = 9. Then since square(1, 1) = square(2, 1) = square(2, 2) = square(2, 3), rule 4 tells us that none of x21 , x22 , nor x23 can be 9. Similarly, since x37 = 9, none of x27 , x28 , nor x29 can be 9. Thus by rule 2 (wi ...
... (that is, if x12 = 8, x13 = 3, x22 = 6 and so on), then x11 = 9. Proof: Suppose x11 = 9. Then since square(1, 1) = square(2, 1) = square(2, 2) = square(2, 3), rule 4 tells us that none of x21 , x22 , nor x23 can be 9. Similarly, since x37 = 9, none of x27 , x28 , nor x29 can be 9. Thus by rule 2 (wi ...