Logic 3
... • Remember, Tautologies are always true. • Thus, if we can use different propositions and logical equivalences to show two statements are tautologies, we can do proofs. • Proofs are conditional and biconditional statements that are tautologies • Notation: p and q are atomic statements, while A and B ...
... • Remember, Tautologies are always true. • Thus, if we can use different propositions and logical equivalences to show two statements are tautologies, we can do proofs. • Proofs are conditional and biconditional statements that are tautologies • Notation: p and q are atomic statements, while A and B ...
Exercise
... P(x) it is not enough to show that P(a) is true for one or some a’s. 2. To show that a statement of the form x P(x) is FALSE, it is enough to show that P(a) is false for one a ...
... P(x) it is not enough to show that P(a) is true for one or some a’s. 2. To show that a statement of the form x P(x) is FALSE, it is enough to show that P(a) is false for one a ...
Logic - Disclaimer
... statements are claimed to follow from others, this may in fact not be the case. • Example: “If I win the lottery, then I’m happy. However, I did not win the lottery. Therefore, I am not happy.” • A piece of reasoning is valid if the statements that are claimed to follow from previous ones do indeed ...
... statements are claimed to follow from others, this may in fact not be the case. • Example: “If I win the lottery, then I’m happy. However, I did not win the lottery. Therefore, I am not happy.” • A piece of reasoning is valid if the statements that are claimed to follow from previous ones do indeed ...
PHIL 160: Introduction to Philosophy of Science
... PHIL 160 What is the kind of evidence that supports scientific hypotheses and/or theories? How strong is that evidence? Suppose a theory includes objects (such as quarks) or historical events/processes (such as geological or evolutionary events/processes) that are not directly observable? What kind ...
... PHIL 160 What is the kind of evidence that supports scientific hypotheses and/or theories? How strong is that evidence? Suppose a theory includes objects (such as quarks) or historical events/processes (such as geological or evolutionary events/processes) that are not directly observable? What kind ...
Resources - CSE, IIT Bombay
... One is allowed to write A1, A2, A3,… An-1 |- B |- B(AnB) |- (AnB); mp-rule ...
... One is allowed to write A1, A2, A3,… An-1 |- B |- B(AnB) |- (AnB); mp-rule ...
PDF
... In this entry, we show that the deduction theorem below holds for intuitionistic propositional logic. We use the axiom system provided in this entry. Theorem 1. If ∆, A `i B, where ∆ is a set of wff ’s of the intuitionistic propositional logic, then ∆ `i A → B. The proof is very similar to that of t ...
... In this entry, we show that the deduction theorem below holds for intuitionistic propositional logic. We use the axiom system provided in this entry. Theorem 1. If ∆, A `i B, where ∆ is a set of wff ’s of the intuitionistic propositional logic, then ∆ `i A → B. The proof is very similar to that of t ...
PDF
... You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. ...
... You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. ...
Introduction to Proofs, Rules of Equivalence, Rules of
... • Generate new lines whose truth value follows from, but is not identical to, the truth of the source lines. • Operate on lines whose statement forms match the statement forms of the lines in the argument form of the rule. • Can be applied ONLY to entire lines, not parts of lines. ...
... • Generate new lines whose truth value follows from, but is not identical to, the truth of the source lines. • Operate on lines whose statement forms match the statement forms of the lines in the argument form of the rule. • Can be applied ONLY to entire lines, not parts of lines. ...
the-right-to-your-opinion-summary
... Generally, it is a stubborn person’s last resort, considering that “they do so at just that point in an argument when they would otherwise be forced to admit error,” because it is a pointless statement which completely changes the subject of the entire argument (Whyte 414). Additionally, the stateme ...
... Generally, it is a stubborn person’s last resort, considering that “they do so at just that point in an argument when they would otherwise be forced to admit error,” because it is a pointless statement which completely changes the subject of the entire argument (Whyte 414). Additionally, the stateme ...
Notes - Conditional Statements and Logic.notebook
... A counterexample is one example that can prove an entire statement false. Example: If a number is prime, then it is an odd number. Counterexample: ...
... A counterexample is one example that can prove an entire statement false. Example: If a number is prime, then it is an odd number. Counterexample: ...
IS IT EASY TO LEARN THE LOGIC
... 6. The reason of the classic principles Frequently one encounters questions like, what is the use of logical principles if they are not used operationally like the De Morgan’s Laws or Modus Ponens? What is the importance of learning them and mention them? In colloquial language, saying “Mary studies ...
... 6. The reason of the classic principles Frequently one encounters questions like, what is the use of logical principles if they are not used operationally like the De Morgan’s Laws or Modus Ponens? What is the importance of learning them and mention them? In colloquial language, saying “Mary studies ...
pptx - CSE, IIT Bombay
... • We investigated the applicability of logic as a language for the representation of a number of medical reasoning models. • It was shown that the language of first-order predicate logic allowed for the precise, and compact, representation of these models. • Generally, in translating domain knowledg ...
... • We investigated the applicability of logic as a language for the representation of a number of medical reasoning models. • It was shown that the language of first-order predicate logic allowed for the precise, and compact, representation of these models. • Generally, in translating domain knowledg ...
Handout 14
... Why would we need a formal system? We are already able to construct wellformed formulas and decide on their truthfulness by means of a truth table. However, imagine we had a set of formulas M and we know that they are true – they represent our knowledge about a certain problem. We would then be inte ...
... Why would we need a formal system? We are already able to construct wellformed formulas and decide on their truthfulness by means of a truth table. However, imagine we had a set of formulas M and we know that they are true – they represent our knowledge about a certain problem. We would then be inte ...
Propositional Logic Proof
... Solve problems like Exercise Set 1.3, #1, 3, 4, 6-32, 36-44. Of these, we’re especially concerned about problems like 12-13 and 3944. Many of these problems go beyond the pre-class learning goals into the in-class goals, but they’re the tightest fit in the text. Complete the open-book, untimed quiz ...
... Solve problems like Exercise Set 1.3, #1, 3, 4, 6-32, 36-44. Of these, we’re especially concerned about problems like 12-13 and 3944. Many of these problems go beyond the pre-class learning goals into the in-class goals, but they’re the tightest fit in the text. Complete the open-book, untimed quiz ...
Slides - centria - Universidade Nova de Lisboa
... • Epistemology will acquire the ability to be shared: with robots, aliens or any other entity that needs cognition to survive and program its future. • Creating situated robots means carrying out our own cognitive evolution by new means, thereby engendering symbiotic, co-evolving, and selfaccelerati ...
... • Epistemology will acquire the ability to be shared: with robots, aliens or any other entity that needs cognition to survive and program its future. • Creating situated robots means carrying out our own cognitive evolution by new means, thereby engendering symbiotic, co-evolving, and selfaccelerati ...
10 Inference
... We have seen a truth table that shows the equivalence of the two statements earlier, in Section 8. Let us look at an example. ...
... We have seen a truth table that shows the equivalence of the two statements earlier, in Section 8. Let us look at an example. ...
Inquiry
An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.