Logic - UNM Computer Science
... Definition 1 Logic is the discipline that studies the method of reasoning. The discipline of logic aims to abstract our thought process and rigorously formalize the rules of inferences. In this course, we study logic to help us form valid arguments and construct correct proofs. However, it would be ...
... Definition 1 Logic is the discipline that studies the method of reasoning. The discipline of logic aims to abstract our thought process and rigorously formalize the rules of inferences. In this course, we study logic to help us form valid arguments and construct correct proofs. However, it would be ...
On the Complexity of Linking Deductive and Abstract Argument
... the two, minimality is generally regarded as an aesthetic criterion, rather than technically essential. Consistency is more important, and of course by relaxing this constraint we admit into our analysis some scenarios that do not seem to have any useful interpretation; but of course this does not i ...
... the two, minimality is generally regarded as an aesthetic criterion, rather than technically essential. Consistency is more important, and of course by relaxing this constraint we admit into our analysis some scenarios that do not seem to have any useful interpretation; but of course this does not i ...
Artificial Intelligence
... method for artificial intelligence, however, it is often the case that when using propositional logic, the meanings of these symbols are very important. • The beauty of this representation is that it is possible for a computer to reason about them in a very general way, without needing to know much ...
... method for artificial intelligence, however, it is often the case that when using propositional logic, the meanings of these symbols are very important. • The beauty of this representation is that it is possible for a computer to reason about them in a very general way, without needing to know much ...
CS 40: Foundations of Computer Science
... b)This question concerns ¬ e → ¬ s. This is equivalent to its contrapositive, s → e. That doesn't seem to follow from our assumptions, so let's find a case in which the assumptions hold but this conditional statement does not. This conditional statement fails in the case in which s is true and e is ...
... b)This question concerns ¬ e → ¬ s. This is equivalent to its contrapositive, s → e. That doesn't seem to follow from our assumptions, so let's find a case in which the assumptions hold but this conditional statement does not. This conditional statement fails in the case in which s is true and e is ...
One Problem with the Material Conditional
... So the denial of (G -> A) is (G & ~A) But wait! This affirms that G (the antecedent) is True and A (the consequent) is false But using our example sentence, this entails that “God exists” is True! So, counter-intuitively, the person who denies that an All-powerful being exists if God exists is logic ...
... So the denial of (G -> A) is (G & ~A) But wait! This affirms that G (the antecedent) is True and A (the consequent) is false But using our example sentence, this entails that “God exists” is True! So, counter-intuitively, the person who denies that an All-powerful being exists if God exists is logic ...
File
... • Reply to Russell on the world as a ‘brute fact’: to ignore the question of how the world arose is to reject a question fundamental to human existence. • Objection to the ‘plurality of causes’ argument: one might apply Ockham’s Razor to the issue of the nature of the first cause (why multiply the c ...
... • Reply to Russell on the world as a ‘brute fact’: to ignore the question of how the world arose is to reject a question fundamental to human existence. • Objection to the ‘plurality of causes’ argument: one might apply Ockham’s Razor to the issue of the nature of the first cause (why multiply the c ...
Propositional Logic Predicate Logic
... Definition. A formula A is valid if A is true no matter how we replace the individual constants in A with concrete individuals and the predicate variables in A with concrete predicates. Note. The set of individuals must be instantiated to a non-empty set. This the reason why (∀x.P (x)) ⇒ (∃x.P (x)) ...
... Definition. A formula A is valid if A is true no matter how we replace the individual constants in A with concrete individuals and the predicate variables in A with concrete predicates. Note. The set of individuals must be instantiated to a non-empty set. This the reason why (∀x.P (x)) ⇒ (∃x.P (x)) ...
Critical Terminology for Theory of Knowledge
... believing that p independently of any evidence in favor of p provided by any other proposition that S believes. For example, a belief in a self-evident truth such as All squares are squares is basic for anyone who understands the meanings of the terms. But arguably not all basic beliefs are analytic ...
... believing that p independently of any evidence in favor of p provided by any other proposition that S believes. For example, a belief in a self-evident truth such as All squares are squares is basic for anyone who understands the meanings of the terms. But arguably not all basic beliefs are analytic ...
Scoring Rubric for Assignment 1
... unclear. Theory is not relevant or only relevant for some aspects; theory is not clearly articulated and/or has incorrect or incomplete components. Relationship between theory and research is unclear or inaccurate, major errors in the logic are present. 0 – 4 pts Conclusion may not be clear and the ...
... unclear. Theory is not relevant or only relevant for some aspects; theory is not clearly articulated and/or has incorrect or incomplete components. Relationship between theory and research is unclear or inaccurate, major errors in the logic are present. 0 – 4 pts Conclusion may not be clear and the ...
Sentential Logic 2 - Michael Johnson's Homepage
... We say that an argument is deductively valid when it has the following property: If the premises of the argument are true, then the conclusion of the argument must be true. A valid argument is “truth-preserving”: the truth of the premises gets passed on to the ...
... We say that an argument is deductively valid when it has the following property: If the premises of the argument are true, then the conclusion of the argument must be true. A valid argument is “truth-preserving”: the truth of the premises gets passed on to the ...
Modus ponens
... of definition" and the "rule of substitution". Modus ponens allows one to eliminate a conditional statement from a logical proof or argument (the antecedents) and thereby not carry these antecedents forward in an everlengthening string of symbols; for this reason modus ponens is sometimes called the ...
... of definition" and the "rule of substitution". Modus ponens allows one to eliminate a conditional statement from a logical proof or argument (the antecedents) and thereby not carry these antecedents forward in an everlengthening string of symbols; for this reason modus ponens is sometimes called the ...
Slides - UCSD CSE
... For the formula to be true, if p is true, then q can’t be false. If p is false, the formula is true ...
... For the formula to be true, if p is true, then q can’t be false. If p is false, the formula is true ...
Reasoning without Contradiction
... result. But I think that this is untrue and that a case can be made that reasoning without contradiction has some very beneficial consequences. Limitations of space prevent me giving more than a sketch, but I set out the argument in such a way that the reader can easily identify where, if anywhere, ...
... result. But I think that this is untrue and that a case can be made that reasoning without contradiction has some very beneficial consequences. Limitations of space prevent me giving more than a sketch, but I set out the argument in such a way that the reader can easily identify where, if anywhere, ...
The Ontological argument 2
... female monarch’ 2) To explain there actually is something: ‘there is such a thing as a vampire’. ...
... female monarch’ 2) To explain there actually is something: ‘there is such a thing as a vampire’. ...
The Ontological argument 2
... female monarch’ 2) To explain there actually is something: ‘there is such a thing as a vampire’. ...
... female monarch’ 2) To explain there actually is something: ‘there is such a thing as a vampire’. ...
sentential logic
... that if the first sentence is true, then second sentence must be false. And if second sentence is true, then first sentence must be false. It can not be case that both of these sentences are true. If a set of sentences could not all be true at same time, like above two sentences, they are said to be ...
... that if the first sentence is true, then second sentence must be false. And if second sentence is true, then first sentence must be false. It can not be case that both of these sentences are true. If a set of sentences could not all be true at same time, like above two sentences, they are said to be ...
The Ontological Argument is a logical sleight of hand
... A pixie is a little man with pointed ears. Therefore there actually exists a pixie. Davies further suggested that if a pixie had to exist in order to have the pointy ears, people would accept that without further disagreement. Despite all the criticisms, the ontological argument does also have its s ...
... A pixie is a little man with pointed ears. Therefore there actually exists a pixie. Davies further suggested that if a pixie had to exist in order to have the pointy ears, people would accept that without further disagreement. Despite all the criticisms, the ontological argument does also have its s ...
Implication
... We assume 0 = 1 and show that ‘I am the Pope’ follows. 0 = 1, by adding 1 to both sides we conclude that 1 = 2. The Pope and I are two. But 2 = 1, hence the Pope and I are one and the same! The word any is very important here. It means literally anything, including things which are true. It is a c ...
... We assume 0 = 1 and show that ‘I am the Pope’ follows. 0 = 1, by adding 1 to both sides we conclude that 1 = 2. The Pope and I are two. But 2 = 1, hence the Pope and I are one and the same! The word any is very important here. It means literally anything, including things which are true. It is a c ...
Logical Arguments - Computer Science, Stony Brook University
... • The key fact about a valid argument is that the truth of the conclusion must necessarily follow from the truth of the premises • One way to determine the validity of an argument is by creating a truth table showing the truth values of all the premises and the conclusion • A row of the truth table ...
... • The key fact about a valid argument is that the truth of the conclusion must necessarily follow from the truth of the premises • One way to determine the validity of an argument is by creating a truth table showing the truth values of all the premises and the conclusion • A row of the truth table ...
Deductive Reasoning
... • Sherlock Holmes knows that whoever was in the kitchen stole the tomatoes • Sherlock Holmes discovers that Mrs. Hudson was in the kitchen • What can he conclude? ...
... • Sherlock Holmes knows that whoever was in the kitchen stole the tomatoes • Sherlock Holmes discovers that Mrs. Hudson was in the kitchen • What can he conclude? ...
323-670 ปัญญาประดิษฐ์ (Artificial Intelligence)
... • Proof is a sequence of sentences First ones are premises (KB) Then, you can write down on line j the result of applying an inference rule to previous lines When f is on a line, you know KB f If inference rules are sound, then KB f ...
... • Proof is a sequence of sentences First ones are premises (KB) Then, you can write down on line j the result of applying an inference rule to previous lines When f is on a line, you know KB f If inference rules are sound, then KB f ...
Chapter 4. Logical Notions This chapter introduces various logical
... representing the form of m-formulas. Thus (p1Zp2) (viewed now as a metaformula) represents a form whose only instance is the formula (p1Zp2) itself, while (AZB) represents a form whose instances are all the disjunctive formulas. Of course, these formula instances will themselves have 'ordinary' sen ...
... representing the form of m-formulas. Thus (p1Zp2) (viewed now as a metaformula) represents a form whose only instance is the formula (p1Zp2) itself, while (AZB) represents a form whose instances are all the disjunctive formulas. Of course, these formula instances will themselves have 'ordinary' sen ...
Basic Logic - Progetto e
... assume that “All men are mortal” and that “Socratis is a man” and hence conclude “Socratis is mortal”. Here, it is intuitively clear that, if the premises are true, then also the conclusi ...
... assume that “All men are mortal” and that “Socratis is a man” and hence conclude “Socratis is mortal”. Here, it is intuitively clear that, if the premises are true, then also the conclusi ...
Thursday Feb 9, at 1:00
... (c) Emma likes all fine restaurants. Emma likes the restaurant “Le Cordon Bleu”. Therefore, “Le Cordon Bleu” is a fine restaurant. Let the domain be the domain of all restaurants, and let F (x) be the predicate “x is a fine restaurant” and L(x) be the predicate “Emma likes x.” Then the argument as s ...
... (c) Emma likes all fine restaurants. Emma likes the restaurant “Le Cordon Bleu”. Therefore, “Le Cordon Bleu” is a fine restaurant. Let the domain be the domain of all restaurants, and let F (x) be the predicate “x is a fine restaurant” and L(x) be the predicate “Emma likes x.” Then the argument as s ...
Logic 3
... Tautologies • 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, ...
... Tautologies • 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, ...