Set Theory and Logic
... Many sets cannot be listed so easily (or at all for that matter), and in many of these cases it is convenient to use a rule to specify a set. For example, suppose we want to define a set S that consists of all real numbers between −1 and 1, inclusive. We use the notation S = {x|x ∈ R and − 1 ≤ x ≤ 1 ...
... Many sets cannot be listed so easily (or at all for that matter), and in many of these cases it is convenient to use a rule to specify a set. For example, suppose we want to define a set S that consists of all real numbers between −1 and 1, inclusive. We use the notation S = {x|x ∈ R and − 1 ≤ x ≤ 1 ...
Exam 1 Solutions for Spring 2014
... 4. (10 points) A number n is a multiple of 3 if n = 3k for some integer k. Prove that if n2 is a multiple of 3, then n is a multiple of 3. Graded by Stacy Note: This question should have specified that n is an integer. To help compensate for this omission, the lowest score you can receive on this qu ...
... 4. (10 points) A number n is a multiple of 3 if n = 3k for some integer k. Prove that if n2 is a multiple of 3, then n is a multiple of 3. Graded by Stacy Note: This question should have specified that n is an integer. To help compensate for this omission, the lowest score you can receive on this qu ...
Logical Implications
... The conditional if-then used in several programming languages should not be confused with logical implications. Suppose we encounter if p then S in some programming language, the statement S will be executed if p is true. If p is false, statement S will not be executed. In general, S is not a statem ...
... The conditional if-then used in several programming languages should not be confused with logical implications. Suppose we encounter if p then S in some programming language, the statement S will be executed if p is true. If p is false, statement S will not be executed. In general, S is not a statem ...
Notes5
... In this part of the course we consider logic. Logic is used in many places in computer science including digital circuit design, relational databases, automata theory and computability, and artificial intelligence. We start with propositional logic, using symbols to stand for things that can be eith ...
... In this part of the course we consider logic. Logic is used in many places in computer science including digital circuit design, relational databases, automata theory and computability, and artificial intelligence. We start with propositional logic, using symbols to stand for things that can be eith ...
Introduction to Logic What is Logic? Simple Statements Which one is
... exclusively upon the truth values of its variables. The truth value of a proposition is known once the truth values of its variables are known. (See E.g. 30 - 32) ...
... exclusively upon the truth values of its variables. The truth value of a proposition is known once the truth values of its variables are known. (See E.g. 30 - 32) ...
F - Teaching-WIKI
... conclusions) from statements that are assumed to be true (called premises) • Natural language is not precise, so the careless use of logic can lead to claims that false statements are true, or to claims that a statement is true, even tough its truth does not necessarily follow from the premises => L ...
... conclusions) from statements that are assumed to be true (called premises) • Natural language is not precise, so the careless use of logic can lead to claims that false statements are true, or to claims that a statement is true, even tough its truth does not necessarily follow from the premises => L ...
Slides from 10/20/14
... --if there is a tilde, the quantifier applies to the tilde and to whatever the tilde applies to --if there is a parenthesis (or bracket), the quantifier applies to everything in that pair of parentheses (or brackets) A variable is bound if and only if it is within the scope of a quantifier that con ...
... --if there is a tilde, the quantifier applies to the tilde and to whatever the tilde applies to --if there is a parenthesis (or bracket), the quantifier applies to everything in that pair of parentheses (or brackets) A variable is bound if and only if it is within the scope of a quantifier that con ...
Elements of Persuasion
... Thesis – the statement that describes the main point/controlling idea of a composition/essay ...
... Thesis – the statement that describes the main point/controlling idea of a composition/essay ...
2/TRUTH-FUNCTIONS
... factually; 2. that both alternatives are in fact possible. The exclusion of joined truth gives the idea of a strict disjunction. Its symbolic formulation: [(pvq).-(p.q)] In logic, as in mathematics, the `or’ is gen. used in its inclusive sense. This is preferred since it provides a minimal common me ...
... factually; 2. that both alternatives are in fact possible. The exclusion of joined truth gives the idea of a strict disjunction. Its symbolic formulation: [(pvq).-(p.q)] In logic, as in mathematics, the `or’ is gen. used in its inclusive sense. This is preferred since it provides a minimal common me ...
T - STI Innsbruck
... conclusions) from statements that are assumed to be true (called premises) • Natural language is not precise, so the careless use of logic can lead to claims that false statements are true, or to claims that a statement is true, even tough its truth does not necessarily follow from the premises => L ...
... conclusions) from statements that are assumed to be true (called premises) • Natural language is not precise, so the careless use of logic can lead to claims that false statements are true, or to claims that a statement is true, even tough its truth does not necessarily follow from the premises => L ...
02_Artificial_Intelligence-PropositionalLogic
... conclusions) from statements that are assumed to be true (called premises) • Natural language is not precise, so the careless use of logic can lead to claims that false statements are true, or to claims that a statement is true, even though its truth does not necessarily follow from the premises => ...
... conclusions) from statements that are assumed to be true (called premises) • Natural language is not precise, so the careless use of logic can lead to claims that false statements are true, or to claims that a statement is true, even though its truth does not necessarily follow from the premises => ...
F - Teaching-WIKI
... conclusions) from statements that are assumed to be true (called premises) • Natural language is not precise, so the careless use of logic can lead to claims that false statements are true, or to claims that a statement is true, even tough its truth does not necessarily follow from the premises => L ...
... conclusions) from statements that are assumed to be true (called premises) • Natural language is not precise, so the careless use of logic can lead to claims that false statements are true, or to claims that a statement is true, even tough its truth does not necessarily follow from the premises => L ...
T - STI Innsbruck
... conclusions) from statements that are assumed to be true (called premises) • Natural language is not precise, so the careless use of logic can lead to claims that false statements are true, or to claims that a statement is true, even tough its truth does not necessarily follow from the premises => L ...
... conclusions) from statements that are assumed to be true (called premises) • Natural language is not precise, so the careless use of logic can lead to claims that false statements are true, or to claims that a statement is true, even tough its truth does not necessarily follow from the premises => L ...
Logic - Humble ISD
... Get Ready To Be Logical! • 1. Books and notebooks out. • 2. Supplies ready to go. • 3. Answer the following: The sum of 2 positive integers is ___________ True or False ...
... Get Ready To Be Logical! • 1. Books and notebooks out. • 2. Supplies ready to go. • 3. Answer the following: The sum of 2 positive integers is ___________ True or False ...
(P Q). - Snistnote
... The theory associated with such rules is known as inference theory because it is concerned with the inferring of a conclusion from certain premises. When a conclusion is derived from a set of premises by using the accepted rules of reasoning, then such a process of ...
... The theory associated with such rules is known as inference theory because it is concerned with the inferring of a conclusion from certain premises. When a conclusion is derived from a set of premises by using the accepted rules of reasoning, then such a process of ...
Introduction to proposition
... two squares”. Logic is the basis of all mathematical reasoning. It has practical applications to the design of computing machines, to the specification of systems, to artificial intelligence, to computer programming, to programming languages, and to other areas of computer science, as well as too ma ...
... two squares”. Logic is the basis of all mathematical reasoning. It has practical applications to the design of computing machines, to the specification of systems, to artificial intelligence, to computer programming, to programming languages, and to other areas of computer science, as well as too ma ...
Introduction to logic
... 1. Logic and Artificial Intelligence: some historical remarks One of the aims of AI is to reproduce human features by means of a computer system. One of these features is reasoning. Reasoning can be viewed as the process of having a knowledge base (KB) and manipulating it to create new knowledge. Re ...
... 1. Logic and Artificial Intelligence: some historical remarks One of the aims of AI is to reproduce human features by means of a computer system. One of these features is reasoning. Reasoning can be viewed as the process of having a knowledge base (KB) and manipulating it to create new knowledge. Re ...
The Logic of Atomic Sentences
... What it takes for an argument to be good (correct): How to demonstrate that an inference is valid: a proof A proof breaks a non-obvious inference down into a series of trivial, obvious steps which lead you from the premises to the conclusion These steps are based on facts about the meaning of the te ...
... What it takes for an argument to be good (correct): How to demonstrate that an inference is valid: a proof A proof breaks a non-obvious inference down into a series of trivial, obvious steps which lead you from the premises to the conclusion These steps are based on facts about the meaning of the te ...
Combining Paraconsistent Logic with Argumentation
... no matter what, while if the rule is defeasible, its consequent must be accepted if there are no good reasons not to accept it. Arguments can be attacked on their (ordinary) premises and on their applications of defeasible inference rules. Some attacks succeed as defeats, which is partly determined ...
... no matter what, while if the rule is defeasible, its consequent must be accepted if there are no good reasons not to accept it. Arguments can be attacked on their (ordinary) premises and on their applications of defeasible inference rules. Some attacks succeed as defeats, which is partly determined ...
Full version - Villanova Computer Science
... A sequent is any finite sequence of formulas (in the sense of Slide 4.7). Here are the rules of one of several equivalent sequent calculus systems for classical propositional logic. Let us call it G1. In the following rules, E,F stand for any formulas, and G,H stand for any sequents. Above the horiz ...
... A sequent is any finite sequence of formulas (in the sense of Slide 4.7). Here are the rules of one of several equivalent sequent calculus systems for classical propositional logic. Let us call it G1. In the following rules, E,F stand for any formulas, and G,H stand for any sequents. Above the horiz ...
Between Truth and Falsity
... More precisely, for any conclusion supported by a finite set of premises, the conclusion must not have less truth than the premise with the least amount of truth. For example: Simon’s got hench (.6) Billiam’s got hench (.3) Therefore, both Simon and Billiam have got hench. (.3) This argument form i ...
... More precisely, for any conclusion supported by a finite set of premises, the conclusion must not have less truth than the premise with the least amount of truth. For example: Simon’s got hench (.6) Billiam’s got hench (.3) Therefore, both Simon and Billiam have got hench. (.3) This argument form i ...
Jordan Bradshaw, Virginia Walker, and Dylan Kane
... Mimics the natural reasoning process, inference rules natural to humans Called “natural” because does not require conversion to (unreadable) normal form ...
... Mimics the natural reasoning process, inference rules natural to humans Called “natural” because does not require conversion to (unreadable) normal form ...
Curry`s Paradox. An Argument for Trivialism
... MPP. We use a notion of naïve deducibility that, in our opinion, should be perfectly acceptable by Priest. In his discussion about Goedel’s theorem, Priest defends the naïve notion of proof: Proof, as understood by mathematicians (not logicians), is that process of deductive argumentation by which w ...
... MPP. We use a notion of naïve deducibility that, in our opinion, should be perfectly acceptable by Priest. In his discussion about Goedel’s theorem, Priest defends the naïve notion of proof: Proof, as understood by mathematicians (not logicians), is that process of deductive argumentation by which w ...
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 ...
1 Deductive Reasoning and Logical Connectives
... and make statements about these objects. For example, consider the statement: No matter what number might be chosen, if it is greater than 3, then its square is greater 9. We introduce a variable to replace the words referring to the number: No matter what number n might be chosen, if n is greater t ...
... and make statements about these objects. For example, consider the statement: No matter what number might be chosen, if it is greater than 3, then its square is greater 9. We introduce a variable to replace the words referring to the number: No matter what number n might be chosen, if n is greater t ...