LOGICAL CONSEQUENCE AS TRUTH-PRESERVATION STEPHEN READ Abstract
... What these proofs show is that, if we suppose that 3 represents implication (real implication), then an impossible proposition implies any proposition, and if ⊃ represents implication, even a false proposition implies any other. Neither proof shows that these are sound principles about implication. ...
... What these proofs show is that, if we suppose that 3 represents implication (real implication), then an impossible proposition implies any proposition, and if ⊃ represents implication, even a false proposition implies any other. Neither proof shows that these are sound principles about implication. ...
slides - Computer and Information Science
... • If there are n different atomic propositions in some formula, then there are different lines in the truth table for that formula. (This is because each proposition can take one 1of 2 values—i.e., true or false.) • Let us write T for truth, and F for falsity. Then the truth table for p q is: ...
... • If there are n different atomic propositions in some formula, then there are different lines in the truth table for that formula. (This is because each proposition can take one 1of 2 values—i.e., true or false.) • Let us write T for truth, and F for falsity. Then the truth table for p q is: ...
Syllogisms and Fallacies 101
... It basically asserts two commonplaces, that peas are good for you and that you should eat what’s good for you. If both premises are true in this case, then the conclusion follows. The only way to establish a fallacy here would be to disprove one of the premises. Enthymeme: No snakes have fur because ...
... It basically asserts two commonplaces, that peas are good for you and that you should eat what’s good for you. If both premises are true in this case, then the conclusion follows. The only way to establish a fallacy here would be to disprove one of the premises. Enthymeme: No snakes have fur because ...
Propositional Logic and Methods of Inference
... symbols of logic, which is the study of the rules of exact reasoning. Logic is also of primary importance in expert systems in which the inference engine reasons from facts to conclusions. A descriptive term for logic programming and expert systems is automated reasoning systems. ...
... symbols of logic, which is the study of the rules of exact reasoning. Logic is also of primary importance in expert systems in which the inference engine reasons from facts to conclusions. A descriptive term for logic programming and expert systems is automated reasoning systems. ...
Logic and Proofs1 1 Overview. 2 Sentential Connectives.
... The symbols ∀ (“for all” or “for every”) and ∃ (“there exists”) are quantifiers. There are a number of important subtleties involving quantifiers. The first subtlety is that, in the math that we will be using, a sentence is well formulated only if every variable is bound by a quantifier. In practice ...
... The symbols ∀ (“for all” or “for every”) and ∃ (“there exists”) are quantifiers. There are a number of important subtleties involving quantifiers. The first subtlety is that, in the math that we will be using, a sentence is well formulated only if every variable is bound by a quantifier. In practice ...
Chapter 15 Logic Name Date Objective: Students will use
... Propositions are statements that may be true or false. Propositions may be indeterminate - a proposition that is not certain. Notations used for propositions Letters such as p, q, and r are used to represent propositions. ...
... Propositions are statements that may be true or false. Propositions may be indeterminate - a proposition that is not certain. Notations used for propositions Letters such as p, q, and r are used to represent propositions. ...
logical axiom
... ponens”, which states that from formulas A and A → B, one my deduce B. It is easy to see that this rule preserves logical validity. The axioms, together with modus ponens, form a sound deductive system for the classical propositional logic. In addition, it is also complete. Note that in the above se ...
... ponens”, which states that from formulas A and A → B, one my deduce B. It is easy to see that this rule preserves logical validity. The axioms, together with modus ponens, form a sound deductive system for the classical propositional logic. In addition, it is also complete. Note that in the above se ...
p q
... Common phrasings for the biconditional • p if and only if q • p is necessary and equivalent for q • p is equivalent to q ...
... Common phrasings for the biconditional • p if and only if q • p is necessary and equivalent for q • p is equivalent to q ...
Logic and Proof
... rise to contradiction (someone loves and does not loves Jill). • We must demonstrate that our specification does not draw the wrong inferences. • We must demonstrate that what we claim holds in the specification does hold. • The demonstration should be given as a proof, which is a systematic way to ...
... rise to contradiction (someone loves and does not loves Jill). • We must demonstrate that our specification does not draw the wrong inferences. • We must demonstrate that what we claim holds in the specification does hold. • The demonstration should be given as a proof, which is a systematic way to ...
CPS130, Lecture 1: Introduction to Algorithms
... theorems are sometimes called lemmas or propositions and immediate consequences of theorems are sometimes called corollaries. Sometimes hypotheses are only implicitly stated; for example, they may be a basic property of the integers when proving something in that context. A valid argument is one suc ...
... theorems are sometimes called lemmas or propositions and immediate consequences of theorems are sometimes called corollaries. Sometimes hypotheses are only implicitly stated; for example, they may be a basic property of the integers when proving something in that context. A valid argument is one suc ...
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: ...
Mathematical Logic
... Learning Objectives • Learn how to use logical connectives to combine statements • Explore how to draw conclusions using various argument forms • Become familiar with quantifiers and predicates • Learn various proof techniques • Explore what an algorithm is dww-logic ...
... Learning Objectives • Learn how to use logical connectives to combine statements • Explore how to draw conclusions using various argument forms • Become familiar with quantifiers and predicates • Learn various proof techniques • Explore what an algorithm is dww-logic ...
The Discovery of the Computer
... expressed in a logical system is true or false, without producing all the possible theorems of the system. This so-called “decision problem” was answered by Alan Turing, who showed that it is not possible to decide if any theorem is true or false. In doing this, he discovered the computer. The story ...
... expressed in a logical system is true or false, without producing all the possible theorems of the system. This so-called “decision problem” was answered by Alan Turing, who showed that it is not possible to decide if any theorem is true or false. In doing this, he discovered the computer. The story ...
ch1_Logic_and_proofs
... 2. Show that ~p is also true. 3. Then we have that p ^ (~p) is true. 4. But this is impossible, since the statement p ^ (~p) is always false. There is a contradiction! 5. So, q cannot be false and therefore it is true. ...
... 2. Show that ~p is also true. 3. Then we have that p ^ (~p) is true. 4. But this is impossible, since the statement p ^ (~p) is always false. There is a contradiction! 5. So, q cannot be false and therefore it is true. ...
Intuitionistic Logic
... disproof of p. But being able to disprove the possibility of a disproof of p isn’t itself a proof of p. Notice that the clauses for conjunction and disjunction (and, in quantification theory, ∃) are classical. The fragment of intuitionistic logic consisting just of ∧ and ∨ is identical to a similar ...
... disproof of p. But being able to disprove the possibility of a disproof of p isn’t itself a proof of p. Notice that the clauses for conjunction and disjunction (and, in quantification theory, ∃) are classical. The fragment of intuitionistic logic consisting just of ∧ and ∨ is identical to a similar ...
Part3
... Example: Suppose that two people play a game taking turns removing, 1, 2, or 3 stones at a time from a pile that begins with 15 stones. The person who removes the last stone wins the game. Show that the first player can win the game no matter what the second player does. Proof: Let n be the last ste ...
... Example: Suppose that two people play a game taking turns removing, 1, 2, or 3 stones at a time from a pile that begins with 15 stones. The person who removes the last stone wins the game. Show that the first player can win the game no matter what the second player does. Proof: Let n be the last ste ...
CS173: Discrete Math
... • P: “you can take the flight”, q: “you buy a ticket” • P q: “You can take the flight if and only if you buy a ticket” – This statement is true • If you buy a ticket and take the flight • If you do not buy a ticket and you cannot take the flight ...
... • P: “you can take the flight”, q: “you buy a ticket” • P q: “You can take the flight if and only if you buy a ticket” – This statement is true • If you buy a ticket and take the flight • If you do not buy a ticket and you cannot take the flight ...
Argumentations and logic
... later realize that they had not settled it at all. Some propositions thought to be known to be true are not really known to be true. In fact, some of them are false. Some propositions thought to be known to be false are not really known to be false. In fact, some of them are true. Hypotheses excite ...
... later realize that they had not settled it at all. Some propositions thought to be known to be true are not really known to be true. In fact, some of them are false. Some propositions thought to be known to be false are not really known to be false. In fact, some of them are true. Hypotheses excite ...
Sample Exam 1 - Moodle
... CSC 4-151 Discrete Mathematics for Computer Science Exam 1 May 7, 2017 ____________________ name For credit on these problems, you must show your work. On this exam, take the natural numbers to be N = {0,1,2,3, …}. 1. (6 pts.) State and prove one of DeMorgan’s Laws for propositional logic, using a t ...
... CSC 4-151 Discrete Mathematics for Computer Science Exam 1 May 7, 2017 ____________________ name For credit on these problems, you must show your work. On this exam, take the natural numbers to be N = {0,1,2,3, …}. 1. (6 pts.) State and prove one of DeMorgan’s Laws for propositional logic, using a t ...
p q
... proposition p, axioms and proven theorems so that the truth of proposition q is obtained. Example: For all real numbers d, d1, d2, and x, if d=min{d1,d2} and xd, then xd1 and xd2. Proof. From the definition of min, it follows that dd1 and dd2. From xd and dd1, we may derive xd1 by the transi ...
... proposition p, axioms and proven theorems so that the truth of proposition q is obtained. Example: For all real numbers d, d1, d2, and x, if d=min{d1,d2} and xd, then xd1 and xd2. Proof. From the definition of min, it follows that dd1 and dd2. From xd and dd1, we may derive xd1 by the transi ...
Rhetorical Analysis
... Syntax (choices in sentence lengths and structure—short, choppy sentences to deliver emphatic, powerful convictions? Or long, fluid sentences to deliver a ...
... Syntax (choices in sentence lengths and structure—short, choppy sentences to deliver emphatic, powerful convictions? Or long, fluid sentences to deliver a ...
Mathematics for Computer Science/Software Engineering
... Heuristic justification for this definition: if p is true and q is false, then the statement ‘if p is true then q is true’ obviously cannot be true, and therefore must be false. On the other hand, if p is false, then the statement ‘if p is true then ...’ is an empty statement—it is saying nothing at ...
... Heuristic justification for this definition: if p is true and q is false, then the statement ‘if p is true then q is true’ obviously cannot be true, and therefore must be false. On the other hand, if p is false, then the statement ‘if p is true then ...’ is an empty statement—it is saying nothing at ...
Geometry Notes 2.2 Logic Determining Truths Values
... Geometry Notes 2.2 Logic Determining Truths Values 1. __________________________ - a sentence that is either true or false A. _______________________ of a statement is either true or false (determining if it is true or false) B. Statements are represented by letters ___ and ____, ____ Example: p: A ...
... Geometry Notes 2.2 Logic Determining Truths Values 1. __________________________ - a sentence that is either true or false A. _______________________ of a statement is either true or false (determining if it is true or false) B. Statements are represented by letters ___ and ____, ____ Example: p: A ...