powerpoint - IDA.LiU.se
... Vocabulary for a logic formula: set of symbols containing all those that occur in the formula (and maybe some more) Interpretation for a logic formula: a mapping from a vocabulary for it, to truth-values T or F Model for a logic formula: an interpretation where the value of the formula is T Joint vo ...
... Vocabulary for a logic formula: set of symbols containing all those that occur in the formula (and maybe some more) Interpretation for a logic formula: a mapping from a vocabulary for it, to truth-values T or F Model for a logic formula: an interpretation where the value of the formula is T Joint vo ...
CHAPTER 1 INTRODUCTION 1 Mathematical Paradoxes
... A more radical interpretation of the paradoxes has been advocated by Brower and his intuitionist school. They refuse to accept the universality of certain basic logical laws, such as the law of excluded middle: A or not A. Such a law, they claim, is true for finite sets, but it is invalid to extend ...
... A more radical interpretation of the paradoxes has been advocated by Brower and his intuitionist school. They refuse to accept the universality of certain basic logical laws, such as the law of excluded middle: A or not A. Such a law, they claim, is true for finite sets, but it is invalid to extend ...
1 Chapter 9: Deductive Reasoning
... She will order coffee or scotch with her lunch. She won’t order scotch, so she will order coffee. The truth of the first two premises guarantees the truth of the conclusion. You may notice, however, that there is nothing about the particular premises that makes the argument valid. Any argument of th ...
... She will order coffee or scotch with her lunch. She won’t order scotch, so she will order coffee. The truth of the first two premises guarantees the truth of the conclusion. You may notice, however, that there is nothing about the particular premises that makes the argument valid. Any argument of th ...
Logical Argument
... Fallacy of False Cause or Non Sequitur. The conclusion can be either true or false, but the argument is a fallacy because the conclusion does not follow from the premise. Any argument that takes the following form is a non sequitur: 1. If A then B. (e.g. If I am a cat then I am a mammal.) 2. B. (e.g ...
... Fallacy of False Cause or Non Sequitur. The conclusion can be either true or false, but the argument is a fallacy because the conclusion does not follow from the premise. Any argument that takes the following form is a non sequitur: 1. If A then B. (e.g. If I am a cat then I am a mammal.) 2. B. (e.g ...
Modus ponens
... Enderton, for example, observes that "modus ponens can produce shorter formulas from longer ones", and Russell observes that "the process of the inference cannot be reduced to symbols. Its sole record is the occurrence of ⊦q [the consequent] . . . an inference is the dropping of a true premise; it i ...
... Enderton, for example, observes that "modus ponens can produce shorter formulas from longer ones", and Russell observes that "the process of the inference cannot be reduced to symbols. Its sole record is the occurrence of ⊦q [the consequent] . . . an inference is the dropping of a true premise; it i ...
AI Principles, Semester 2, Week 2, Lecture 5 Propositional Logic
... (ii) NEGATION, if Φ is a wff, then the expression denoted by ¬Φ is also a wff (iii) CONJUNCTION, if Φ and Ψ are both wffs, then the expression denoted by ( Φ ∧ Ψ) is a wff (iv) DISJUNCTION if Φ and Ψ are both wffs, then the expression denoted by (Φ ∨ Ψ) is a wff (v) CONDITIONAL (with ANTECEDENT and ...
... (ii) NEGATION, if Φ is a wff, then the expression denoted by ¬Φ is also a wff (iii) CONJUNCTION, if Φ and Ψ are both wffs, then the expression denoted by ( Φ ∧ Ψ) is a wff (iv) DISJUNCTION if Φ and Ψ are both wffs, then the expression denoted by (Φ ∨ Ψ) is a wff (v) CONDITIONAL (with ANTECEDENT and ...
Name:
... Write statements in if-then format; identify the hypothesis and conclusion Write the converse, inverse, and contrapositive of a conditional statement. Give a counterexample to disprove a statement. Rewrite a bi-conditional statement as a conditional and its converse Identify whether reasoning used i ...
... Write statements in if-then format; identify the hypothesis and conclusion Write the converse, inverse, and contrapositive of a conditional statement. Give a counterexample to disprove a statement. Rewrite a bi-conditional statement as a conditional and its converse Identify whether reasoning used i ...
Chapter 2 Notes Niven – RHS Fall 12-13
... Inductive reasoning is when you find a pattern is specific cases and then write a conjecture for the general case. A conjecture is an unproven statement that is based on observations. Inductive reasoning boils down to analyzing a given set of data or observations, recognizing patterns, and making a ...
... Inductive reasoning is when you find a pattern is specific cases and then write a conjecture for the general case. A conjecture is an unproven statement that is based on observations. Inductive reasoning boils down to analyzing a given set of data or observations, recognizing patterns, and making a ...
ppt
... statements are true, what other statements can you also deduce are true? • If I tell you that all men are mortal, and Socrates is a man, what can you deduce? ...
... statements are true, what other statements can you also deduce are true? • If I tell you that all men are mortal, and Socrates is a man, what can you deduce? ...
Discrete Computational Structures (CS 225) Definition of Formal Proof
... When we write a proof, we will number each line, and justify it by citing its source. When justifying the application of equivalency rules and argument forms, we will give the name of the logical principle we are using, along with the line number(s) to which the rule or form is applied. For example, ...
... When we write a proof, we will number each line, and justify it by citing its source. When justifying the application of equivalency rules and argument forms, we will give the name of the logical principle we are using, along with the line number(s) to which the rule or form is applied. For example, ...
Basic Terms in Logic - Law, Politics, and Philosophy
... The truth value of a statement is not proven by logicians but of empirical scientists, researchers and private detectives. Logicians only study the reasoning found on statements and not the question of their truth values. ...
... The truth value of a statement is not proven by logicians but of empirical scientists, researchers and private detectives. Logicians only study the reasoning found on statements and not the question of their truth values. ...
Lesson 12
... Notice that inference is not directly related to truth; i.e. we can infer a sentence provided we have rules of inference that produce the sentence from the original sentences. However, if rules of inference are to be useful we wish them to be related to entailment. Ideally we would like: ...
... Notice that inference is not directly related to truth; i.e. we can infer a sentence provided we have rules of inference that produce the sentence from the original sentences. However, if rules of inference are to be useful we wish them to be related to entailment. Ideally we would like: ...
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.