PPT-More About Syllogisms The quantifiers, causes, and validity of Syllogisms

Quantifiers We have already learned about the universal affirmative a All S are P Example All humans are mortal As we discussed last week there are three more Quantifiers The Universal Negative. All dogs can fly Fido is a dog Fido can fly That is a perfectly valid argument in terms of logic but this flawless logic is based on an untrue premise If a person accepts the major and minor premises of an argument the conclusion follows undeniably Logic and Proof. Fall . 2011. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . P(x. ). . The pictures describe an incident. Write sentences based on the pictures and words given. You must add your own words to make the story interesting. Brainstorm the verbs for each of the picture. taxi driver – passenger – airport – Noir Hotel. Propositional Logic Not Enough. Given the statements: . “All men are mortal.”. “Socrates is a man.”. It follows that “Socrates is mortal.”. This can’t be represented in propositional logic. . Chapter 2. Predicates and quantifiers. Can be used to express the meaning of a. . wide range of statements. Allow us to reason and explore relationship between objects. 2. Predicates. statements involving variables, . A. n. v. e. s. h. . K. o. murave. l. l. i. work done at Carnegie Mellon University. Joint work with . Nikolaj. . Bjørner. , . Arie. . Gurfinkel. , and Kenneth McMillan. In essence…. 1. Efficiently under-approximating projections,. What . is your quantifier quotient (QQ)?. Barbara . Zurer. . Pearson. bpearson@research.umass.edu. University of Massachusetts . Amherst. Language Acquisition . Colloquium. Background. This work is part of the preliminary studies for an . Basic Argumentation. Definition. A . syllogism is two statements or propositions, one major and one minor, that combine to produce a conclusion.. Example #1. Major Proposition: . Every automobile has a seat for its driver.. Structures. Logic and Proof. Spring 2014. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . Section 1.4. Section Summary. Predicates . Variables. Quantifiers. Universal Quantifier. Existential Quantifier. Negating Quantifiers. De Morgan’s Laws for Quantifiers. Translating English to Logic. Fall . 2011. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . P(x. ). . P(4) . is true, but . Easier to understand. Easier to measure. More formulas (like stats!). Base for validity. Need for validity. Does test measure what it claims?. Can test be used to make decisions?. Validity. Reliability is a necessary, but not a sufficient condition for validity.. Modulo Theories . Manchester 2009. Leonardo de Moura. Microsoft Research. Symbolic Reasoning. Quantifiers in . Satisfiability. Modulo Theories. PSpace. -complete. (QBF). Undecidable. (First-order logic). Exercise 4. Exercise . Translate . these statements into English, where C(x) is “. x. . is a comedian” and F(x) is “x is funny” and the domain . consists . of all people. . . a)∀. x(C(x)→F(x)) .