PPT-Quantifiers and logical inference

Adapted from Patrick J Hurley A Concise Introduction to Logic Belmont Thomson Wadsworth 2008 Predicate Logic Before I go on to explain quantifiers first let me address different ways of symbolizing statements Previously we used one letter to symbolize one statement But there is another way to symbolize certain kinds of statements that are relevant to quantifiers We can also symbolize statements by symbolizing the predicate and subject separately . Goals. : . Explain . how to work with nested . quantifiers. S. how that . the order . of quantification . matters. . Work . with . logical . expressions involving multiple . quantifiers.. Copyright © . 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. ). . Goal. : . Introduce predicate logic, . including existential . & universal quantification. Introduce translation between English sentences & logical expressions.. Copyright © Peter . Cappello. 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. . CS482, CS682, MW 1 – 2:15, SEM 201, MS 227. Prerequisites: 302, 365. Instructor: . Sushil. Louis, . sushil@cse.unr.edu. , . http://www.cse.unr.edu/~. sushil. Logic. Logical Agents. Truth . tables you know. Peter M. Maurer. Propositions. A proposition is a declarative sentence that can be either true or false. Earth is a planet – True. The Moon is made of green cheese – False. There is life on Mars – We don’t know yet, but either there is or there isn’t. Logic and Proof. Fall 2014. 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) . 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 . Satisfiability. Modulo Theories . Frontiers . of . Computational Reasoning . 2009 . –. MSR Cambridge. Leonardo de Moura. Microsoft Research. Symbolic Reasoning. Quantifiers in . Satisfiability. Class 9/15 - Video on Watson playing Jeopardy . HW 2 (Logic). coming out later this week. No office hours today!. Last Time: Propositional Inference. Logical Agents. Use information about how states change to choose actions. Bart Selman. selman@cs.cornell.edu. Module: Knowledge, Reasoning, and Planning. Logical Agents. Model . Theoretic Semantics. Entailment . and Proof Theory. R&N: Chapter 7. Logical agents:. . . Section 1.4. Section Summary. Predicates . Variables. Quantifiers. Universal Quantifier. Existential Quantifier. Negating Quantifiers. De Morgan’s Laws for Quantifiers. Translating English to Logic. Bart Selman. selman@cs.cornell.edu. Module: Knowledge, Reasoning, and Planning. Part 1. Logical Agents. R&N: Chapter 7. A Model-Based Agent. Requires: Knowledge and Reasoning. Knowledge and Reasoning . 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 .