Download Propositional Logic - Flow Chart | CS 1502 and more Study notes Computer Science in PDF only on Docsity! Propositional Logic Modeling concept Model: define scope of possibilities of worlds World: a particular circumstance involving interested objects, their names, and their properties and relationships Language : names, predicates, functions for talking about objects in a world Forming sentences Atomic Predicates Constants Functions Complex /\, \/, ~, ... skills Translation English --> logic logic --> English model and language are given World Describe a given world Create world according to a spec model and language are given Modeling Given an English description of a real-world situation, create model and language no model nor language are given going back and forth between real-world situations and logic models Properties of and relationship between sentences properties and relationships Truth Possibility Equivalence Arguments and Consequences Properties Validity Soundness Demonstration Valid: proof, truth table, resolution, (equivalence) Invalid: counterexample different interpretations of predicates and sentences Tautological Logical Taski's worlds model Ex: What is the difference between (a) tautological truth (Tautology) (b) logical truth, and (c) Task's worlds model truth? Proofs deduction inference rules Proof by cases Proof by contradiction Conditional proof ... proof strategy: when to use which proof rule Truth table resolution method Equivalences DeMorgan Commutative, Associative, Distributive ... Normal forms: NNF, DNF, CNF Formalizing ways to reason about claims Formalizing ways to state relationship among claims Formalizing ways to state claims representative problem Suppose the following are true. The wizard is either happy or angry. The dragon is afraid whenever the wizard is angry. The dragon hides in his lair if he is afraid. The dragon is out playing in the sky. The wizard is angry if he can't find his hat Can we conclude the following? The wizard has his hat Create a logic model for this situation. Determine whether the last sentence is true Demonstrate that the last sentence is true (or false) by Patchrawat Uthaisombut Copyright 2007 Patchrawat Uthaisombut University of Pittsburgh utp@cs.pitt.edu www.cs.pitt.edu/~utp
