CS2800-Logic_part1_v.2

# CS2800-Logic_part1_v - Discrete Structures CS 2800 Prof Bart Selman [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */ Module Logic(part 1 Rosen Chapter 1 1 Logic in general

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1 Discrete Structures CS 2800 Prof. Bart Selman [email protected] Module Logic (part 1) Rosen, Chapter 1

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Logic in general Logics are formal languages for formalizing reasoning, in particular for representing information such that conclusions can be drawn A logic involves: A language with a syntax for specifying what is a legal expression in the language; syntax defines well formed sentences in the language Semantics for associating elements of the language with elements of some subject matter. Semantics defines the "meaning" of sentences (link to the world); i.e., semantics defines the truth of a sentence with respect to each possible world Inference rules for manipulating sentences in the language Original motivation: Early Greeks, settle arguments based on purely rigorous (symbolic/syntactic) reasoning starting from a given set of premises . “Reasoning based on form, content.”
3 Example of a formal language: Arithmetic E.g., the language of arithmetic x+2 ≥ y is a sentence; x2+y > {} is not a sentence x+2 ≥ y is true iff the number x+2 is no less than the number y x+2 ≥ y is true in a world where x = 7, y = 1 x+2 ≥ y is false in a world where x = 0, y = 6

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4 Several systems – biological, mechanical, electric, etc --- can be represented by appropriate sets of “features” with constraints among the features encoding physical or other laws relevant to the organism or device; Reasoning can then be used among other purposes, to diagnose malfunctions in these systems; for example, features associated with “causes” can be inferred from features associated with “symptoms”. This general approach is key to an important class of AI applications. Language to Specify Systems as Constrained Featured Sets
5 Simple Robot Domain Consider a robot that is able to lift a block, if that block is liftable (i.e., not too heavy), and if the robot’s battery power is adequate. If both of these conditions are satisfied, then when the robot tries to lift a block it is holding, its arm moves. block Feature 1: BatIsOk (True or False) Feature 2: BlockLiftable (True or False) Feature 3: RobotMoves (True or False)

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6 Simple Robot Domain ( BatIsOk and BlockLiftable ) implies RobotMoves block We need a language to express the features/properties/assertions and constraints among them ; also inference mechanisms , i.e, principled ways of performing reasoning. Example logical statement about the robot:
7 Binary valued featured descriptions Consider the following description: The router can send packets to the edge system only if it supports the new address space. For the router to support the new address space it is necessary that the latest software release be installed. The router can send packets to the edge system if the latest software release is installed. The router does not support the new address space. Features:

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## This note was uploaded on 01/16/2010 for the course CS 2800 at Cornell University (Engineering School).

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CS2800-Logic_part1_v - Discrete Structures CS 2800 Prof Bart Selman [email protected] Module Logic(part 1 Rosen Chapter 1 1 Logic in general

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