MIT16_410F10_lec10

MIT16_410F10_lec10 - Propositional Logic and Satisfiability...

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± ± 1 Propositional Logic and Satisfiability Brian C. Williams 16.410-13 October 13 th , 2010 Slides draw upon material from: Prof. Bart Selman Cornell University Assignments ± Assignment: ± Problem Set #5: Activity Planning, due today Wednesday, October 13 th , 2010. ± Problem Set #6: Propositional Logic and Satisfiability, out today; due October 27 th , 2010 (in 2 weeks). ± Reading: ± Today: [AIMA] Ch. 7, 8 ± Monday: TBD ± Exam: ± Mid-Term - October 20 th . Brian Williams, Fall 10 2
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± ± 2 Hidden Failures Require Reasoning from a Model: STS-93 Brian Williams, Fall 10 3 ± ± Symptoms:± •± Engine temp sensor high± •± LOX level low± •± GN&C detects low thrust± •± H2 level possibly low ² ± ± Problem: Liquid hydrogen leak± ± ± Effect: ± •± LH2 used to cool engine± •± Engine runs hot± •± Consumes more LOX ² How Do We Reason About Complex Systems using Commonsense Models? Brian Williams, Fall 10 4 Helium tank± Fuel tank± Oxidizer tank± Main± Engines± Flow 1 = zero± Pressure 2 = nominal± Acceleration = zero± Model-based Reasoning: ± Reason from a single model to operate, diagnose, repair± ± Model using Logic . ± Reason using Sat . Task: Monitor engine operation ± You open the valves, and observe . . . ± Is the engine ok? ± Could the valve in red be stuck closed? Pressure 1 = nominal± Image credit: NASA.
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± ± 3 Modeling an Engine in Propositional Logic # An Engine E1 can either be okay, or broken in some unknown way. When E1 is okay, it will thrust when there is a flow through V1 and v2. $ Brian Williams, Fall 10 5 E1 V1 V2 (mode(E1) = ok or mode(E1) = unknown) and not (mode(E1) = ok and mode(E1) = unknown) and (mode(E1) = ok implies (thrust(E1) = on if and only if flow(V1) = on and flow(V2) = on)) Monitoring: Are the observations O consistent with model M? Fault Diagnosis: What fault modes of M are consistent with O? Reconfiguration: What component modes of M produce behavior G? ± ± Propositional Satisfiability: Find a truth assignment that satisfies some logical sentence S: 1. ± Reduce S to clausal form. 2. ± Perform search similar to MAC = (BT+CP) [Davis, Logmann & Loveland, 1962] Brian Williams, Fall 10 6 Reasoning From the Model
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± ± 4 Find a truth assignment that satisfies logical sentence T: ± Reduce sentence T to clausal form. ± Perform search similar to MAC = (BT+CP) [Davis, Logmann & Loveland, 1962] Propositional satisfiability testing : 1990: 100 variables / 200 clauses (constraints) 1998: 10,000 - 100,000 vars / 10^6 clauses 2010: millions Novel applications : e.g. diagnosis, planning, software verification, circuit testing, machine learning, and protein folding Brian Williams, Fall 10 7 Propositional Satisfiability What Formal Languages Exist for Describing Constraints? ± Algebra values of variables ± Probability degree of belief ± Propositional logic truth of facts ± Temporal logic time, ±.
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This note was uploaded on 12/26/2011 for the course SCIENCE 16.410 taught by Professor Prof.brianwilliams during the Fall '10 term at MIT.

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MIT16_410F10_lec10 - Propositional Logic and Satisfiability...

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