Suppose an agent inhabits a world with two states: S and -S, can do exactly one of two actions, a and b. Action a does nothing (i.e. stays in the same state) and action b flips from one state to the other. Let S' be the proposition that the agent is in state Sat time t (similarly -S), and let a' be the proposition that the agent does action a at time t (similarly for b' ). a) Write a successor-state axiom for St+1. Think about the conditions at time t that defines St+1 using a biconditional. b) Convert the sentence in (a) into CNF. c) Show a resolution refutation proof that if the agent is in -S at time t and does a it will still be in -S at time t + 1.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Suppose an agent inhabits a world with two states: S and -S, can do exactly one of two actions, a
and b. Action a does nothing (i.e. stays in the same state) and action b flips from one state to the
other. Let S' be the proposition that the agent is in state Sat time t (similarly -S), and let a' be the
proposition that the agent does action a at time t (similarly for b' ).
a) Write a successor-state axiom for St+1. Think about the conditions at time t that defines St+1
using a biconditional.
b) Convert the sentence in (a) into CNF.
c) Show a resolution refutation proof that if the agent is in -S at time t and does a it will still be in -S
at time t + 1.
Transcribed Image Text:Suppose an agent inhabits a world with two states: S and -S, can do exactly one of two actions, a and b. Action a does nothing (i.e. stays in the same state) and action b flips from one state to the other. Let S' be the proposition that the agent is in state Sat time t (similarly -S), and let a' be the proposition that the agent does action a at time t (similarly for b' ). a) Write a successor-state axiom for St+1. Think about the conditions at time t that defines St+1 using a biconditional. b) Convert the sentence in (a) into CNF. c) Show a resolution refutation proof that if the agent is in -S at time t and does a it will still be in -S at time t + 1.
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