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This is a complex matter. To begin with, when you move your mouse, there is so much going on at once, that I cannot even begin to explain everything here. So, I will focus on the most fundamental thing: How does the computer actually compute? As you are probably familiar with, computers have memory called RAM, and a CPU that is able to execute "commands&...


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TL;DR: Use the SAT solver to search for a counterexample. To check that $KB \models \varphi$, you need to know whether there is any assignment that is consistent with $KB$ but that does not satisfy $\varphi$. In other words, you need to know whether $KB \land \neg \varphi$ is satisfiable or not. If $KB \land \neg \varphi$ is satisfiable, then you have ...


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You can use your oracle to construct a process that is guaranteed to be correct, and will most likely be fast. The basic idea is that a proof that a formula is unsatisfiable might be huge - but if that's the answer we get, we can trust it. On the other hand, we can easily convince ourselves that the formula is satisfiable by inspecting a satisfying ...


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Edit: I wrongly read the question, therefore the following answer is incorrect. It would be correct if the oracle worked as followed: "if the instance is unsatisfiable, then the oracle always says it is unsatisfiable otherwise, there is a 57% chance the answer is that the instance is satisfiable, and a 43% chance that it is not". The key here is to ...


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We have that $A \Rightarrow B$ is same with $\neg A \lor B$. This gives, that $(I \lor M)\Rightarrow H$ is same with $\neg(I \lor M)\lor H$. And we have that $\neg(I \lor M)$ is same with $\neg I \land \neg M$ Putting together we have that $(I \lor M)\Rightarrow H $ is same with $\neg I \land \neg M \lor H = (\neg I \land \neg M) \lor H = (\neg I \lor H) \...


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First thing is to accept and understand, that $A \Rightarrow C$ is same as $(\neg A) \lor C$. Using your example we obtain, that "If the battery is charged, then the phone is working" is same with "the battery is not charged or the phone is working". Now following initial sentence $(A \land B) \Rightarrow C$ we have $\neg(A \land B) \lor ...


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