One of the major theological arguments of Neo, or Open, Theism is that God changes His mind in Scripture. It's said that He does this in a few places. In the flood narrative, God is said to have changed His mind about making humanity. He is said to change His mind when Moses asks Him to relent from destroying Israel. He is said to change His mind about Saul being His anointed king. In each of these instances, God's "changing His mind" is described with the word Mxn, usually in the Niphal.
Yet, we are also told in that same passage (1 Sam 15) that YHWH does not Mxn as a man might Mxn. But what does this mean? The relevant sentences of the passage reads:
"I Mxn that I have made Saul king, for he has turned back from following Me, and has not carried out My commands." (v. 11)
"And also the Glory of Israel will not lie or Mxn; for He is not a man that He should Mxn." (v. 29)
And Samuel did not see Saul again until the day of his death; for Samuel grieved over Saul. And the Lord Mxn that He had made Saul king over Israel. (v. 35)
And how does this accord with passages like Malachi 3:6, or more closely, Numbers 23:19: "God is not a man, that He should lie, Nor a son of man, that He should Mxn; Has He said, and will He not do it? Or has He spoken, and will He not make it good?"
The author of Numbers is the same author of Exodus 32 and Genesis 6, and he is aware of First Samuel. So what does this word mean that it can be said of God that He both does it, but does not do it as a human does it? I think the first observation we need to make about the word is that it doesn't deal with changing one's mind in the sense that one reconsiders his thoughts by way of learning something new. If we look at each of these passages, they have to do with God's anger or grief or compassion upon a person or group of people. In other words, they are in the context of emotion, not ignorance, that once it has been educated, changes its mind. We might even translate this that YHWH had a change of heart in terms of emotion, but absent of the idea of learning something, since a decision based upon emotion, not just bald facts, is what is present in these contexts. Incidentally, the phrase that is often translated as "had a change of heart" really is dealing with cognitive thought based upon new information, since "heart" in the Bible refers, not to emotion, as in these Mxn passages, but to the seat of the mind.
Hence, the decision being made is one that is primarily an emotional response to YHWH's experience of humans in time and place. It has nothing to do with God not knowing or learning something new.
Second to this, the term is often contrasted with lying. It is said in both Numbers and Samuel, where the distinction is made that God does not lie, but instead brings about what He has declared. This is something that only God can do, since only God knows the future and the future cannot alter what He has declared to be. So what does the text mean when it says that God does Mxn?
I think the word refers to God, making individual judgments based upon the actions of men in time, to redirect favor. I say "redirect" favor, because it can go from someone who has it or to someone who does not. In other words, based upon the actions of humans, gauged by His emotional response, YHWH decides to place favor upon an individual who did not have it, or He decides to take it away from someone who does. What has changed His mind in the moment of time is not new information, but the actual experience of the human actions that have also mustered an emotional response from Him in time and space.
Hence, God does not Mxn as a man might Mxn, because our emotions are based both on experience of an action and the learning of that action in order to experience it. We learn new information, and change our minds accordingly, but God does not learn. He knows all things. Hence, He cannot Mxn as a human does, but He can experience in space and time what He already knew would occur, and still have an emotional response to such repentance or evil.
So in Judges 2:18, the NASB translation of the word as "moved with compassion" is appropriate:
And when the Lord raised up judges for them, the Lord was with the judge and delivered them from the hand of their enemies all the days of the judge; for the Lord was moved to pity [Mxn] by their groaning because of those who oppressed and afflicted them.
This fits the Niphal well, as it is a passive that often depicts the action as taking place upon the individual. The Israelites do not have God's favor, but they do gain it by groaning for Him to aid them in their affliction.
In Exodus 32, He is moved with anger to redirect His favor away from the Israelites who had it, but then is asked by Moses to redirect it again in compassion.
Likewise, in Genesis 6, God is grieved and redirects the favor He once had upon making humanity upon the earth. He will now destroy them. But one, Noah, finds Nx "favor" with God (cf. Ruth 2:13, where Boaz finds favor with Ruth and thus has Mxn concerning her). In fact, the word is often in contexts of consoling people, and seeking to bring them to an emotional state of acceptance (i.e., favor) rather than non-acceptance and disfavor.
Hence, God can be moved emotionally by our actions (i.e., prayers, good or evil deeds, etc.) that seem like He is merely responding to new information, when in fact, He is responding to His experience of our actions in time and space that is expressed through the language of emotion (it may be that God has emotions such as these, or that these references are anthropopathic, i.e., described in terms of human emotions even though the subject does not have human emotions). It is important to note here that God is said to not be like a man and change His mind like a man, so He is not changing His mind based upon His mood in the moment. That's not the point at all. Rather the emotion exists in the passage to describe for us that God has experienced human actions in a very imminent and real way, and it is upon the nature of those individual actions that God is basing His judgments in time and space. In other words, these passages have nothing to do with the nature of God's knowledge. They only have to do with the nature of God experiencing what He may or may not already know (and according to other passages, as well as what some of these passages indicate themselves, He is experiencing what He eternally knows in time and space.
What this means is that God is a good judge, who doesn't merely judge from the heavens as someone who is disengaged from His subjects, but rather as someone who waits for humans to act in order to judge them, and is intimately acquainted with what they have done, even being described as one who is emotionally moved to judge the action accordingly, and redirect His favor toward what the human(s) has/have done.
So we may answer the question, Does God change His mind? with the answer, No, not really, but also qualify that with a "but" that describes God as reacting in time with favor or disfavor toward what we do. Of course, this merely describes God from one view, our human viewpoint. This is the imminent view of God. If we were to describe the transcendent view of God (i.e., the view from the divine standpoint) then God is completely sovereign and the reason why human action X occurred is because decreed it to occur, so that He is the mover of the human movers who move Him--hence, He is the mover of Himself through human agents, bringing about His preplanned will in space and time. The point here, however, is that our part to play is in what we do in space and time. We pray, knowing that God may be moved with compassion upon us to grant us favor, even though the larger picture tells us that God is moving us to pray in the first place.
So God does not change His mind in the same way a human changes His mind, but He does redirect favor according to our actions, and to us, there's little difference in the matter. My point here is simply to say that we cannot nor should we draw from these passages to create a theological understanding of God's knowledge, as that is not what they were ever intended to communicate to us.