John Frame's Systematic Theology, chapter 15
Knowledge is more than just propositions. Knowing God is most important for us.
All our knowledge is learning about God and His world, thinking His thoughts after Him.
God knows all His creation in an owning and covenantal way, as our Lord (Amos 3:2; Isa. 40:12-14). He knows our sins, thoughts, desires.
Calvinists say God foreknows and foreordains everything.
Arminians say God foreknows all but does not foreordain things.
Socinians say God does not foreknow the future, since He doesn't foreordain it.
The open theists of today are in the Socinian category.
Prophecy in Scripture shows that God knows the future.
Many prophecies involve human decisions, which God also must know.
For a human choice to be free, it need not be unpredictable.
Scriptures that seem to show God as ignorant are His judgment beginning (Gen 3:9; 11:5; 18:21), or anthropomorphic appearance, or His testing of us (Gen 22:12; Deut 13:3). When He remembers, He keeps promises. It isn't that He calls to mind things He forgot.
God knows not only what is actually true, but also what is possible. Some argue for a middle knowledge that allows God to know possible free human choices. He creates a world such that people necessarily make the free choices God ordains. This is incoherent. Choices cannot be both free and determined by the world God makes. No, there is no difference between God knowing all possible worlds, and God knowing the possible choices people could make.
Wisdom is also an attribute of God. Proverbs 8:22 says God got wisdom when He started to create. It refers to righteousness, the skill of godly living, the way of salvation. Christ is the wisdom of God, and He calls out an invitation like wisdom does (Prov 9:1-4; Matt 11:28-30).
God has thoughts and a will that are rational and logical, though He is not bound by fallible human systems of logic. Several doctrines in Scripture don't seem reconcilable to logic (problem of evil, Trinity), but we should keep trying instead of declaring them beyond us. Many "problem texts" can be resolved through further study of Scripture.