What does it mean when a proof system is complete for a model system?

What does it mean when a proof system is sound for a model system?

Here is an intuitionistic model; call it M:

Which of the following claims are true about the model M? Choose all that apply, and none that don't.

Here is a presentation of a frame:

True or false: the following assignment of sets of atomics to points in this frame is a legitimate valuation on the frame.

• 1 : \{p\}
• 2 : \{p, q\}
• 3 : \{p, q, r\}
• 4 : \{p, q, s\}
• 5 : \{p, q, s, t\}

Here is a presentation of a particular frame. Choose, from among the answers, all of the reachability claims that are true in this frame, and none of the other answers.

Here is an intuitionistic model; call it M:

Which of the following claims are true about the model M? Choose all that apply, and none that don't.

In intuitionistic models, there are some connectives such that, when one of them is the main connective of a formula, then we can always evaluate that formula at a point just by knowing the values of its components at that point. Which connectives are these? Choose all that apply and none that don't.

Here is a presentation of a frame:

True or false: the following assignment of sets of atomics to points in this frame is a legitimate valuation on the frame.

• 1 : \{p\}
• 2 : \{p, q\}
• 3 : \{p, q, r\}
• 4 : \{p, q, s\}
• 5 : \{p, q, s, t\}

Here is a presentation of a particular frame. Choose, from among the answers, all of the reachability claims that are true in this frame, and none of the other answers.

Consider the following proof. What is the measure of its non-normality?