I will explain how the clues in a logic puzzle can be expressed as facts, and how facts can be categorized by type. A fact is a static statement of the form:
"Noun 1 Verb Link Noun 2.", where (1) the verb is positive or negative, and (2) the verb and link is the relationship between the two nouns.
If we look at the logic puzzle "Five Houses", the first clue can be expressed directly as a fact: "The Englishman lives in the red house." In fact (hey, I made a pun), what makes this puzzle unique is that each clue is a fact.
The types of facts are given below. While the first type of fact yields only one mark, the other types of facts usually produce more than one mark.
A type 1 fact has the default link "with". It is the easiest to process, and the easiest to notice when a mark contradicts it. Most of the facts in our example puzzle are type 1 facts.
I must point out that both nouns in a type 1 fact cannot have the same noun type. Why? Because in any logic grid puzzle, two nouns of the same noun type can never be together! If you had the fact with two first names such as "Abe is with Bob", this would be a violation. And if you had the fact "Abe is not with Bob", this would simply be redundant.
A type 2 fact has exactly one noun where its noun type matches the noun type of the link. It is slightly harder to process, and is harder to catch when a mark contradicts it. This puzzle, along with most puzzles, does not have this type of fact.
A logic puzzle that does have facts of type 2 is "Lucky Streets". In this puzzle, fact 15 states "She found the quarter earlier than Friday." This means the quarter was not found on Friday or Saturday. The quarter has the noun type "Coin", while the link "earlier than" and Friday both have the noun type "Day". In this puzzle, facts 16 and 17 are type 2 facts as well.
Again, I must point out that both nouns in a type 2 fact cannot have the same noun type. Why? Because this is like saying "Thursday is earlier than Friday." While this may be factually true, this is already defined within the link "earlier than". Don't be a silly human.
A type 3 fact has the same noun type for both nouns, but this noun type is different from the noun type of the link. A fact of type 3 from our example puzzle is fact 5: "The green house is directly to the right of the white one." The green house and the white house have the noun type "Color", and the link "directly to the right of" has the noun type "House".
A type 4 fact is where the noun types for both nouns and the link are all different. From our example puzzle, facts 10, 12, and 14 are facts of type 4. Let's examine fact 10: "The man who sings lives next to the man with the fox." The man who sings has the noun type "Hobby". The link "next to" has the noun type "House". And the man with the fox has the noun type "Pet".
I hope you can see how important it is to build facts from the clues in a logic puzzle. If a clue cannot be expressed as a fact, then it must be expressed as a rule. It is my belief that any puzzle that can be fully expressed as facts can be solved without making assumptions.