Reference Request – Typed First Order Book

Computer scientists interested in untyped first-order logic are numerous, such as Melvin Fitting's "First-order Logic and Automated Demonstration of Theorems" or John Harrison's "Manual of Practical Logic and Automatic Reasoning."

However, I struggled to find a solid reference that deals specifically with first-order typewritten (or "sorted out") logic.

Although many knowledge of untyped first-order logic is correctly transferred to a typed parameter, there are some interesting questions specific to the first order typed logic for which rigorous processing, possibly with implementation examples, is required. # 39; interests. Type checking is an obvious example, but it also makes it possible to determine whether, in a typed parameter, it is useful to distinguish formulas and terms syntactically, or whether the formulas should only be treated as type terms. booland the consequences of such decisions on the calculation of normal forms. I am sure there are also other interesting issues.

Are there any books that you can recommend that have a purpose, or even just a long enough chapter, dealing specifically with the typical first order logic?