求Robinson算术与Peano算术的自然演绎证明习题及解答获取渠道

Hey there! Great question—natural deduction proofs for Robinson (Q) and Peano (PA) arithmetic can be tough to get the hang of, so having solid exercises with solutions is really important. Here are some reliable options I’ve used or recommended to others over the years:

Textbooks with Built-In Exercises & Solutions #

• "Mathematical Logic" by Ebbinghaus, Flum, & Thomas: This classic text dedicates chapters to both Q and PA, with natural deduction-focused exercises scattered throughout. A number of the harder problems have detailed hints or full solutions in the appendix, which is super helpful when you get stuck.
• "Introduction to Mathematical Logic" by Elliott Mendelson: While not every exercise has a solution, the ones that do cover core natural deduction proofs for Q and PA (like proving basic arithmetic identities or induction principles). The book also walks you through foundational proofs step-by-step, which you can use as a template for solving similar problems.
• "Logic: Techniques of Formal Reasoning" by Kalish, Montague, & Mar: This workbook-style text has tons of hands-on natural deduction exercises, including sections on formalizing arithmetic statements in Q/PA and proving them. Most exercises come with complete solutions at the back of the book, making it perfect for self-study.

University Course Materials #

Many top universities post their logic course materials publicly, including problem sets and graded solutions. Look for courses titled "Mathematical Logic," "Formal Reasoning," or "Foundations of Mathematics"—these often include units on Q and PA with natural deduction practice. For example, courses from institutions like MIT, Stanford, or Cambridge frequently share these resources (you can search for course codes like 6.042 or PHIL 150 to find relevant materials).

Interactive Proof Assistants & Platforms #

• Coq/Isabelle/HOL: These proof assistants have extensive libraries for Peano arithmetic, and many tutorials guide you through writing natural deduction-style proofs in them. For example, Coq's standard library includes PA definitions, and there are beginner-friendly exercises that come with step-by-step solutions or walkthroughs. Even if you're new to proof assistants, working through these can help you internalize natural deduction rules for arithmetic.
• ProofWeb: This web-based tool is designed specifically for practicing natural deduction. It has a section on arithmetic where you can solve problems and get immediate feedback, and some exercises include sample solutions to reference if you're stuck.

Community-Driven Resources #

Stack Exchange itself (like Math Stack Exchange or Computer Science Stack Exchange) is a great place. If you're working on a specific problem and can't find a solution, post your attempt and ask for guidance—many experts here are happy to walk through natural deduction proofs for Q/PA. Also, some users have shared curated lists of exercises and solutions in past posts, so searching keywords like "Robinson arithmetic natural deduction exercises" might turn up useful threads.

Hope these help you find the practice you need!

内容的提问来源于stack exchange，提问作者Sachama