Generation and Use of Hints and Feedback in a Hilbert-Style Axiomatic Proof Tutor

This paper describes logax, an interactive tutoring tool that gives hints and feedback to a student who stepwise constructs a Hilbert-style axiomatic proof in propositional logic. logax generates proofs to calculate hints and feedback. We compare these generated proofs with expert proofs and student solutions, and conclude that the quality of the generated proofs is comparable to that of expert proofs. logax recognizes most steps that students take when constructing a proof. Even if a student diverges from the generated solution, logax still provides hints, including next steps or reachable subgoals, and feedback. With a few improvements in the design of the set of buggy rules, logax will cover about 80% of the mistakes made by students by buggy rules. The hints help students to complete the exercises.

A Comprehensive Evaluation Method of Network Public Opinion Based On Similarity Measure Between Vague Soft Sets

Aiming at the limitation of existing similarity measure method based on Vague soft sets, the similarity measure formula between Vague soft sets is modified and a novel similarity measure between Vague soft sets in consideration of the difference of interval center of Vague values is introduced, the axiomatic proof is given too. The experimental results of comprehensive evaluation of the network public opinion show that this method is reasonable, effective and practical, which has a good application prospect and effect in the study of internet public opinion.

Axiomatic Proof of J. Lambek's Homological Theorem

A category with zero-maps is called "quasi-exact" in the sense of D. Puppe (see [4], page 8, 2. 4), if it satisfies the following axioms:(Q1)Every may f is a product f=με of an epimorphisrn εfollowed by a monomorphism μ(Q2)a) Every epimorphism ε has a kernel k = ker εb) Every monomorphism μ has a cokernel γ = Coker ε, where Ker and Coker are characterized by the familiar universality properties (see [3], page 252, (1. 10) and (1. 11)).