Automatic inductive theorem proving using prolog

Focused Inductive Theorem Proving

Focused proof systems provide means for reducing and structuring the non-determinism involved in searching for sequent calculus proofs. We present a focused proof system for a first-order logic with inductive and co-inductive definitions in which the introduction rules are partitioned into an asynchronous phase and a synchronous phase. These focused proofs allow us to naturally see proof search...

Connection-Driven Inductive Theorem Proving

We present a method for integrating rippling-based rewriting into matrix-based theorem proving as a means for automating inductive specification proofs. The selection of connections in an inductive matrix proof is guided by symmetries between induction hypothesis and induction conclusion. Unification is extended by decision procedures and a rippling/reverse-rippling heuristic. Conditional subst...

Matrix-Based Inductive Theorem Proving

R.Dyckhoff, ed., International Conference TABLEAUX-2000, LNAI 1847, pp. 294–309, c ©Springer Verlag, 2000. Abstract. We present an approach to inductive theorem proving that integrates rippling-based rewriting into matrix-based logical proof search. The selection of appropriate connections in a matrix proof is guided by the symmetries between induction hypothesis and induction conclusion while ...

Automatic Geometric Theorem Proving using Gröbner Bases

External Analogy in Inductive Theorem Proving

This paper investigates analogy-driven proof plan construction in inductive theorem proving. Given a proof plan of a source theorem, we identify constraints of second-order mappings that enable a replay of the source plan to produce a similar plan for the target theorem. In addition, the analogical replay is controlled by justiications that have to be satissed in the target. Our analogy procedu...