Strategic Issues, Problems and Challenges in Inductive Theorem Proving

Abstract(Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving. Typically, (Automated) Theorem Proving (TP) refers to methods, techniques and tools for automatically proving general (most often first-order) theorems. Nowadays, the field of TP has reached a certain degree of maturity and powerful TP systems are widely available and used. The situation with ITP is strikingly different, in the sense that proving inductive theorems in an essentially automatic way still is a very challenging task, even for the most advanced existing ITP systems. Both in general TP and in ITP, strategies for guiding the proof search process are of fundamental importance, in automated as well as in interactive or mixed settings. In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging. More generally, we will systematically isolate, investigate and classify the main problems and challenges in ITP w.r.t. automation, on different levels and from different points of views. Finally, based on this analysis we will present some theses about the state of the art in the field, possible criteria for what could be considered as substantial progress, and promising lines of research for the future, towards (more) automated ITP

Automated deduction with built-in theories: completeness results and constraint solving techniques

Postprint (published version

Equality elimination for the inverse method and extension procedures

We demonstrate how to handle equality in the inverse method using equality elimination. In the equality elimination method, proofs consist of two parts. In the first part we try to solve equations obtaining so called solution clauses. Solution clauses are obtained by a very refined strategy — basic superposition with selection function. In the second part, we perform the usual sequent proof search by the inverse method. Our approach is called equality elimination because we eliminate all occurrences of equality in the first part of the proof. Unlike the previous approach proposed by Maslov, our method uses most general substitutions, orderin

A Posthumous Contribution by {Larry Wos}: {E}xcerpts from an Unpublished Column

International audienceShortly before Larry Wos passed away, he sent a manuscript for discussion to Sophie Tourret, the editor of the AAR newsletter. We present excerpts from this final manuscript, put it in its historic context and explain its relevance for today’s research in automated reasoning