Internal analogy tries to reuse solutions of subproblems within the same problem solving process. In mathematical theorem proving several patterns are known where internal analogy suggests itself. Hence, we propose the use of internal analogy in automated theorem proving. This paper investigates the possibility of incorporating internal analogy into the inductive proof planner CL A M. It introd...

Traditionally, computer simulation techniques are used to perform probabilistic analysis. However, they provide less accurate results and cannot handle large-scale problems due to their enormous CPU time requirements. Recently, a significant amount of formalization has been done in the HOL theorem prover that allows us to conduct precise probabilistic analysis using theorem proving and thus ove...

Interactive theorem proving systems for mathematics require user interfaces which allow for user interaction that is as natural as possible. However, this interaction is often limited by the traditional calculi underlying most theorem proving systems. This is particularly problematic with respect to the application of assertions and intuitive presentation of proof states. In this paper we show ...

Is it possible to compute in which logics a given formula is deducible? The aim of this paper is to provide a formal basis to answer positively this question in the context of substructural logics. Such a basis is founded on structurally-free logic, a logic in which the usual structural rules are replaced by complex combinator rules , and thus constitute a generalization of traditional sequent ...

syntax, 6, 54 ACL2, 18, 27, 29, 32, 34, 35, 40, 44,48, 55, 60

As one aspect of the endeavor to c r e a te new i n t e l l e c t u a l t o o l s f o r mankind, we w ish to enable computers to p rove , and t o a s s i s t i n the p roo f s o f , theorems o f mathematics and ( e v e n t u a l l y ) o t h e r d i s c i p l i n e s which have ach ieved the r e q u i s i t e l o g i c a l p r e c i s i o n . For t h i s purpose, a p a r t i c u l a r l y s u i ...

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 ...

Higher-order representation techniques allow elegant encod-ings of logics and programming languages in the logical framework LF, but unfortunately they are fundamentally incompatible with induction principles needed to reason about them. In this paper we develop a meta-logic M2 which allows inductive reasoning over LF encodings, and describe its implementation in Twelf, a special-purpose automa...

We describe how clauses in resolution programs can be represented and used Without applying substitutions or cons-ing lists of literals. The amount of space required by our representation of a clause is independent of the number of literals in the clause and the depth of function nesting. We introduce the concept of the value of an expression in a binding environment which we use to standardize...