Full First-Order Sequent and Tableau Calculi With Preservation of Solutions and the Liberalized δ-Rule but Without Skolemization

نویسنده

  • Claus-Peter Wirth
چکیده

We present a combination of raising, explicit variable dependency representation, the liberalized δrule, and preservation of solutions for first-order deductive theorem proving. Our main motivation is to provide the foundation for our work on inductive theorem proving.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Full First-Order Sequent and Tableau Calculi with Preservation of Solutions and the Liberalized delta-Rule but without Skolemization

We present a combination of raising, explicit variable dependency representation, the liberalized δrule, and preservation of solutions for first-order deductive theorem proving. Our main motivation is to provide the foundation for our work on inductive theorem proving.

متن کامل

Descente Infinie + Deduction

Although induction is omnipresent, inductive theorem proving in the form of descente infinie has not yet been integrated into full first-order deductive calculi. We present such an integration that even works for higher-order logic. This integration is based on lemma and induction hypothesis application for free variable sequent and tableau calculi. We discuss the appropriateness of these types...

متن کامل

Semantical Investigation of Simultaneous Skolemization for First-order Sequent Calculus Semantical Investigation of Simultaneous Skolemization for First-order Sequent Calculus

Simultaneous quantiier elimination in sequent calculus is an improvement over the well-known skolemization. It allows a lazy handling of instantiations as well as of the order of certain reductions. We prove the soundness of a sequent calculus which incorporates a rule for simultaneous quantiier elimination. The proof is performed by semantical arguments and provides some insights into the depe...

متن کامل

Admissible Substitutions in Sequent Calculi

For first-order classical logic a new notion of admissible substitution is defined. This notion allows optimizing the procedure of the application of quantifier rules when logical inference search is made in sequent calculi. Our objective is to show that such a computer-oriented sequent technique may be created that does not require a preliminary skolemization of initial formulas and that is ef...

متن کامل

The Even More Liberalized δ–Rule in Free Variable Semantic Tableaux

In this paper we have a closer look at one of the rules of the tableau calculus presented in [3], called the δ–rule, and the modification of this rule, that has been proved to be sound and complete in [6], called the δ–rule, which uses fewer free variables. We show that an even more liberalized version, the δ + –rule, that in addition reduces the number of different Skolem–function symbols that...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013