Associative-Commutative Superposition

نویسندگان

  • Leo Bachmair
  • Harald Ganzinger
چکیده

We present an associative-commutative paramodulation calculus that generalizes the associativecommutative completion procedure to first-order clauses. The calculus is parametrized by a selection function (on negative literals) and a well-founded ordering on terms. It is compatible with an abstract notion of redundancy that covers such simplification techniques as tautology deletion, subsumption, and simplification by (associative-commutative) rewriting. The proof of refutational completeness of the calculus is comparatively simple, and the techniques employed may be of independent interest.

برای دانلود رایگان 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

Associative-commutative Deduction with Constraints Associative-commutative Deduction with Constraints

Associative-commutative equational reasoning is known to be highly complex for theorem proving. Hence, it is very important to focus deduction by adding constraints, such as uniication and ordering, and to deene eecient strategies, such as the basic requirements a la Hullot. Constraints are formulas used for pruning the set of ground instances of clauses deduced by a theorem prover. We propose ...

متن کامل

Max-planck-institut F Ur Informatik Associative-commutative Superposition K I N F O R M a T I K

We present an associative-commutative paramodulation calculus that generalizes the associativecommutative completion procedure to rst-order clauses. The calculus is parametrized by a selection function (on negative literals) and a well-founded ordering on terms. It is compatible with an abstract notion of redundancy that covers such simpli cation techniques as tautology deletion, subsumption, a...

متن کامل

Combining Algebra and Universal Algebra in First-Order Theorem Proving: The Case of Commutative Rings

We present a general approach for integrating certain mathematical structures in rst-order equational theorem provers. More specifically , we consider theorem proving problems speciied by sets of rst-order clauses that contain the axioms of a commutative ring with a unit element. Associative-commutative superposition forms the deduc-tive core of our method, while a convergent rewrite system for...

متن کامل

Positive Deduction modulo Regular Theories ? Laurent

We propose a new technique for dealing with an equational theory E in the clausal framework. This consists of the deenition of two inference rules called contextual superposition and extended superposi-tion, and of an algorithm for computing the only needed applications of these last inference rules only by examining the axioms of E. We prove the refutational completeness of this technique for ...

متن کامل

Ultra and Involution Ideals in $BCK$-algebras

In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1994