The Role of Quantifier Alternations in Cut Elimination

نویسنده

  • Philipp Gerhardy
چکیده

Extending previous results from the author’s master’s thesis, subsequently published in the proceedings of CSL 2003, on the complexity of cut elimination for the sequent calculus LK, we discuss the role of quantifier alternations and develope a measure to describe the complexity of cut elimination in terms of quantifier alternations in cut formulas and contractions on such formulas.

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

Refined Complexity Analysis of Cut Elimination

In [1, 2] Zhang shows how the complexity of cut elimination depends primarily on the nesting of quantifiers in cut formulas. By studying the role of contractions in cut elimination we can refine that analysis and show how the complexity depends on a combination of contractions and quantifier nesting. With the refined analysis the upper bound on cut elimination coincides with Statman’s lower bou...

متن کامل

Tree Grammars for the Elimination of Non-prenex Cuts

Recently a new connection between proof theory and formal language theory was introduced. It was shown that the operation of cut elimination for proofs with prenex Π1-cuts in classical first-order logic corresponds to computing the language of a particular type of tree grammars. The present paper extends this connection to arbitrary (i.e. non-prenex) cuts without quantifier alternations. The ke...

متن کامل

Term Algebras with Length Function and Bounded Quantifier Alternation

Term algebras have wide applicability in computer science. Unfortunately, the decision problem for term algebras has a nonelementary lower bound, which makes the theory and any extension of it intractable in practice. However, it is often more appropriate to consider the bounded class, in which formulae can have arbitrarily long sequences of quantifiers but the quantifier alternation depth is b...

متن کامل

Evaluating QBF Solvers: Quantifier Alternations Matter

Competitions of quantified Boolean formula (QBF) solvers are an important driving force for solver development. We consider solvers and benchmarks in prenex conjunctive normal form (PCNF) that participated in the recent QBF competition (QBFEVAL’16) and take a fresh look at the number of solved instances as a measure of solver performance. Rather than ranking solvers by the total number of solve...

متن کامل

Strong Cut-Elimination, Coherence, and Non-deterministic Semantics

An (n, k)-ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical systems with (n, k)-ary quantifiers form a natural class of Gentzen-type systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a quantifier is introduced. The semantics for these systems is provided usin...

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:
  • Notre Dame Journal of Formal Logic

دوره 46  شماره 

صفحات  -

تاریخ انتشار 2005