Algorithmic introduction of quantified cuts
نویسندگان
چکیده
We describe a method for inverting Gentzen’s cut-elimination in classical first-order logic. Our algorithm is based on first computing a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize such a compression. Finally, a proof using these cut-formulas is constructed. This method allows an exponential compression of proof length. It can be applied to the output of automated theorem provers, which typically produce analytic proofs. An implementation is available on the web and described in this paper.
منابع مشابه
Algorithmic Structuring of Cut-free Proofs
The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB LK where blocks of quanti ers can be introduced in one step is investigated where a distinction is made between linear proofs and proofs in tree form In this framework structuring coincides with the introduction of cuts into a proof The algorithmic solvability of this problem can be reduced to the question of k l...
متن کاملIntroducing Quantified Cuts in Logic with Equality
Cut-introduction is a technique for structuring and compressing formal proofs. In this paper we generalize our cut-introduction method for the introduction of quantified lemmas of the form ∀x.A (for quantifier-free A) to a method generating lemmas of the form ∀x1 . . .∀xn.A. Moreover, we extend the original method to predicate logic with equality. The new method was implemented and applied to t...
متن کاملThe problem of Π2-cut-introduction
We describe an algorithmic method of proof compression based on the introduction of Π2-cuts into a cut-free LK-proof. This method extends previous research on the introduction of Π1-cuts and is based on a connection between proof theory and formal language theory. Given is a cut-free proof π of a sequent S and a so called schematic Π2-grammar G, a grammar formalizing the substitutions of quanti...
متن کاملParallel Genetic Algorithm Using Algorithmic Skeleton
Algorithmic skeleton has received attention as an efficient method of parallel programming in recent years. Using the method, the programmer can implement parallel programs easily. In this study, a set of efficient algorithmic skeletons is introduced for use in implementing parallel genetic algorithm (PGA).A performance modelis derived for each skeleton that makes the comparison of skeletons po...
متن کاملProbabilistic Sufficiency and Algorithmic Sufficiency from the point of view of Information Theory
Given the importance of Markov chains in information theory, the definition of conditional probability for these random processes can also be defined in terms of mutual information. In this paper, the relationship between the concept of sufficiency and Markov chains from the perspective of information theory and the relationship between probabilistic sufficiency and algorithmic sufficien...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 549 شماره
صفحات -
تاریخ انتشار 2014