Proof Confluent Tableau Calculi

نویسندگان

  • Reiner Hähnle
  • Bernhard Beckert
چکیده

A tableau calculus is proof confluent if every partial tableau proof for an unsatisfiable formula can be extended to a closed tableau. A rule application may be redundant but it can never prevent the construction of a proof; there are no “dead ends” in the proof search. Proof confluence is a prerequisite of (a) backtrackingfree proof search and (b) the generation of counter examples to non-theorems. In this tutorial we discuss the rôle and perspectives of proof confluent calculi in tableau-based theorem proving. For the sake of simplicity the discussion focuses on clause tableaux.

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

A Cut-free Tableau Calculus for the Logic of Common Knowledge

In this paper we focus on the development of a cut-free finitary tableau calculus with histories for n-agent modal logics with common knowledge (LCK). Thus, we get a proof system where proof-search becomes feasible and we lay the basis for developing a uniform framework for the treatment of the family of logics of common knowledge. Unlike proof calculi based on temporal logics, our calculus giv...

متن کامل

Tableau Calculi for KLM Logics: extended version

We present tableau calculi for some logics of nonmonotonic reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered, and w...

متن کامل

Tableau Calculi for the Logics of Finite k-Ary Trees

We present tableau calculi for the logics Dk (k ≥ 2) semantically characterized by the classes of Kripke models built on finite k-ary trees. Our tableau calculi use the signs T and F, some tableau rules for Intuitionistic Logic and two rules formulated in a hypertableau fashion. We prove the Soundness and Completeness Theorems for our calculi. Finally, we use them to prove the main properties o...

متن کامل

Restart Tableaux with Selection Function

Recently, several diierent sound and complete tableau cal-culi were introduced, all sharing the idea to use a selection function and so-called restart clauses: A-ordered tableaux, tableaux with selection function, and strict restart model elimination. We present two new sound and complete abstract tableau calculi which generalize these on the ground level. This makes diierences and similarities...

متن کامل

Accelerating Tableaux Proofs Using Compact Representations

In this article a modiied form of tableau calculus, called Tableau Graph Calculus, is presented for overcoming the well-known ineeciencies of the traditional tableau calculus to a large extent. This calculus is based on a compact representation of analytic tableaux by using graph structures called tableau graphs. These graphs are obtained from the input formula in linear time and incorporate mo...

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 1999