Filters








25 Hits in 2.3 sec

Formalizing Bachmair and Ganzinger's Ordered Resolution Prover [chapter]

Anders Schlichtkrull, Jasmin Christian Blanchette, Dmitriy Traytel, Uwe Waldmann
2018 Lecture Notes in Computer Science  
We present an Isabelle/HOL formalization of the first half of Bachmair and Ganzinger's chapter on resolution theorem proving, culminating with a refutationally complete first-order prover based on ordered  ...  resolution with literal selection.  ...  Conclusion We presented a formal proof that captures the core of Bachmair and Ganzinger's Handbook chapter on resolution theorem proving.  ... 
doi:10.1007/978-3-319-94205-6_7 fatcat:hmjoecj5obe2ji6ldifhh3yfbu

Preface: Special Issue of Selected Extended Papers from IJCAR 2018

Didier Galmiche, Stephan Schulz, Roberto Sebastiani
2020 Journal of automated reasoning  
The paper "Formalizing Bachmair and Ganzinger's Ordered Resolution Prover" presents a formalization of the first half of Bachmair and Ganzinger's chapter on resolution theorem proving in Isabelle/HOL,  ...  providing a refutationally complete first-order prover based on ordered resolution with literal selection.  ...  as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.  ... 
doi:10.1007/s10817-020-09556-x fatcat:u32hsri2yjh57nuqcevx75234y

A verified prover based on ordered resolution

Anders Schlichtkrull, Jasmin Christian Blanchette, Dmitriy Traytel
2019 Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2019  
The superposition calculus, which underlies first-order theorem provers such as E, SPASS, and Vampire, combines ordered resolution and equality reasoning.  ...  As a step towards verifying modern provers, we specify, using Isabelle/HOL, a purely functional first-order ordered resolution prover and establish its soundness and refutational completeness.  ...  Eugene Kotelnikov, Stephan Schulz, and Geoff Sutcliffe graciously answered our questions about Vampire, E, and TPTP.  ... 
doi:10.1145/3293880.3294100 dblp:conf/cpp/SchlichtkrullBT19 fatcat:ftlcitpp7rbsbevdkf6nl6r25y

Formalizing the metatheory of logical calculi and automatic provers in Isabelle/HOL (invited talk)

Jasmin Christian Blanchette
2019 Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2019  
In this paper, I describe and reflect on three verification subprojects to which I contributed: a first-order resolution prover, an imperative SAT solver, and generalized term orders for λ-free higher-order  ...  IsaFoL (Isabelle Formalization of Logic) is an undertaking that aims at developing formal theories about logics, proof systems, and automatic provers, using Isabelle/HOL.  ...  Another perspective is to improve Bachmair and Ganzinger's framework.  ... 
doi:10.1145/3293880.3294087 dblp:conf/cpp/Blanchette19 fatcat:n7delklh2nejvh4zspbcljamwy

A Comprehensive Framework for Saturation Theorem Proving [chapter]

Uwe Waldmann, Sophie Tourret, Simon Robillard, Jasmin Blanchette
2020 Lecture Notes in Computer Science  
We present a framework for formal refutational completeness proofs of abstract provers that implement saturation calculi, such as ordered resolution or superposition.  ...  It allows us to extend redundancy criteria so that they cover subsumption, and also to model entire prover architectures in such a way that the static refutational completeness of a calculus immediately  ...  We thank Alexander Bentkamp for discussions about prover architectures for higher-order logic and for feedback from instantiating the framework, Mathias  ... 
doi:10.1007/978-3-030-51074-9_18 fatcat:2fb33hm7djhu5pofxbdca3cggu

From Search to Computation: Redundancy Criteria and Simplification at Work [chapter]

Thomas Hillenbrand, Ruzica Piskac, Uwe Waldmann, Christoph Weidenbach
2013 Lecture Notes in Computer Science  
We present Harald Ganzinger's work in the light of the simplification and redundancy techniques that have been developed for concrete problem areas.  ...  Hence, the key to successfully applying first-order theorem proving to a problem domain is to find those simplifications and redundancy criteria that fit this domain and can be effectively implemented.  ...  The completeness proof for the procedure implemented in CEC extends the proof ordering technique of Leo Bachmair, Nachum Dershowitz and Jieh Hsiang [3] : while Bachmair, Dershowitz and Hsiang use linear  ... 
doi:10.1007/978-3-642-37651-1_7 fatcat:fr4uqtwvubbtvgjepamaamojeu

Twenty Years Later [chapter]

Jean-Pierre Jouannaud
2005 Lecture Notes in Computer Science  
What has happened is that many research areas, such as programming languages, constraint solving, first-order provers, proof assistants, security theory, and verification have all been fertilized by ideas  ...  powerful provers that would make a difference with the state of art and help address real applications such as software verification.  ...  Acknowledgments: to all those I met during these 20 years and helped me understand that their problems were more important than mine.  ... 
doi:10.1007/978-3-540-32033-3_27 fatcat:6xggpx3i7ve7rfewekdb4vfiv4

Stratified resolution

Anatoli Degtyarev, Robert Nieuwenhuis, Andrei Voronkov
2003 Journal of symbolic computation  
To prove the completeness of stratified resolution with redundancies, we use a novel combination of Bachmair and Ganzinger's model construction technique and a hierarchical construction of orderings and  ...  We introduce a calculus of stratified resolution, in which special attention is paid to clauses that "define" relations.  ...  Harald Ganzinger explained that the SATURATE system tries to use an ordering under which the heads of "definition-like" clauses are the greatest in their clauses, and hence can be selected.  ... 
doi:10.1016/s0747-7171(03)00036-1 fatcat:f4pu7wm3jbgi5ov66xzkhya3de

Stratified Resolution [chapter]

Anatoli Degtyarev, Andrei Voronkov
2000 Lecture Notes in Computer Science  
To prove the completeness of stratified resolution with redundancies, we use a novel combination of Bachmair and Ganzinger's model construction technique and a hierarchical construction of orderings and  ...  We introduce a calculus of stratified resolution, in which special attention is paid to clauses that "define" relations.  ...  Harald Ganzinger explained that the SATURATE system tries to use an ordering under which the heads of "definition-like" clauses are the greatest in their clauses, and hence can be selected.  ... 
doi:10.1007/10721959_28 fatcat:fes7iqnuprfkpgbphjf4fv6nda

Superposition for Lambda-Free Higher-Order Logic [article]

Alexander Bentkamp, Jasmin Blanchette, Simon Cruanes, Uwe Waldmann
2021 arXiv   pre-print
We introduce refutationally complete superposition calculi for intentional and extensional clausal λ-free higher-order logic, two formalisms that allow partial application and applied variables.  ...  We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks.  ...  We want to thank Petar Vukmirović for his work on Zipperposition and for his advice. We thank Christoph Benzmüller, Sander Dahmen, Johannes Hölzl, Anders Schlichtkrull,  ... 
arXiv:2005.02094v4 fatcat:e336v4smjrfe3h7xdnvhasw7ke

Superposition with Lambdas [article]

Alexander Bentkamp, Jasmin Blanchette, Sophie Tourret, Petar Vukmirović, Uwe Waldmann
2021 arXiv   pre-print
We implemented the calculus in the Zipperposition prover and evaluated it on TPTP and Isabelle benchmarks. The results suggest that superposition is a suitable basis for higher-order reasoning.  ...  The inference rules work on βη-equivalence classes of λ-terms and rely on higher-order unification to achieve refutational completeness.  ...  Evaluation We evaluated our prototype implementation of the calculus in Zipperposition with other higher-order provers and with Zipperposition's modes for less expressive logics.  ... 
arXiv:2102.00453v1 fatcat:3b2wgsb755cbvdlpz5tnfetoi4

First-Order Resolution Methods for Modal Logics [chapter]

Renate A. Schmidt, Ullrich Hustadt
2013 Lecture Notes in Computer Science  
Without going into too much detail, we survey different ways of translating modal logics into first-order logic, we explore different ways of using first-order resolution theorem provers, and we discuss  ...  In this paper we give an overview of results for modal logic which can be shown using techniques and methods from first-order logic and resolution.  ...  Before we go on we want to note that most modern first-order logic theorem provers are implementations based on the Bachmair-Ganzinger framework of resolution.  ... 
doi:10.1007/978-3-642-37651-1_15 fatcat:pta3fxqsnfal3cigcnryyxjcba

Verified heap theorem prover by paramodulation

Gordon Stewart, Lennart Beringer, Andrew W. Appel
2012 Proceedings of the 17th ACM SIGPLAN international conference on Functional programming - ICFP '12  
within the reach of formal methods.  ...  By efficient, we mean that the prover implements a state-of-the-art algorithm for deciding heap entailments and uses highly tuned verified functional data structures.  ...  Aleksandar Nanevski and David Walker gave the first author advice on appropriate venues for this work. This work was supported in part by AFOSR grant FA9550-09-1-0138 and NSF grant CNS-0910448.  ... 
doi:10.1145/2364527.2364531 dblp:conf/icfp/StewartBA12 fatcat:bdihjfjz2vfsrhf3vy5zjhwnca

Teaching a Formalized Logical Calculus

Asta Halkjær From, Alexander Birch Jensen, Anders Schlichtkrull, Jørgen Villadsen
2020 Electronic Proceedings in Theoretical Computer Science  
We present soundness and completeness proofs of a sequent calculus for first-order logic, formalized in the interactive proof assistant Isabelle/HOL.  ...  We strive to not only present the results of the proofs of soundness and completeness, but also to provide a deep dive into a programming-like approach to the formalization of first-order logic syntax,  ...  Schlichtkrull, Jasmin Christian Blanchette, Dmitriy Traytel & Uwe Waldmann (2018): Formalizing Bachmair and Ganzinger’s Ordered Resolution Prover.  ... 
doi:10.4204/eptcs.313.5 fatcat:6mjb5dae3beizfqa2ncyjtmo4y

Verified heap theorem prover by paramodulation

Gordon Stewart, Lennart Beringer, Andrew W. Appel
2012 SIGPLAN notices  
within the reach of formal methods.  ...  By efficient, we mean that the prover implements a state-of-the-art algorithm for deciding heap entailments and uses highly tuned verified functional data structures.  ...  Aleksandar Nanevski and David Walker gave the first author advice on appropriate venues for this work. This work was supported in part by AFOSR grant FA9550-09-1-0138 and NSF grant CNS-0910448.  ... 
doi:10.1145/2398856.2364531 fatcat:m7w4h5tdxjgzrh6sc67l3turli
« Previous Showing results 1 — 15 out of 25 results