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Blocked Clauses in First-Order Logic [article]

Benjamin Kiesl, Martin Suda, Martina Seidl, Hans Tompits, Armin Biere
2017 arXiv   pre-print
In addition, we give a polynomial algorithm for checking whether a clause is blocked. Based on our new notions of blocking, we implemented a novel first-order preprocessing tool.  ...  We introduce two types of blocked clauses, one for first-order logic with equality and the other for first-order logic without equality, and prove their redundancy.  ...  Acknowledgements We thank Andrei Voronkov for performing the mock portfolio construction experiment.  ... 
arXiv:1702.00847v1 fatcat:kwzzzo36bvamdiqblrf3a2bhdq

Faster, Higher, Stronger: E 2.3 [chapter]

Stephan Schulz, Simon Cruanes, Petar Vukmirović
2019 Lecture Notes in Computer Science  
E 2.3 is a theorem prover for many-sorted first-order logic with equality. We describe the basic logical and software architecture of the system, as well as core features of the implementation.  ...  We particularly discuss recently added features and extensions, including the extension to many-sorted logic, optional limited support for higher-order logic, and the integration of SAT techniques via  ...  It has been under development for about 20 years, adding support for full first-order logic with E 0.82 in 2004, many-sorted first-order logic with E 2.0 in 2017, and both optional support for λ-free higher-order  ... 
doi:10.1007/978-3-030-29436-6_29 fatcat:qowtx2utabbi5ou6twtlbd3u24

Faster, Higher, Stronger

Bruce K. Rubin
2013 American Journal of Respiratory and Critical Care Medicine  
E 2.3 is a theorem prover for many-sorted first-order logic with equality. We describe the basic logical and software architecture of the system, as well as core features of the implementation.  ...  We particularly discuss recently added features and extensions, including the extension to many-sorted logic, optional limited support for higher-order logic, and the integration of SAT techniques via  ...  It has been under development for about 20 years, adding support for full first-order logic with E 0.82 in 2004, many-sorted first-order logic with E 2.0 in 2017, and both optional support for λ-free higher-order  ... 
doi:10.1164/rccm.201307-1371ed pmid:24032379 fatcat:wkohfj6vdncqjaesh5utfffx7i

Using Automated Theorem Provers to Certify Auto-generated Aerospace Software [chapter]

Ewen Denney, Bernd Fischer, Johann Schumann
2004 Lecture Notes in Computer Science  
For full automation, however, the obligations must be aggressively preprocessed and simplified.  ...  The system uses Hoare-style program verification technology to generate proof obligations which are then processed by an automated first-order theorem prover (ATP).  ...  Theorem Provers For the experiments, we selected several high-performance theorem provers for untyped first-order formulas with equality.  ... 
doi:10.1007/978-3-540-25984-8_12 fatcat:ragxctc5fvexhhb5ovhhliu5ru

Effective Normalization Techniques for HOL [chapter]

Max Wisniewski, Alexander Steen, Kim Kern, Christoph Benzmüller
2016 Lecture Notes in Computer Science  
In this work we present an adaption of advanced first-order normalization techniques for higher-order theorem proving which have been bundled in a stand-alone tool.  ...  It can be used in conjunction with any higher-order theorem prover, even though the implemented techniques are primarily targeted on resolution-based provers.  ...  Higher-order (HO) ATPs have not yet developed as sophisticated methods as their first-order counterparts and use hardly any sophisticated pre-processing techniques regarding clausification.  ... 
doi:10.1007/978-3-319-40229-1_25 fatcat:c46ta7reevguxabjqq5ljle5wm

AN EMPIRICAL EVALUATION OF AUTOMATED THEOREM PROVERS IN SOFTWARE CERTIFICATION

EWEN DENNEY, BERND FISCHER, JOHANN SCHUMANN
2006 International journal on artificial intelligence tools  
The system uses Hoare-style program verification technology to generate proof obligations which are then processed by an automated first-order theorem prover (ATP).  ...  For full automation, the obligations must be aggressively preprocessed and simplified, and we demonstrate how the individual simplification stages, which are implemented by rewriting, influence the ability  ...  First-order predicate logic suffices for proving the verification tasks generated from our Hoare-style formulation of safety policies and so they can be handled by first-order ATPs.  ... 
doi:10.1142/s0218213006002576 fatcat:ngisg2ralvdfvbwq2wb5wogs2u

FEMaLeCoP: Fairly Efficient Machine Learning Connection Prover [chapter]

Cezary Kaliszyk, Josef Urban
2015 Lecture Notes in Computer Science  
FEMaLeCoP is a connection tableau theorem prover based on leanCoP which uses efficient implementation of internal learningbased guidance for extension steps.  ...  FEMaLeCoP is thus the first AI/ATP system convincingly demonstrating that guiding the internal inference algorithms of theorem provers by knowledge learned from previous proofs can significantly improve  ...  some discussion of the minimization techniques and issues).  ... 
doi:10.1007/978-3-662-48899-7_7 fatcat:dy5o5qdd5jaglpuu2qhl2z3x6i

Scalable Fine-Grained Proofs for Formula Processing [chapter]

Haniel Barbosa, Jasmin Christian Blanchette, Pascal Fontaine
2017 Lecture Notes in Computer Science  
Clausification, skolemization, theory-specific simplifications, and expansion of 'let' expressions are instances of this framework.  ...  This allowed us to dramatically simplify the code base while increasing the number of problems for which detailed proofs can be produced, which is important for independent checking and reconstruction  ...  , Sophie Tourret, and the anonymous reviewers for suggesting many textual improvements.  ... 
doi:10.1007/978-3-319-63046-5_25 fatcat:7tmcxekxzbhwvktbm4ogvunvpe

FEMaLeCoP: Fairly Efficient Machine Learning Connection Prover

Cezary Kaliszyk, Josef Urban
2015 Zenodo  
FEMaLeCoP is a connection tableau theorem prover based on leanCoP which uses efficient implementation of internal learning- based guidance for extension steps.  ...  FEMaLeCoP is thus the first AI/ATP system convincingly demonstrating that guiding the internal inference algorithms of theorem provers by knowledge learned from previous proofs can significantly improve  ...  some discussion of the minimization techniques and issues).  ... 
doi:10.5281/zenodo.4543866 fatcat:anmtjxrm6jgwfbaz2c5j73hrx4

Machine Learning Guidance for Connection Tableaux

Michael Färber, Cezary Kaliszyk, Josef Urban
2020 Journal of automated reasoning  
for machine learning.  ...  Connection calculi allow for very compact implementations of goal-directed proof search.  ...  Connections were considered among others for classical first-order logic [49] , for higher-order logic [3] and for linear logic [23] .  ... 
doi:10.1007/s10817-020-09576-7 pmid:33678931 pmcid:PMC7900060 fatcat:ipgat65s4rfivp4myeuyhqvk4u

Agent-Based HOL Reasoning [chapter]

Alexander Steen, Max Wisniewski, Christoph Benzmüller
2016 Lecture Notes in Computer Science  
In the Leo-III project, a new agent-based deduction system for classical higher-order logic is developed.  ...  Key goals of the system's development involve parallelism on various levels of the proof search, adaptability for different external specialists, and native support for reasoning in expressive non-classical  ...  In first-order theorem proving, many successful systems use calculi based on ordered paramodulation [BG94] (or its even more restricted form, superposition), which improves naive resolution not only  ... 
doi:10.1007/978-3-319-42432-3_10 fatcat:zh42ihlxzbgwxfj5idt7lvuin4

PIE – Proving, Interpolating and Eliminating on the Basis of First-Order Logic [article]

Christoph Wernhard
2019 arXiv   pre-print
PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic.  ...  for second-order quantifier elimination.  ...  Conclusion The PIE system tries to supplement what is needed to use automated first-order proving techniques for developing and analyzing formalizations.  ... 
arXiv:1908.11137v1 fatcat:u5mchnvtwndmzatmeh76zy3cpy

Extensional Higher-Order Paramodulation in Leo-III [article]

Alexander Steen, Christoph Benzmüller
2021 arXiv   pre-print
Leo-III supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics.  ...  The prover may cooperate with multiple external specialist reasoning systems such as first-order provers and SMT solvers.  ...  Leo-III makes use of external (mostly first-order) ATP systems for discharging proof obligations.  ... 
arXiv:1907.11501v2 fatcat:hv3uysew6fdrtixvtv5d7ydgb4

Deciding expressive description logics in the framework of resolution

Ullrich Hustadt, Boris Motik, Ulrike Sattler
2008 Information and Computation  
This rule can be used for general first-order theorem proving with any resolution-based calculus compatible with the standard notion of redundancy.  ...  We present a decision procedure for the description logic SHIQ based on the basic superposition calculus, and show that it runs in exponential time for unary coding of numbers.  ...  Acknowledgment We thank the anonymous reviewer for many useful suggestions for improvement of this paper.  ... 
doi:10.1016/j.ic.2007.11.006 fatcat:jp5zmxjejbdatezwk422asxuc4

Extensional Paramodulation for Higher-Order Logic and Its Effective Implementation Leo-III

Alexander Steen
2019 Künstliche Intelligenz  
The completeness proof hereby unifies and simplifies existing abstract consistency techniques for a formulation of higher-order logic that is based on primitive equality as sole logical connective.  ...  The system encompasses a flexible mechanism for asynchronous cooperation with first-order reasoning systems, a powerful proof search procedure and a sophisticated and efficient set of underlying data structures  ...  This includes the search for ordering techniques as employed in first-order superposition. (4) Equational simplification procedures.  ... 
doi:10.1007/s13218-019-00628-8 fatcat:b6yfenxgxndb3myskqushsm6uy
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