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Strategic Issues, Problems and Challenges in Inductive Theorem Proving

Bernhard Gramlich
2005 Electronical Notes in Theoretical Computer Science  
Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving.  ...  In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging.  ...  I'm very grateful to Maria Paola Bonacina and Thierry Boy de la Tour, the Program Co-Chairs of STRATEGIES 2004, for this kind invitation and for their helpful comments on a draft version of this paper.  ... 
doi:10.1016/j.entcs.2005.01.006 fatcat:reml2iecwfexhlnmr4d22a7sj4

Parallelization of Termination Checkers for Algebraic Software

Rui Ding, Haruhiko Sato, Masahito Kurihara
2014 Transactions on Machine Learning and Artificial Intelligence  
Well-known as a method for inductive theorem proving is the Rewriting Induction (RI) proposed by Reddy.  ...  In the field of formal verification of information systems, most of the properties of such a system are formalized as inductive theorems, which are equations over terms which hold on recursivelydefined  ...  The termination property is a very important property especially in automated inductive theorem proving, which tries to prove inductive theorems, which are equations over terms which hold on recursively-defined  ... 
doi:10.14738/tmlai.24.368 fatcat:r4huox3sc5fbrfruzj3xlzy5si

The Strategy Challenge in SMT Solving [chapter]

Leonardo de Moura, Grant Olney Passmore
2013 Lecture Notes in Computer Science  
This issue is becoming increasingly pressing as SMT solvers begin to gain the attention of practitioners in diverse areas of science and engineering.  ...  We present evidence that the adaptation of ideas of strategy prevalent both within the Argonne and LCF theorem proving paradigms can go a long way towards realizing this goal. Prologue.  ...  Jackson, Joost Joosten and Larry Paulson for helpful comments on a draft of this paper. We thank the referees for their many useful corrections and suggestions.  ... 
doi:10.1007/978-3-642-36675-8_2 fatcat:op5iarzvnvfkddz5ycsgyzo264

Proof planning with multiple strategies

Erica Melis, Andreas Meier, Jörg Siekmann
2008 Artificial Intelligence  
This strategic control guides the cooperation of the problem solving strategies by meta-reasoning.  ...  Proof planning is a technique for theorem proving which replaces the ultra-efficient but blind search of classical theorem proving systems by an informed knowledge-based planning process that employs mathematical  ...  Acknowledgement The work reported in this paper was done in a time span of several years and this paper reports the state of development up to and including the year 2004.  ... 
doi:10.1016/j.artint.2007.11.004 fatcat:g4keqaoqjjartcaufcspbv3fz4

An Open Challenge Problem Repository for Systems Supporting Binders

Amy Felty, Alberto Momigliano, Brigitte Pientka
2015 Electronic Proceedings in Theoretical Computer Science  
In this paper we design an open repository ORBI (Open challenge problem Repository for systems supporting reasoning with BInders).  ...  key aspects that arise in the presence of binders.  ...  In this paper, we propose a common infrastructure for representing challenge problems and a central, Open challenge problem Repository for systems supporting reasoning with BInders (ORBI) for sharing benchmark  ... 
doi:10.4204/eptcs.185.2 fatcat:3rjitd2lxngqrppl77fytjulvm

Strategic Argumentation is NP-Complete [article]

Guido Governatori, Francesco Olivieri, Simone Scannapieco, Antonino Rotolo, Matteo Cristani
2013 arXiv   pre-print
We show how to model dialogue games in a skeptical, non-monotonic formalism, and we show that the problem of deciding what move (set of rules) to play at each turn is an NP-complete problem.  ...  In this paper we study the complexity of strategic argumentation for dialogue games. A dialogue game is a 2-player game where the parties play arguments.  ...  It is included in this paper to show how to reduce the restoring sociality problem into the strategic argumentation problem, proving thus that the later is also an NP-complete problem.  ... 
arXiv:1312.4287v1 fatcat:nqkfmizmlzcinobf2clcarknvm

Strategic sequential voting in multi-issue domains and multiple-election paradoxes

Lirong Xia, Vincent Conitzer, Jérôme Lang
2011 Proceedings of the 12th ACM conference on Electronic commerce - EC '11  
In each step, the voters simultaneously vote on one issue, and the order of the issues is determined before the process. We call this model strategic sequential voting.  ...  We show several multiple-election paradoxes in strategic sequential voting: there exists a profile for which the winner under strategic sequential voting is ranked nearly at the bottom in all votes, and  ...  issues is an extremely challenging problem for which probably no perfect solution exists.  ... 
doi:10.1145/1993574.1993602 dblp:conf/sigecom/XiaCL11 fatcat:jkk5n5qlyrg5dc2rbkji3qz5iy

The AProS Project: Strategic Thinking & Computational Logic

W. Sieg
2007 Logic Journal of the IGPL  
The Proof Lab is a sophisticated interface for constructing natural deduction proofs and is central, as strategically guided discovery of proofs is the distinctive focus of the course.  ...  (I recommend that the reader enter the virtual classroom of Logic & Proofs: the interactive components just cannot be properly reflected in a narrative.  ...  For the longest time they were considered as ''unsuitable for automated theorem proving''; that's how Fitting expressed it in the first edition of his book [9] on theorem proving.  ... 
doi:10.1093/jigpal/jzm026 fatcat:wgf66qtnrvb2doksuly24dgoda

The Cantor–Bernstein theorem: how many proofs?

Wilfried Sieg
2019 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
This article is part of the theme issue 'The notion of 'simple proof' -Hilbert's 24th problem'.  ...  It is a non-trivial task to establish the structural identity when c is defined in this way; Dedekind of course addressed and solved the problem (in theorems #57 and #58 of WZ).  ...  Appendix A Here is the list of lemmas that are actually used in the top-level proof of the Cantor-Bernstein  ... 
doi:10.1098/rsta.2018.0031 fatcat:6mn65xece5gutdqkd7iryvivcq

Integrating Automated and Interactive Theorem Proving [chapter]

Ahrendt, Beckert, Hähnle, Menzel, Reif, Schellhorn, Schmitt
1998 Applied Logic Series  
Inductive Theorems Many theorems can only be proved inductively from the axioms, but most automated theorem provers (including 3 T A P) are not capable of finding inductive proofs.  ...  The presence of inductive theorems is a fundamental problem. It can be mitigated by adding previously derived (inductive) theorems as lemmas.  ... 
doi:10.1007/978-94-017-0435-9_4 fatcat:nsfxar65jbhybcrsdvi2stys6u

Failure Reasoning in Multiple-Strategy Proof Planning

Andreas Meier, Erica Melis
2005 Electronical Notes in Theoretical Computer Science  
Monitoring a solution process and applying the right action at the right moment are at the heart of intelligent problem solving by humans.  ...  Because of the flexible control in Multi failures can be exploited to guide subsequent proof plan manipulations and refinements.  ...  Bledsoe proposed several versions of the problem Lim+ as a challenge problem for automated theorem proving [2] .  ... 
doi:10.1016/j.entcs.2005.01.004 fatcat:2ep6krwoofg6re3psieiurp2te

A normal simulation of coalition logic and an epistemic extension

Jan Broersen, Andreas Herzig, Nicolas Troquard
2007 Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge - TARK '07  
In this paper we show how coalition logic can be reduced to the fusion of a normal modal STIT logic for agency and a standard normal temporal logic for discrete time, and how this multi-modal system can  ...  In accordance with established terminology in the planning community, we call this version of STIT the 'conformant STIT'.  ...  Acknowledgement We would like to thank Philippe Balbiani, Olivier Gasquet and François Schwarzentruber for useful discussions concerning parts of the paper.  ... 
doi:10.1145/1324249.1324264 dblp:conf/tark/BroersenHT07 fatcat:6zvg6myqvzeobpwsweije3jjya

Automated Reasoning in Social Choice Theory - Some Remarks [article]

Siddharth Chatterjee, Arunava Sen
2014 arXiv   pre-print
We also provide statements and brief descriptions of the results discussed in this note.  ...  We shall specifically comment on two papers, one by Tang and Lin (2009) and another by Geist and Endriss (2011).  ...  Heuristically the median voter rule is a more complex rule than a dictatorship and proving a reduction, especially on the number of alternatives is a more challenging task.  ... 
arXiv:1403.3391v1 fatcat:xb6pvwxolrhuxahg7wtxaxfe24

A Unified Approach to Dynamic Decision Problems with Asymmetric Information - Part I: Non-Strategic Agents [article]

Hamidreza Tavafoghi, Yi Ouyang, Demosthenis Teneketzis
2018 arXiv   pre-print
We study a general class of dynamic multi-agent decision problems with asymmetric information and non-strategic agents, which includes dynamic teams as a special case.  ...  beliefs over time, and enables us to formulate a dynamic program to determine a globally optimal policy via backward induction.  ...  Next, we prove condition (b) by backward induction.  ... 
arXiv:1812.01130v1 fatcat:4g5bmwx5srfeteufavgi5ephv4

Some fixed points of expansion mappings

H. K. Pathak, S. M. Kang, J. W. Ryu
1996 International Journal of Mathematics and Mathematical Sciences  
Wang et al. [11] proved some fixed point theorems on expansion mappings, which correspond some contractive mappings.  ...  Recently, several authors generalized their results by some ways.In this paper, we give some fixed point theorems for expansion mappings, which improve the results of some authors.  ...  Inductively, we can define a sequence {y,,} in S(X.) such that Taking the limit as n c in each case yields y St,. A similar argument applies to proving that y Su.  ... 
doi:10.1155/s0161171296000154 fatcat:kvkph73zwvbopo4yg4iuhrdlym
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