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Page 5300 of Mathematical Reviews Vol. , Issue 2000h [page]

2000 Mathematical Reviews  
Symbolic Logic 63 (1998), no. 3, 831-859.  ...  2000h:03106 preparation], the procedure given here provides technical tools that allow us to treat cut-elimination for all such logics in a modular way.”  ... 

Metareasoning for Multi-agent Epistemic Logics [chapter]

Konstantine Arkoudas, Selmer Bringsjord
2005 Lecture Notes in Computer Science  
We present an encoding of a sequent calculus for a multiagent epistemic logic in Athena, an interactive theorem proving system for many-sorted first-order logic.  ...  We then use Athena as a metalanguage in order to reason about the multi-agent logic an as object language. This facilitates theorem proving in the multi-agent logic in several ways.  ...  Introduction Multi-agent modal logics are widely used in Computer Science and AI.  ... 
doi:10.1007/11533092_7 fatcat:eegohnqdojc7feu4gx4jnj4xay

The KeY Platform for Verification and Analysis of Java Programs [chapter]

Wolfgang Ahrendt, Bernhard Beckert, Daniel Bruns, Richard Bubel, Christoph Gladisch, Sarah Grebing, Reiner Hähnle, Martin Hentschel, Mihai Herda, Vladimir Klebanov, Wojciech Mostowski, Christoph Scheben (+2 others)
2014 Lecture Notes in Computer Science  
We use the current release of the KeY system as an example to explain and prove this claim.  ...  The KeY system offers a platform of software analysis tools for sequential Java. Foremost, this includes full functional verification against contracts written in the Java Modeling Language.  ...  A proof in KeY consists of logical rule applications on DL sequents, using a proof strategy called symbolic execution.  ... 
doi:10.1007/978-3-319-12154-3_4 fatcat:3eunuqfaxzhdvg6xcr5muxx2sq

LJQ: A Strongly Focused Calculus for Intuitionistic Logic [chapter]

Roy Dyckhoff, Stéphane Lengrand
2006 Lecture Notes in Computer Science  
LJQ is a focused sequent calculus for intuitionistic logic, with a simple restriction on the first premisss of the usual left introduction rule for implication.  ...  We discuss its history (going back to about 1950, or beyond), present the underlying theory and its applications both to terminating proof-search calculi and to call-by-value reduction in lambda calculus  ...  Introduction Proof systems for intuitionistic logic close to natural deduction are well-known to be related to computation.  ... 
doi:10.1007/11780342_19 fatcat:bzzrvpy2jrhcpbpmk5lswpd4ty

A Multi-level Approach to Program Synthesis [chapter]

W. Bibel, D. Korn, C. Kreitz, F. Kurucz, J. Otten, S. Schmitt, G. Stolpmann
1998 Lecture Notes in Computer Science  
We present an approach to a coherent program synthesis system which integrates a variety of interactively controlled and automated techniques from theorem proving and algorithm design at different levels  ...  Besides providing an overall view we summarize the individual research results achieved in the course of this development.  ...  foundation for the automated derivation of global search algorithms within the integrated synthesis system.  ... 
doi:10.1007/3-540-49674-2_1 fatcat:ks4d6vdjp5hd5im5yhoi4hebpi

The Sequent Calculus Trainer with Automated Reasoning - Helping Students to Find Proofs

Arno Ehle, Norbert Hundeshagen, Martin Lange
2018 Electronic Proceedings in Theoretical Computer Science  
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic.  ...  In this paper we describe the didactical motivation behind the tool and the techniques used to address issues on the syntactic as well as on the semantic level.  ...  Although, the KEY-System is meant as a verification tool for JAVA-Programs it can be used as an interactive prover of sequents in first-order logic.  ... 
doi:10.4204/eptcs.267.2 fatcat:kp34qcruqzbifgu6penq2hzdjq

Automated Theorem Proving in Intuitionistic Propositional Logic by Deep Reinforcement Learning [article]

Mitsuru Kusumoto, Keisuke Yahata, Masahiro Sakai
2018 arXiv   pre-print
In this paper, we propose a deep reinforcement learning algorithm for proof search in intuitionistic propositional logic.  ...  Using the large volume of augmented data, we train highly accurate graph neural networks that approximate the value function for the set of the syntactic structures of formulas.  ...  We represent proofs and sequents in IPL as the terms in simply-typed lambda calculus, implemented in the Rust programming language.  ... 
arXiv:1811.00796v1 fatcat:z7u47hrii5hwbm2at2utkv5lgq

Specifying Real-Time Systems in Rewriting Logic

Peter Csaba Ölveczky, José Meseguer
1996 Electronical Notes in Theoretical Computer Science  
We present a general method to specify and symbolically simulate such systems in rewriting logic and illustrate it with a well-known benchmark.  ...  This work investigates the suitability of rewriting logic as a semantic framework for modeling real-time and hybrid systems.  ...  helped us in the development of these ideas and in improving their presentation.  ... 
doi:10.1016/s1571-0661(04)00044-1 fatcat:apsdwr6bsbdh7bcjihus6mumzy

Strong Cut-Elimination Systems for Hudelmaier's Depth-Bounded Sequent Calculus for Implicational Logic [chapter]

Roy Dyckhoff, Delia Kesner, Stéphane Lengrand
2006 Lecture Notes in Computer Science  
In contrast to previous papers which gave different arguments for Cut-admissibility suggesting weakly normalising procedures for Cut-elimination, our main reduction system and all its variations are strongly  ...  Inspired by the Curry-Howard correspondence, we study normalisation procedures in the depth-bounded intuitionistic sequent calculus of Hudelmaier (1988) for the implicational case, thus strengthening existing  ...  The merits of G4ip for proof-search and automated reasoning have been discussed in many papers (see [ORK05] for some recent pointers; note its use of an old name LJT for G4ip).  ... 
doi:10.1007/11814771_31 fatcat:jb3ubatigjg4pa2npzima57vlq

Distributed Theorem Proving for Distributed Hybrid Systems [chapter]

David W. Renshaw, Sarah M. Loos, André Platzer
2011 Lecture Notes in Computer Science  
We address the problem of automated theorem proving for distributed hybrid systems.  ...  Quantified Differential Dynamic Logic (QdL) has been identified as a promising approach for getting a handle in this domain.  ...  Conclusions and Future Work We introduce automation techniques for theorem proving for distributed hybrid systems using quantified differential dynamic logic.  ... 
doi:10.1007/978-3-642-24559-6_25 fatcat:hzb2queslvcqdizjuasomws2u4

Automated Theorem Proving for Assertions in Separation Logic with All Connectives [chapter]

Zhé Hóu, Rajeev Goré, Alwen Tiu
2015 Lecture Notes in Computer Science  
We give a sound labelled sequent calculus for this logic.  ...  We extend the calculus with rules for linked lists and binary trees, giving a sound, complete and terminating proof system for a popular fragment called symbolic heaps.  ...  It is impossible to obtain a finite, sound and complete sequent system for this logic, so we focused on soundness, usefulness, and efficiency.  ... 
doi:10.1007/978-3-319-21401-6_34 fatcat:byopcdeyu5arjamegrfdlqbjhe

Explicit Provability and Constructive Semantics

Sergei N. Artemov
2001 Bulletin of Symbolic Logic  
LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and λ-calculus.  ...  In 1933 Gödel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem.  ...  are present in single-conclusion as well as in multi-conclusion proof systems. On the other hand, "+" is an operation for multi-conclusion proof systems only.  ... 
doi:10.2307/2687821 fatcat:twz2ui2ckzabzp6b2f64nlhm6i

Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics [chapter]

Tim Lyon, Kees van Berkel
2019 Lecture Notes in Computer Science  
This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics.  ...  In the single-agent case, we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent  ...  In the present work, we employ the labelled sequent calculus-a useful formalism for a large class of modal logics [14, 18] -and introduce labelled sequent calculi G3Ldm m n (with n, m ∈ N) for multi-agent  ... 
doi:10.1007/978-3-030-33792-6_13 fatcat:pqnsjkw7p5di7g4jfylzq34mjq

Simultaneous rigid E-unification and other decision problems related to the Herbrand theorem

Andrei Voronkov
1999 Theoretical Computer Science  
A sequent is an expression r 4 d, where r and d are multisets of formulas. In  ...  We shall also use ordinals and wildcards in the notation for signatures.  ...  I am also grateful to the editor of this volume Sergei Adian for his patience and to an anonymous referee for helpful comments.  ... 
doi:10.1016/s0304-3975(98)00317-x fatcat:f2gi56tez5hlnck3ech6uj26nu

A Survey of the Proof-Theoretic Foundations of Logic Programming [article]

Dale Miller
2021 arXiv   pre-print
In this paper, we will survey the use of structural proof theory as an alternative foundation.  ...  Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming.  ...  Acknowledgments: I thank Miroslaw Truszczynski and several anonymous reviewers for their comments on an earlier version of this paper.  ... 
arXiv:2109.01483v2 fatcat:fp3c746m5zaavd56ltn2d43kp4
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