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Towards the Automated Generation of Focused Proof Systems

Vivek Nigam, Giselle Reis, Leonardo Lima
2015 Electronic Proceedings in Theoretical Computer Science  
We then show that from the permutation graph of a given proof system, it is possible to construct a complete focused proof system, and additionally infer for which formulas contraction is admissible.  ...  We apply our technique to generate the focused proof systems MALLF, LJF and LKF for linear, intuitionistic and classical logics, respectively.  ...  Let α and β be two inference rules in a sequent calculus system S.  ... 
doi:10.4204/eptcs.197.1 fatcat:5gag6nfrxnhgpof2k7uyok75ny

Logic Programming with Focusing Proofs in Linear Logic

1992 Journal of Logic and Computation  
However, proofs in this system may be redundant, in that two proofs can be syntactically di erent although identical up to some irrelevant reordering or simpli cation of the applications of the inference  ...  To overcome this problem, a subclass of proofs, called the \focusing" proofs, which is both complete (any derivable formula in Linear Logic has a focusing proof) and tractable (many irrelevant choices  ...  I am indebted to the members of the jury for their helpful comments and suggestions. I also thank G. Comyn and A. Herold for their encouragement and support at ECRC. Special thanks are due to R.  ... 
doi:10.1093/logcom/2.3.297 fatcat:xfbkveid4fcvfiaiyy7vdxqohm

Focused Labeled Proof Systems for Modal Logic [chapter]

Dale Miller, Marco Volpe
2015 Lecture Notes in Computer Science  
Focused proofs are sequent calculus proofs that group inference rules into alternating positive and negative phases.  ...  We show here that the inference rules of labeled proof systems for modal logics can similarly be described as pairs of such phases within the LKF focused proof system for first-order classical logic.  ...  This work was carried out during the tenure of an ERCIM Alain Bensoussan Fellowship Programme by the second author and was funded by the ERC Advanced Grant ProofCert.  ... 
doi:10.1007/978-3-662-48899-7_19 fatcat:76e33jclefg27cisg6juqbxyxi

A New Proof-Theoretical Linear Semantics for CHR

Igor Stéphan, Michael Wagner
2018 International Conference on Logic Programming  
We demonstrate completeness and soundness of our semantics w.r.t. operational ω t semantics. We propose also a translation from this semantics to linear logic.  ...  The Focusing inference rule flips from the non focused ω ⊗ l system to the focused ω ⊗ l system by focusing on an identified constraint.  ...  We first define our sequents for the ω l and ω ⊗ l systems. Definition 3 (non focused and focused ω l and ω ⊗ l sequents).  ... 
doi:10.4230/oasics.iclp.2018.4 dblp:conf/iclp/Stephan18 fatcat:qgstjeg2cjfytakgb54fcuym3m

A Proposal for Broad Spectrum Proof Certificates [chapter]

Dale Miller
2011 Lecture Notes in Computer Science  
naturally from the structure of such focused proof systems.  ...  After presenting focused proof systems for first-order classical logics (one with and one without fixed points and equality) we illustrate several examples of proof certificates formats that are derived  ...  I wish to thank Alberto Momigliano, Gopalan Nadathur, Alwen Tiu, and the referees for their comments on an earlier draft of this paper.  ... 
doi:10.1007/978-3-642-25379-9_6 fatcat:a2l3al6pznh4vgescdsdqifedu

Conditional Inference and Activation of Knowledge Entities in ACT-R [article]

Marco Wilhelm, Diana Howey, Gabriele Kern-Isberner, Kai Sauerwald, Christoph Beierle
2021 arXiv   pre-print
Therewith, our approach integrates several aspects of human reasoning into expert systems such as focusing, forgetting, and remembering.  ...  the current query and its usage history.  ...  Acknowledgments This work is supported by DFG Grant KE 1413/10-1 awarded to Gabriele Kern-Isberner and DFG Grant BE 1700/9-1 awarded to Christoph Beierle as part of the priority program "Intentional Forgetting  ... 
arXiv:2110.15214v1 fatcat:flfos3nxkfbxda2i6iperlxvo4

Least and Greatest Fixed Points in Linear Logic

David Baelde
2012 ACM Transactions on Computational Logic  
In particular, µMALL = satisfies cut-elimination, which implies consistency, and has a complete focused proof system.  ...  We then consider applying these two results about µMALL = to derive a focused proof system for an intuitionistic logic extended with induction and co-induction.  ...  This work has been supported in part by INRIA through the "Equipes Associées" Slimmer and by the Information Society Technologies programme of the European Commission, Future and Emerging Technologies  ... 
doi:10.1145/2071368.2071370 fatcat:zicllwzchvbjpopgi2uf3swaae

Page 82 of Library & Information Science Abstracts Vol. , Issue 9 [page]

1995 Library & Information Science Abstracts  
Focuses on the classification of inference target classes and the use of conceptual graphs for database inference detection. Original abstract-amended.  ...  SE 10862 Computers learn to smell and taste. N. Ryman-Tubb. Expert Systems, 12 (2) May 95, p.157-61. il.refs.  ... 

Characteristics of Pro-c Analogies and Blends between Research Publications

Yalemisew M. Abgaz, Diarmuid P. O'Donoghue, Donny Hurley, Ehtzaz Chaudhry, Jian-Jun Zhang
2017 International Conference on Computational Creativity  
Surprisingly, our results show that metrics focused on the mapping appear to have less relevance to creativity than metrics assessing the inferences (blended space).  ...  Dr Inventor processes original research documents using a combination of lexical analysis and cognitive computation to identify novel comparisons that suggest new research hypotheses, with the objective  ...  Let i signify an individual inference and |i| represent its trigram frequency in the repository, then the novelty of the inference, N(i) is given by 𝑁 𝑖 = 0 𝑖 > 0 1 − 𝑃 𝑖 𝑖 = 0 where P(i) is the  ... 
dblp:conf/icccrea/AbgazOHC017 fatcat:d6i7gy35s5hcbksbuzaptl3mwa

A Proof Theory for Model Checking

Quentin Heath, Dale Miller
2018 Journal of automated reasoning  
are described using the proof-theoretic notions of polarization and focused proof systems.  ...  In order to accommodate more expressive and finitary inference rules, we also allow multiplicative rules but limit their use to the construction of additive synthetic inference rules: such synthetic rules  ...  the use of focusing proof systems to build synthetic inference rules.  ... 
doi:10.1007/s10817-018-9475-3 fatcat:d523nlxverhplggq4ix2s34ppi

Specifying Proof Systems in Linear Logic with Subexponentials

Vivek Nigam, Elaine Pimentel, Giselle Reis
2011 Electronical Notes in Theoretical Computer Science  
We demonstrate this by encoding the system G1m for minimal, the multi-conclusion system, mLJ, and the focused system LJQ * , for intuitionistic logic.  ...  This work shows that one can encode a wider range of proof systems by using focused linear logic with subexponentials.  ...  The cut and initial inference rules are "dual" inference rules.  ... 
doi:10.1016/j.entcs.2011.03.009 fatcat:wyzvjdecyvaebolnebwgliih6i

Axiom Directed Focusing [chapter]

Clément Houtmann
2009 Lecture Notes in Computer Science  
In this paper we revisit the superdeduction paradigm by comparing it with the focusing approach.  ...  modulo system, provided our synchrony hypotheses hold.  ...  Acknowledgements: The author thanks Claude Kirchner for his useful comments and advices.  ... 
doi:10.1007/978-3-642-02444-3_11 fatcat:ex67vbd6jjfzbh54oiwvhieula

Learning, Planning, and Control in a Monolithic Neural Event Inference Architecture [article]

Martin V. Butz and David Bilkey and Dania Humaidan and Alistair Knott and Sebastian Otte
2019 arXiv   pre-print
We introduce REPRISE, a REtrospective and PRospective Inference SchEme, which learns temporal event-predictive models of dynamical systems.  ...  Moreover, we show that REPRISE can exploit the learned model to induce goal-directed, model-predictive control, that is, approximate active inference: Given a goal state, the system imagines a motor command  ...  system scalability and focusing learning in general, the identified event boundary signals may be particularly useful.  ... 
arXiv:1809.07412v2 fatcat:mgonsszyorcxvpsobdnyktqobm

Focused Inductive Theorem Proving [chapter]

David Baelde, Dale Miller, Zachary Snow
2010 Lecture Notes in Computer Science  
Focused proof systems provide means for reducing and structuring the non-determinism involved in searching for sequent calculus proofs.  ...  We present a focused proof system for a first-order logic with inductive and co-inductive definitions in which the introduction rules are partitioned into an asynchronous phase and a synchronous phase.  ...  Opinions, findings, and conclusions or recommendations expressed in this papers are those of the authors and do not necessarily reflect the views of the National Science Foundation.  ... 
doi:10.1007/978-3-642-14203-1_24 fatcat:lebzhuoterbs5g6ux2lqr4gqyi

Separating Functional Computation from Relations

Ulysse Gérard, Dale Miller, Marc Herbstritt
2017 Annual Conference for Computer Science Logic  
Instead, we use the familiar twophase construction of focused proofs and capture functional computation entirely within one of these phases.  ...  Both Hilbert and Church added choice operators (such as the epsilon operator) to logic in order to coerce relations that happen to encode functions into actual functions.  ...  We thank Beniamino Accattoli, Roberto Blanco, and the anonymous reviewers for their comments on an earlier draft of this paper.  ... 
doi:10.4230/lipics.csl.2017.23 dblp:conf/csl/GerardM17 fatcat:pz4rcvjdu5hgpabqtav2e5osv4
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