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On the Semantics of Gringo [article]

Amelia Harrison, Vladimir Lifschitz, Fangkai Yang
2013 arXiv   pre-print
We propose to approach the problem of defining the semantics of gringo programs by translating them into the language of infinitary propositional formulas.  ...  This semantics allows us to study equivalent transformations of gringo programs using natural deduction in infinitary propositional logic.  ...  Acknowledgements Many thanks to Roland Kaminski and Torsten Schaub for helping us understand the input language of gringo.  ... 
arXiv:1312.6149v1 fatcat:nk6y2i53wvhuxcvewyjfvqctd4

Strong Equivalence of Logic Programs with Counting [article]

Vladimir Lifschitz
2022 arXiv   pre-print
In some cases, strong equivalence of programs in the input language of the grounder gringo can be established by deriving rules of each program from rules of the other.  ...  The possibility of such proofs has been demonstrated for a subset of that language that includes comparisons, arithmetic operations, and simple choice rules, but not aggregates.  ...  Acknowledgements Many thanks to Jorge Fandinno, Michael Gelfond, Yuliya Lierler, and the anonymous referees for comments on preliminary versions of this paper.  ... 
arXiv:2205.07783v1 fatcat:6utqunxqs5daflktcgl656gu6u

Abstract gringo

MARTIN GEBSER, AMELIA HARRISON, ROLAND KAMINSKI, VLADIMIR LIFSCHITZ, TORSTEN SCHAUB
2015 Theory and Practice of Logic Programming  
AbstractThis paper defines the syntax and semantics of the input language of the ASP groundergringo.  ...  The definition covers several constructs that were not discussed in earlier work on the semantics of that language, including intervals, pools, division of integers, aggregates with non-numeric values,  ...  Acknowledgements We are grateful to the anonymous referees for useful comments. Abstract Gringo  ... 
doi:10.1017/s1471068415000150 fatcat:kfv3n7tmlbbjxbsurl3tliyyri

Abstract gringo

Martin Gebser, Amelia Harrison, Roland Kaminski, Vladimir Lifschitz, Torsten Schaub
2018 Postprints der Universität Potsdam: Mathematisch-Naturwissenschaftliche Reihe  
This paper defines the syntax and semantics of the input language of the ASP grounder gringo.  ...  The definition covers several constructs that were not discussed in earlier work on the semantics of that language, including intervals, pools, division of integers, aggregates with non-numeric values,  ...  Acknowledgements We are grateful to the anonymous referees for useful comments.  ... 
doi:10.25932/publishup-41475 fatcat:w2cjwfcb5fcp5eso2cyjkloxt4

Program Completionin the Input Language of GRINGO [article]

Amelia Harrison, Vladimir Lifschitz, Dhananjay Raju
2017 arXiv   pre-print
Accordingly, it may be useful to define completion for a large class of ASP programs and to automate the process of generating and simplifying completion formulas.  ...  As a step toward this goal, we propose here a definition of program completion for a large class of programs in the input language of the ASP grounder GRINGO, and study its properties.  ...  Many thanks to Michael Gelfond, Joohyung Lee, Patrick Lühne, and Torsten Schaub for useful discussions related to the topic of this paper, and to the anonymous referees for their comments.  ... 
arXiv:1707.05848v2 fatcat:e43nvbquyrbwjjgdjzy2kkjixq

Program completion in the input language of GRINGO

AMELIA HARRISON, VLADIMIR LIFSCHITZ, DHANANJAY RAJU
2017 Theory and Practice of Logic Programming  
As a step toward this goal, we propose here a definition of program completion for a large class of programs in the input language of the ASP grounder gringo, and study its properties.  ...  Accordingly, it may be useful to define completion for a large class of Answer Set Programming (ASP) programs and to automate the process of generating and simplifying completion formulas.  ...  Many thanks to Michael Gelfond, Joohyung Lee, Patrick Lühne, and Torsten Schaub for useful discussions related to the topic of this paper, and to the anonymous referees for their comments.  ... 
doi:10.1017/s1471068417000394 fatcat:jfw27bmlhrhirhxholsxb33utq

Infinitary Equilibrium Logic and Strong Equivalence [chapter]

Amelia Harrison, Vladimir Lifschitz, David Pearce, Agustín Valverde
2015 Lecture Notes in Computer Science  
Equilibrium logic was used to show that propositional formulas are strongly equivalent if and only if they are equivalent in the logic of here-and-there.  ...  We extend equilibrium logic to formulas with infinitely long conjunctions and disjunctions, define and axiomatize an infinitary counterpart to the logic of here-and-there, and show that the theorem on  ...  Acknowledgements Thanks to Pedro Cabalar and Yuliya Lierler, and to the anonymous referees for helpful comments.  ... 
doi:10.1007/978-3-319-23264-5_33 fatcat:ireikpz6pzexrptt7rblwslpbu

Infinitary equilibrium logic and strongly equivalent logic programs

Amelia Harrison, Vladimir Lifschitz, David Pearce, Agustín Valverde
2017 Artificial Intelligence  
We extend this line of work to formulas with infinitely long conjunctions and disjunctions, show that the infinitary logic of here-and-there characterizes strong equivalence of infinitary formulas, and  ...  Equilibrium logic was used to prove that sets of rules expressed as propositional formulas are strongly equivalent if and only if they are equivalent in the logic of here-and-there.  ...  Thanks also to Pedro Cabalar, Yuliya Lierler, Victor Marek, Dhananjay Raju, John Schlipf, and Mirek Truszczynski for useful discussions related to the topic of this paper.  ... 
doi:10.1016/j.artint.2017.02.002 fatcat:wbv5o7de5nfelin4fut7zrxdqm

On the Foundations of Grounding in Answer Set Programming [article]

Roland Kaminski, Torsten Schaub
2022 arXiv   pre-print
We address an expressive class of logic programs that incorporates recursive aggregates and thus amounts to the scope of existing ASP modeling languages.  ...  This is accompanied with a plain algorithmic framework detailing the grounding of recursive aggregates. The given algorithms correspond essentially to the ones used in the ASP grounder gringo.  ...  programs with infinitary propositional formulas [63] .  ... 
arXiv:2108.04769v2 fatcat:bas6bi75czgsblnsfqerqylb3u

Verifying Tight Logic Programs with anthem and Vampire [article]

Jorge Fandinno, Vladimir Lifschitz, Patrick Lühne, Torsten Schaub
2020 arXiv   pre-print
We extend the definition of program completion to programs with input and output in a subset of the input language of the ASP grounder gringo, study the relationship between stable models and completion  ...  Proofs of theorems are based on a lemma that relates the semantics of programs studied in this paper to stable models of first-order formulas. Under consideration for acceptance in TPLP.  ...  Acknowledgments We thank Michael Gelfond and the anonymous referees for their valuable comments. Jorge Fandinno is funded by the Alexander von Humboldt Foundation.  ... 
arXiv:2008.02025v3 fatcat:gtup3izmtrdkzmzwli5qi5brde

Verification of Locally Tight Programs [article]

Jorge Fandinno, Vladimir Lifschitz
2022 arXiv   pre-print
ANTHEM is a proof assistant that can be used for verifying the correctness of tight programs in the input language of the answer set grounder GRINGO with respect to specifications expressed by first-order  ...  formulas.  ...  Strong equivalence of infinitary propositional formulas was defined and studied by Harrison et al. (2017) .  ... 
arXiv:2204.10789v1 fatcat:yu2gqhtcevdwdhz5cdk435f4iq

ASP-Core-2 Input Language Format [article]

Francesco Calimeri, Wolfgang Faber, Martin Gebser, Giovambattista Ianni, Roland Kaminski, Thomas Krennwallner, Nicola Leone, Marco Maratea, Francesco Ricca, Torsten Schaub
2019 arXiv   pre-print
Standardization of solver input languages has been a main driver for the growth of several areas within knowledge representation and reasoning, fostering the exploitation in actual applications.  ...  In this document we present the ASP-Core-2 standard input language for Answer Set Programming, which has been adopted in ASP Competition events since 2013.  ...  The semantics of Abstract Gringo (Gebser et al. 2015) handles such cases by means of infinitary propositional formulas, while the Abstract Gringo language avoids infinite collections of aggregate elements  ... 
arXiv:1911.04326v1 fatcat:xh2elec6fvcxtdgsybztswwnky

Grounding Recursive Aggregates: Preliminary Report [article]

Martin Gebser and Roland Kaminski and Torsten Schaub
2016 arXiv   pre-print
In this paper, we elaborate upon the treatment of aggregates during grounding in Gringo series 4.  ...  In particular, we provide a series of algorithms detailing the treatment of recursive aggregates and illustrate this by a running example.  ...  Acknowledgments This work was funded by AoF (grant 251170), DFG (grants SCHA 550/8 and 550/9), as well as DAAD and AoF (joint project 57071677 / 279121).  ... 
arXiv:1603.03884v1 fatcat:6zxlz277yzcmnga3f5pdafdbuq

Formal methods for answer set programming [article]

Amelia J. Harrison
2018
The semantics represents gringo rules as infinitary propositional formulas. We develop methods for using this semantics to prove properties of gringo programs, such as verifying program correctness.  ...  Even so, manuals written by the designers of answer set solvers usually described the semantics of the input languages of their systems using examples and informal comments that appeal to the users' intuition  ...  Acknowledgements My sincere thanks to my friend and mentor Vladimir Lifschitz. Thanks also to the anonymous reviewers.  ... 
doi:10.15781/t2t727z61 fatcat:xadmrn36fzgrne5k4dfe7lffva

Automata Techniques for Temporal Answer Set Programming

Susana Hahn
2021 Electronic Proceedings in Theoretical Computer Science  
Temporal and dynamic extensions of Answer Set Programming (ASP) have played an important role in addressing dynamic problems, as they allow the use of temporal operators to reason with dynamic scenarios  ...  In my Ph.D. research, I intend to exploit the relationship between automata theory and dynamic logic to add automata-based techniques to the ASP solver CLINGO helping us to deal with theses type of problems  ...  Listing 2: Declarative representation of the AFW in Figure 2 obtained by translating formula (1). to First-order infinitary logic, and the other inspired on the definition of [48] for LTL f .  ... 
doi:10.4204/eptcs.345.42 fatcat:3f37xiiesbda7hhrs74amnebla
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