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Logics for probabilistic programming (Extended Abstract)

John H. Reif
1980 Proceedings of the twelfth annual ACM symposium on Theory of computing - STOC '80  
PROB-QBF (for probabilistic boolean logic) which has some interesting applications to the theory of probabilistic programming.  ...  The Definition of PROB-DL We define here only a propositional version of our probabilistic program logic (though in Section 5 we describe how to extend the logic to first order) ~.  ... 
doi:10.1145/800141.804647 dblp:conf/stoc/Reif80 fatcat:mlloowwaxvaedcuy4wlpki6kt4

Interval –valued probabilistic logic for logic programs

Phan Dinh Dieu, Phan Hong Giang
2016 Journal of Computer Science and Cybernetics  
It is shown that in the case of probabilistic logic programs the set of such prime implicants can be found by using the SLD-resolution method for usual definte logic programs.  ...  This paper presents an approximate method for probabilistic entailment problem in knowledge bases where a portion of knowledge is given by a sentence in propositional logic accompanied with an interval  ...  It is shown to be very efficient for probabilistic logic programs, i.e.. when logical skeletons of knowledge  ... 
doi:10.15625/1813-9663/10/3/8193 fatcat:mj3u6xxydnetnp35jf2gbd6kdy

An Assertion-Based Program Logic for Probabilistic Programs [chapter]

Gilles Barthe, Thomas Espitau, Marco Gaboardi, Benjamin Grégoire, Justin Hsu, Pierre-Yves Strub
2018 Lecture Notes in Computer Science  
We also show that Ellora allows convenient reasoning about complex probabilistic concepts by developing a new program logic for probabilistic independence and distribution law, and then smoothly embedding  ...  Ellora features new proof rules for loops and adversarial code, and supports richer assertions than existing program logics.  ...  We thank the reviewers for their helpful comments. This work benefited from discussions with Dexter Kozen, Annabelle McIver, and Carroll Morgan.  ... 
doi:10.1007/978-3-319-89884-1_5 fatcat:vuxgmjepovgslhqggyidblsyxe

An Assertion-Based Program Logic for Probabilistic Programs [article]

Gilles Barthe and Thomas Espitau and Marco Gaboardi and Benjamin Grégoire and Justin Hsu and Pierre-Yves Strub
2018 arXiv   pre-print
We also show that Ellora allows convenient reasoning about complex probabilistic concepts by developing a new program logic for probabilistic independence and distribution law, and then smoothly embedding  ...  Ellora features new proof rules for loops and adversarial code, and supports richer assertions than existing program logics.  ...  We thank the reviewers for their helpful comments. This work benefited from discussions with Dexter Kozen, Annabelle McIver, and Carroll Morgan.  ... 
arXiv:1803.05535v1 fatcat:6rsr2vcc6ve3xjwraql75uhh7q

Quantitative separation logic: a logic for reasoning about probabilistic pointer programs

Kevin Batz, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja, Thomas Noll
2019 Proceedings of the ACM on Programming Languages (PACMPL)  
This calculus is a conservative extension of both Reynolds' separation logic for heap-manipulating programs and Kozen's / McIver and Morgan's weakest preexpectations for probabilistic programs.  ...  Furthermore, we develop a weakest precondition calculus for quantitative reasoning about probabilistic pointer programs in QSL.  ...  Our work extends the calculus of McIver and Morgan to formally reason about heap manipulating probabilistic programs. Separation Logic.  ... 
doi:10.1145/3290347 fatcat:dj7hars2j5fmnny7ycy246ejum

An asymptotic analysis of probabilistic logic programming, with implications for expressing projective families of distributions [article]

Felix Weitkämper
2021 arXiv   pre-print
In this representation, determinate logic programs correspond to quantifier-free theories, making asymptotic quantifier elimination results available for the setting of probabilistic logic programming.  ...  We conclude that every probabilistic logic program inducing a projective family of distributions is in fact everywhere equivalent to a program from this fragment, and we investigate the consequences for  ...  Since then, many different frameworks have been developed under this heading, which can broadly be classified into those who extend logic programming to incorporate probabilistic information (probabilistic  ... 
arXiv:2102.08777v3 fatcat:hfopscohframvfixzzsfdbzhhq

An Asymptotic Analysis of Probabilistic Logic Programming, with Implications for Expressing Projective Families of Distributions

FELIX Q. WEITKÄMPER
2021 Theory and Practice of Logic Programming  
We conclude that every probabilistic logic program inducing a projective family of distributions is in fact everywhere equivalent to a program from this fragment, and we investigate the consequences for  ...  In this contribution we show that every probabilistic logic program under the distribution semantics is asymptotically equivalent to an acyclic probabilistic logic program consisting only of determinate  ...  Since then, many different frameworks have been developed under this heading, which can broadly be classified into those who extend logic programming to incorporate probabilistic information (probabilistic  ... 
doi:10.1017/s1471068421000314 fatcat:ikquu4vf6nft5hfj4j35dza2gm

Semantics for probabilistic programming

Sam Staton, Hongseok Yang, Frank Wood, Chris Heunen, Ohad Kammar
2016 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16  
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture  ...  We define a metalanguage (an idealised version of Anglican) for probabilistic computation with the above features, develop both operational and denotational semantics, and prove soundness, adequacy, and  ...  Introduction Probabilistic programming is the idea to use programs to specify probabilistic models; probabilistic programming languages blend programming constructs with probabilistic primitives.  ... 
doi:10.1145/2933575.2935313 dblp:conf/lics/StatonYWHK16 fatcat:ggvgmheyang6ffdofh3civco2a

Generating counterexamples for quantitative safety specifications in probabilistic B

Ukachukwu Ndukwu
2012 The Journal of Logic and Algebraic Programming  
Probabilistic annotations generalise standard Hoare Logic [20] to quantitative properties of probabilistic programs.  ...  As for standard program development, probabilistic assertions can be checked mechanically relative to an appropriate program semantics.  ...  McIver for her very useful comments on the early drafts of this paper.  ... 
doi:10.1016/j.jlap.2011.06.001 fatcat:cb22mabglrao3btbpv7tyt4uqy

Three-valued abstraction for probabilistic systems

Joost-Pieter Katoen, Daniel Klink, Martin Leucker, Verena Wolf
2012 The Journal of Logic and Algebraic Programming  
It is shown that this provides a conservative abstraction for both negative and affirmative verification results for a three-valued semantics of PCTL (Probabilistic Computation Tree Logic).  ...  In a similar way as for the discrete case, this is shown to yield a conservative abstraction for a three-valued semantics of CSL (Continuous Stochastic Logic).  ...  For the discrete-time setting, we consider abstractions for the branchingtime logic PCTL (Probabilistic Computation Tree Logic [23] ), whereas for the continuous-time case the logic CSL (Continuous Stochastic  ... 
doi:10.1016/j.jlap.2012.03.007 fatcat:mizyiftd3bdd5epnbbefixi6bu

A Specification Logic for Programs in the Probabilistic Guarded Command Language (Extended Version) [article]

Raúl Pardo and Einar Broch Johnsen and Ina Schaefer and Andrzej Wąsowski
2022 arXiv   pre-print
This paper introduces the probabilistic dynamic logic pDL, a specification logic for programs in the probabilistic guarded command language (pGCL) of McIver and Morgan.  ...  The satisfaction relation is modeled after PCTL, but extended from propositional to first-order setting of dynamic logic, so also embedding program fragments.  ...  Other extensions of program logics to probabilistic programs, such as separation logic for probabilistic programs [25] , expected run-time analysis for probabilistic programs [26] and relational reasoning  ... 
arXiv:2205.04822v1 fatcat:7v7hy6ayonbzdaomt6gf4xhfue

Beyond the Grounding Bottleneck: Datalog Techniques for Inference in Probabilistic Logic Programs (Technical Report) [article]

Efthymia Tsamoura, Victor Gutierrez-Basulto, Angelika Kimmig
2019 arXiv   pre-print
State-of-the-art inference approaches in probabilistic logic programming typically start by computing the relevant ground program with respect to the queries of interest, and then use this program for  ...  This effectively eliminates the grounding bottleneck that so far has prohibited the application of probabilistic logic programming in query answering scenarios over knowledge graphs, while also providing  ...  Background We provide some basics on probabilistic logic programming. We use standard notions of propositional logic and logic programming, cf. Appendix.  ... 
arXiv:1911.07750v1 fatcat:r7akzemdajd3zhiadzqetc2tcq

On the Termination Problem for Probabilistic Higher-Order Recursive Programs

Naoki Kobayashi, Ugo Dal Lago, Charles Grellois
2019 Logical Methods in Computer Science  
In the last two decades, there has been much progress on model checking of both probabilistic systems and higher-order programs.  ...  As a first step towards our goal, we introduce PHORS, a probabilistic extension of higher-order recursion schemes (HORS), as a model of probabilistic higher-order programs.  ...  We would like to thank Kazuyuki Asada and Takeshi Tsukada for discussions on the topic, and anonymous referees for useful comments.  ... 
doi:10.23638/lmcs-16(4:2)2020 fatcat:nq4rufu6mrfwhavixxztkmlrke

Probabilistic description logic programs under inheritance with overriding for the Semantic Web

Thomas Lukasiewicz
2008 International Journal of Approximate Reasoning  
Towards uncertainty reasoning in the Rules, Logic, and Proof layers of the Semantic Web, we present a novel approach to probabilistic description logic programs, which combine probabilistic logic programs  ...  We also present algorithms for solving the main computational problems related to probabilistic description logic programs under inheritance with overriding.  ...  Many thanks also to the reviewers of this paper and of its UAI-2001 abstract for their constructive comments, which helped to improve this work.  ... 
doi:10.1016/j.ijar.2007.08.005 fatcat:uyzm743abzb3zkhyvc24e4nmtu

Implementing a Library for Probabilistic Programming Using Non-strict Non-determinism

SANDRA DYLUS, JAN CHRISTIANSEN, FINN TEEGEN
2019 Theory and Practice of Logic Programming  
This paper presents PFLP, a library for probabilistic programming in the functional logic programming language Curry.  ...  It demonstrates how the concepts of a functional logic programming language support the implementation of a library for probabilistic programming.  ...  of probabilistic programming with the features of a functional logic programming language.  ... 
doi:10.1017/s1471068419000085 fatcat:32fav6eltrg3lft4tpdagi5are
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