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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
Research on deductive verification of probabilistic programs has considered expectation-based logics, where pre- and post-conditions are real-valued functions on states, and assertion-based logics, where  ...  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

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 present Ellora, a sound and relatively complete assertion-based program logic, and demonstrate its expressivity by verifying several classical examples of randomized algorithms using an implementation  ...  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

Uncertainty Reasoning for the Semantic Web [chapter]

Thomas Lukasiewicz
2017 Lecture Notes in Computer Science  
probabilistic inference based on lexicographic entailment in probabilistic logic (for combining assertional and terminological probabilistic knowledge) terminological and assertional probabilistic inference  ...  probabilistic knowledge about instances of concepts and roles terminological probabilistic inference based on lexicographic entailment in probabilistic logic (stronger than logical entailment) assertional  ... 
doi:10.1007/978-3-319-61033-7_8 fatcat:hszvhxxiind3pjxrw6d6rnmmse

Uncertainty Reasoning for the Semantic Web [chapter]

Thomas Lukasiewicz
2009 Lecture Notes in Computer Science  
probabilistic inference based on lexicographic entailment in probabilistic logic (for combining assertional and terminological probabilistic knowledge) terminological and assertional probabilistic inference  ...  probabilistic knowledge about instances of concepts and roles terminological probabilistic inference based on lexicographic entailment in probabilistic logic (stronger than logical entailment) assertional  ... 
doi:10.1007/978-3-642-05082-4_3 fatcat:ojaedt2s6jc2jmocn2ie2ewejy

Page 6642 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews  
It is proved that uninterpreted first-order DL with terminated assertions is complete. In the case of nonterminated assertions, this logic is made complete by adding an w-type rule.  ...  Probabilistic programs consider probabilistic distributions over the states.  ... 

onto2problog: A Probabilistic Ontology-Mediated Querying System using Probabilistic Logic Programming

Timothy van Bremen, Anton Dries, Jean Christoph Jung
2020 Künstliche Intelligenz  
We present onto2problog, a tool that supports ontology-mediated querying of probabilistic data via probabilistic logic programming engines.  ...  Our tool supports conjunctive queries on probabilistic data under ontologies encoded in the description logic ELH dr , thus capturing a large part of the OWL 2 EL profile.  ...  AcademicSupervisor(x) , we have: Probabilistic Logic Programs We introduce a variant of probabilistic logic programs that is sufficient for our purposes, though some systems support more features.  ... 
doi:10.1007/s13218-020-00670-x pmid:33343088 pmcid:PMC7732808 fatcat:pv2pcdetkvgenmmyd2did552y4

VPHL: A Verified Partial-Correctness Logic for Probabilistic Programs

Robert Rand, Steve Zdancewic
2015 Electronical Notes in Theoretical Computer Science  
We introduce a Hoare-style logic for probabilistic programs, called VPHL, that has been formally verified in the Coq proof assistant.  ...  VPHL's assertions are partial correctness assertions, meaning that their conclusions are dependent upon (deterministic) program termination.  ...  two programs simultaneously and pHL, a Probabilistic Hoare Logic for reasoning about a single program.  ... 
doi:10.1016/j.entcs.2015.12.021 fatcat:7u7jnegamvcopmjhag5cci2ahq

Providing an Uncertainty Reasoning Service for Semantic Web Application [chapter]

Lei Li, Qiaoling Liu, Yunfeng Tao, Lei Zhang, Jian Zhou, Yong Yu
2006 Lecture Notes in Computer Science  
In order to provide an uncertainty reasoning service for semantic web applications, we propose a probabilistic extension of Description Logic, namely Probabilistic Description Logic Program (PDLP).  ...  In this paper, we introduce the syntax and intensional semantics of PDLP, and present a fast reasoning algorithm making use of Logic Programming techniques.  ...  inferencing in LP in order to take advantage of powerful logic programming technology for inference [6]  ... 
doi:10.1007/11610113_55 fatcat:io76s6ll4faivl5ooo2smkh6vy

ADDING PROBABILITIES AND RULES TO OWL LITE SUBSETS BASED ON PROBABILISTIC DATALOG

HENRIK NOTTELMANN, NORBERT FUHR
2006 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
program.  ...  As inference engines for probabilistic Datalog are available, description logics and information retrieval systems can easily be combined.  ...  We wish to thank Umberto Straccia for fruitful discussions. The constructive comments of the reviewers helped improving the paper significantly.  ... 
doi:10.1142/s0218488506003819 fatcat:otvi4idllvg4zidvjjkkhlyuoi

Uncertainty in the Semantic Web [chapter]

Thomas Lukasiewicz
2009 Lecture Notes in Computer Science  
Probabilistic knowledge base: KB = ({bird ⇐ eagle} , {(have_legs | bird)[1, 1], (fly | bird)[0.95, 1]}) . KB is satisfiable, since Pr with Pr(bird ∧ eagle ∧ have_legs ∧ fly ) = 1 is a model.  ...  Some conclusions under logical entailment: KB ||= (have_legs | bird)[0.3, 1], KB ||= (fly | bird)[0.6, 1].  ...  entailment) assertional probabilistic inference based on lexicographic entailment in probabilistic logic (for combining assertional and terminological probabilistic knowledge) terminological and assertional  ... 
doi:10.1007/978-3-642-04388-8_2 fatcat:agvmnwwpq5a7xmn7vc7l2vczhy

Description logic programs under probabilistic uncertainty and fuzzy vagueness

Thomas Lukasiewicz, Umberto Straccia
2009 International Journal of Approximate Reasoning  
More concretely, we present probabilistic fuzzy description logic programs, which combine fuzzy description logics, fuzzy logic programs (with stratified default-negation), and probabilistic uncertainty  ...  This paper is directed towards an infrastructure for handling both uncertainty and vagueness in the Rules, Logic, and Proof layers of the Semantic Web.  ...  We thank the reviewers of this paper and its ECSQARU-2007 preliminary version for their useful and constructive comments, which have helped to improve this work.  ... 
doi:10.1016/j.ijar.2009.03.004 fatcat:yycaw6pcjvcz7j6xtqrv54fbqm

Description Logic Programs Under Probabilistic Uncertainty and Fuzzy Vagueness [chapter]

Thomas Lukasiewicz, Umberto Straccia
2007 Lecture Notes in Computer Science  
More concretely, we present probabilistic fuzzy description logic programs, which combine fuzzy description logics, fuzzy logic programs (with stratified default-negation), and probabilistic uncertainty  ...  This paper is directed towards an infrastructure for handling both uncertainty and vagueness in the Rules, Logic, and Proof layers of the Semantic Web.  ...  We thank the reviewers of this paper and its ECSQARU-2007 preliminary version for their useful and constructive comments, which have helped to improve this work.  ... 
doi:10.1007/978-3-540-75256-1_19 fatcat:5d3l2xuh5zdf3h4adltf6y4tjq

Reasoning About States of Probabilistic Sequential Programs [chapter]

R. Chadha, P. Mateus, A. Sernadas
2006 Lecture Notes in Computer Science  
The state logic is then used to obtain a sound Hoare-style calculus for basic probabilistic sequential programs.  ...  A complete and decidable propositional logic for reasoning about states of probabilistic sequential programs is presented.  ...  We would like to thank Luís Cruz-Filipe and Peter Selinger for useful and interesting discussions.  ... 
doi:10.1007/11874683_16 fatcat:ri4vxmijhvhalh4rggozysthc4

Abstraction and refinement in probabilistic systems

Annabelle McIver, Carroll Morgan
2005 Performance Evaluation Review  
We summarise a verification method for probabilistic systems that is based on abstraction and refinement, and extends traditional assertional styles of verification.  ...  The approach makes extensive use of the expectation transformers of pGCL [17, 16, 13], a compact probabilistic programming language with an associated logic of real-valued functions.  ...  The expectation transformers' logic of probabilistic programs combines a weakened form of "expectation logics" found in standard probability theory [18] , together with the logic based on Dijkstra's predicate  ... 
doi:10.1145/1059816.1059824 fatcat:xxajgnpmkvedjnandmua3v4cvq

Managing Uncertainty and Vagueness in Description Logics, Logic Programs and Description Logic Programs [chapter]

Umberto Straccia
2008 Lecture Notes in Computer Science  
Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages.  ...  In probabilistic generalizations of (annotated) logic programs (see [122] ) based on probabilistic logic fall works such as [44, 45, 46, 47, 48, 201, 202] In probabilistic generalizations of logic programs  ...  Probabilistic Uncertainty and Logic Programs. The variety of proposals of logic programming under probability theory is huge and an description of most of them is out of the scope of this work.  ... 
doi:10.1007/978-3-540-85658-0_2 fatcat:6ijgfocetbfixonkur2lrnabjy
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