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Relational Reasoning via Probabilistic Coupling [chapter]

Gilles Barthe, Thomas Espitau, Benjamin Grégoire, Justin Hsu, Léo Stefanesco, Pierre-Yves Strub
2015 Lecture Notes in Computer Science  
Couplings are powerful tools proving properties about the relation between two processes, include reasoning about convergence of distributions and stochastic dominance---a probabilistic version of a monotonicity  ...  Probabilistic coupling is a powerful tool for analyzing pairs of probabilistic processes.  ...  Introduction Probabilistic couplings [9, 7, 10] are a powerful mathematical tool for reasoning about pairs of probabilistic processes: streams of values that evolve randomly according to some rule.  ... 
doi:10.1007/978-3-662-48899-7_27 fatcat:6ag4dncmnrbxzhxiax36j6xhmm

Heuristic Ranking in Tightly Coupled Probabilistic Description Logics [article]

Thomas Lukasiewicz, Maria Vanina Martinez, Giorgio Orsi, Gerardo I. Simari
2012 arXiv   pre-print
This extension is tightly coupled, meaning that probabilistic annotations in formulas can refer to objects in the ontology.  ...  Reasoning under uncertainty has recently taken a leading role in this arena, given the nature of data found on theWeb.  ...  In this setting, probabilistic DL formalisms are well-suited to the task, since they couple powerful modeling capabilities with sound and complete reasoning procedures. Example 1.  ... 
arXiv:1210.4894v1 fatcat:jq2itwcfmvcnrizskdvgf5cvmm

Business Rules Uncertainty Management with Probabilistic Relational Models [chapter]

Hamza Agli, Philippe Bonnard, Christophe Gonzales, Pierre-Henri Wuillemin
2016 Lecture Notes in Computer Science  
This solution has a coupling approach with Probabilistic Relational Models (PRMs) and facilitates the inter-operability, hence, the separation between business and probabilistic logic.  ...  In this paper we present a solution allowing modern OO-BRMS to effectively integrate probabilistic reasoning for uncertainty management.  ...  Subscriber ( sub . risk == true | hp . risk == true ) in hp . subs ; Fig. 6: BIS coupling engines are related via an observation mechanism and both are notified, 8 see https://dslpitt.org/genie/wiki  ... 
doi:10.1007/978-3-319-42019-6_4 fatcat:3hfebgvay5hmtdo7bbxpyw5hne

Relational Reasoning for Markov Chains in a Probabilistic Guarded Lambda Calculus [chapter]

Alejandro Aguirre, Gilles Barthe, Lars Birkedal, Aleš Bizjak, Marco Gaboardi, Deepak Garg
2018 Lecture Notes in Computer Science  
In addition, our proof system leverages a well-known theorem from the coupling literature to justify better proof rules for relational reasoning about probabilistic expressions.  ...  We extend the simply-typed guarded λ-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations.  ...  We provide sound proof rules for reasoning about probabilistic couplings. Our rules make several improvements over prior relational verification logics based on couplings.  ... 
doi:10.1007/978-3-319-89884-1_8 fatcat:dq4oqbtembbmloqadvtwexdx7q

Proving Differential Privacy via Probabilistic Couplings [article]

Gilles Barthe, Marco Gaboardi, Benjamin Grégoire, Justin Hsu, Pierre-Yves Strub
2017 arXiv   accepted
Our methods are based on the observation that differential privacy has deep connections with a generalization of probabilistic couplings, an established mathematical tool for reasoning about stochastic  ...  We verify these examples in a relational program logic apRHL+, which can construct approximate couplings.  ...  Differential privacy via approximate probabilistic liftings Relational program logics [2, 4] and relational refinement type systems [8] are currently the most flexible techniques for reasoning formally  ... 
arXiv:1601.05047v4 fatcat:ebuijcjdzvbalcbqephgryxoyy

Probabilistic inference for structured planning in robotics

Marc Toussaint, Christian Goerick
2007 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems  
We propose a new approach to planning in robotics based on probabilistic inference.  ...  The scalability of planning and reasoning methods to cope with complex problems in such environments crucially depends on exploiting this structure.  ...  The transitions P (q t+1 | q t ) are the free parameters of the problems and relate to the control signals that we will learn via probabilistic inference.  ... 
doi:10.1109/iros.2007.4399296 dblp:conf/iros/ToussaintG07 fatcat:p25hq5vh7fglznlp3hxdht57ym

Constraint-Based Synthesis of Coupling Proofs [chapter]

Aws Albarghouthi, Justin Hsu
2018 Lecture Notes in Computer Science  
∀X. ϕ, making probabilistic reasoning unnecessary.  ...  Proof by coupling is a classical technique for proving properties about pairs of randomized algorithms by carefully relating (or coupling) two probabilistic executions.  ...  While coupling proofs can simplify reasoning about probabilistic properties, they are not so easy to use; most existing proofs are carried out manually in relational program logics using interactive theorem  ... 
doi:10.1007/978-3-319-96145-3_18 fatcat:mjv7leejdvazzdwrv4riyqhkku

Relational Reasoning for Markov Chains in a Probabilistic Guarded Lambda Calculus [article]

Alejandro Aguirre, Gilles Barthe, Lars Birkedal, Aleš Bizjak, Marco Gaboardi, Deepak Garg
2018 arXiv   pre-print
In addition, our proof system leverages a well-known theorem from the coupling literature to justify better proof rules for relational reasoning about probabilistic expressions.  ...  We extend the simply-typed guarded λ-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations.  ...  We provide sound proof rules for reasoning about probabilistic couplings. Our rules make several improvements over prior relational verification logics based on couplings.  ... 
arXiv:1802.09787v1 fatcat:67ysfpksobfulpi7ie3ox2lxpm

Uncertainty Reasoning for the Semantic Web [chapter]

Thomas Lukasiewicz
2017 Lecture Notes in Computer Science  
Explicitly representing numeric confidence values as error probabilities, resolving inconsistencies via trust probabilities, and reasoning about these on a numeric level.  ...  Tightly coupled probabilistic description logic programs for the Semantic Web. Journal on Data Semantics, 12, 95-130, June 2009. T. Lukasiewicz, L. Predoiu, H. Stuckenschmidt.  ... 
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  
Explicitly representing numeric confidence values as error probabilities, resolving inconsistencies via trust probabilities, and reasoning about these on a numeric level.  ...  Tightly coupled probabilistic description logic programs for the Semantic Web. Journal on Data Semantics, 12, 95-130, June 2009. T. Lukasiewicz, L. Predoiu, H. Stuckenschmidt.  ... 
doi:10.1007/978-3-642-05082-4_3 fatcat:ojaedt2s6jc2jmocn2ie2ewejy

Constraint-Based Synthesis of Coupling Proofs [article]

Aws Albarghouthi, Justin Hsu
2018 arXiv   pre-print
Proof by coupling is a classical technique for proving properties about pairs of randomized algorithms by carefully relating (or coupling) two probabilistic executions.  ...  Third, we demonstrate how to reduce the proof-search problem to a purely logical synthesis problem of the form ∃ f∀ Xϕ, making probabilistic reasoning unnecessary.  ...  While coupling proofs can simplify reasoning about probabilistic properties, they are not so easy to use; most existing proofs are carried out manually in relational program logics using interactive theorem  ... 
arXiv:1804.04052v1 fatcat:voa5gdpbrbbhhgydfyc7olp6bm

Keyword Query Expansion Paradigm Based on Recommendation and Interpretation in Relational Databases

Yingqi Wang, Nianbin Wang, Lianke Zhou
2017 Scientific Programming  
First, a probabilistic recommendation algorithm is put forward by constructing a term similarity matrix and Viterbi model.  ...  Due to the ambiguity and impreciseness of keyword query in relational databases, the research on keyword query expansion has attracted wide attention.  ...  The reason for this phenomenon is that -coupling only uses keyword coupling relationship matrix to analyze the original query, while ReInterpretQE conducts the similar words and related items expansion  ... 
doi:10.1155/2017/7613026 fatcat:igrxbycdejekli4zl5rigk5wii

Truth maintenance system with probabilistic constraints for enhanced level two fusion

Subrata Das, D. Lawless
2005 2005 7th International Conference on Information Fusion  
The approach is applicable to any relational database by converting database entries into evidence for the probabilistic constraints.  ...  Inconsistencies in the SA BN are resolved by a combination of techniques including sensitivity analysis, default reasoning, consistency 'forcing', or seeking new evidence.  ...  of a tightly coupled belief network engine.  ... 
doi:10.1109/icif.2005.1591966 fatcat:qmhmibrcyveafgapbufdz3gjvi

Proving uniformity and independence by self-composition and coupling [article]

Gilles Barthe and Thomas Espitau and Benjamin Grégoire and Justin Hsu and Pierre-Yves Strub
2017 arXiv   pre-print
More recently, couplings have been investigated as a useful abstraction for formal reasoning about relational properties of probabilistic programs, in particular for modeling reduction-based cryptographic  ...  In this paper, we demonstrate that probabilistic couplings can be used for verifying non-relational probabilistic properties.  ...  Probabilistic Relational Hoare Logic Probabilistic Relational Hoare Logic (pRHL) is a program logic for reasoning about relational properties of probabilistic programs.  ... 
arXiv:1701.06477v2 fatcat:faiapgfy6bgmhi2dvjbzr2722m

Trends and Issues in Description Logics Frameworks for Image Interpretation [chapter]

Stamatia Dasiopoulou, Ioannis Kompatsiaris
2010 Lecture Notes in Computer Science  
Differences in the formulation of image interpretation semantics have resulted in varying configurations with respect to the adopted modelling paradigm, the utilised form of reasoning, and the way imprecision  ...  A promising pursuit for the future is to investigate the coupling of fuzzy and probabilistic reasoning, while preserving clean semantics.  ...  non monotonic probabilistic reasoner built on top of Pellet [34] , that however supports only terminological probabilistic knowledge.  ... 
doi:10.1007/978-3-642-12842-4_10 fatcat:4lxjtgj22javhbknwky4gepnii
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