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Probabilistic Logic with Strong Independence [chapter]

Fabio G. Cozman, Cassio P. de Campos, José Carlos F. da Rocha
2006 Lecture Notes in Computer Science  
This papers investigates the manipulation of statements of strong independence in probabilistic logic.  ...  The resulting model generalizes Bayesian networks, allowing probabilistic assessments and logical constraints to be mixed.  ...  We thank Barbara Vantaggi and Thomas Lukasiewicz for helping with our understanding of independence in probabilistic logic.  ... 
doi:10.1007/11874850_65 fatcat:rf6v7df7pfhytpmo5far55qhgm

Logical approaches to imprecise probabilities

Thomas Lukasiewicz
2008 International Journal of Approximate Reasoning  
After reviewing propositional probabilistic logics without and with probabilistic independence, Cozman et al. present graph-theoretic representations for propositional probabilistic logic with independence  ...  The first four articles deal with probabilistic logics, focusing on probabilistic independence relations, an application in the Semantic Web, an application in formalizing agent behavior, and on approximate  ...  Last, but not least, I would like to thank the reviewers who contributed with their time to improve the quality of the papers in this special issue. Thomas Lukasiewicz  ... 
doi:10.1016/j.ijar.2007.08.004 fatcat:zlenk5w55fey5juugthfvcq3rm

Unifying Hidden-Variable Problems from Quantum Mechanics by Logics of Dependence and Independence [article]

Rafael Albert, Erich Grädel
2022 arXiv   pre-print
Connections between probabilistic and relational entailment in dependence and independence logic allow us to simplify proofs.  ...  We study hidden-variable models from quantum mechanics, and their abstractions in purely probabilistic and relational frameworks, by means of logics of dependence and independence, based on team semantics  ...  Researchers studying logics of dependence and independence have  ... 
arXiv:2102.10931v2 fatcat:pkzld6qlk5dr3etid4hwpiuerm

Confluence Reduction for Probabilistic Systems [chapter]

Mark Timmer, Mariëlle Stoelinga, Jaco van de Pol
2011 Lecture Notes in Computer Science  
To support the technique, we introduce a method for detecting confluent transitions in the context of a probabilistic process algebra with data, facilitated by an earlier defined linear format.  ...  In this presentation we introduce a novel technique for state space reduction of probabilistic specifications, based on a newly developed notion of confluence for probabilistic automata.  ...  We developed a method for probabilistic confluence to be detected in the context of a probabilistic process algebra with data by proving formulas in first-order logic.  ... 
doi:10.1007/978-3-642-19835-9_29 fatcat:b3hko3y7irdkng7ubpnvce34ee

Team Semantics and Independence Notions in Quantum Physics [article]

Samson Abramsky, Joni Puljujärvi, Jouko Väänänen
2021 arXiv   pre-print
This leads to new developments also in independence logic and probabilistic independence logic.  ...  We study dependence and independence concepts found in quantum physics, especially those related to hidden variables and non-locality, through the lens of team semantics and probabilistic team semantics  ...  This extends also to probabilistic models with independence logic replaced by the probabilistic independence logic of [10] , capturing the probabilistic notions of [6] .  ... 
arXiv:2107.10817v1 fatcat:lic2dadk75eevlgqhtxg73u33i

PLOW: Probabilistic Logic Over the Well-Founded Semantics

Benjamin N. Grosof, Theresa Swift
2019 AAAI Spring Symposia  
In particular, a class of recent logic programming systems, called Rulelog systems, semantically extend database logic and provide high expressiveness together with strong explainability (Grosof 2013;  ...  Significantly, KRR can be essential for complying with organizational policies, ethics, and pertinent legal regulations; and for applying human social and experiential knowledge.  ...  The probabilistic semantics supported include: -The full distribution semantics, which extends logic programs with full Bayesian reasoning.  ... 
dblp:conf/aaaiss/GrosofS19 fatcat:ikxo7ygdkfhndpne6u3ghcgslq

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  
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  ...  the projective families of distributions expressible by probabilistic logic programs.  ...  asymptotic representation of a probabilistic logic program invoking probabilistic rules is in fact independent of the probability with which the rule is annotated.  ... 
doi:10.1017/s1471068421000314 fatcat:ikquu4vf6nft5hfj4j35dza2gm

Assembling a consistent set of sentences in relational probabilistic logic with stochastic independence

Cassio Polpo de Campos, Fabio Gagliardi Cozman, José Eduardo Ochoa Luna
2009 Journal of Applied Logic  
We examine the representation of judgements of stochastic independence in probabilistic logics.  ...  We discuss issues of knowledge representation and inference that arise from our particular combination of graphs, stochastic independence, logical formulas and probabilistic assessments.  ...  Introduction In this paper we wish to discuss probabilistic logics that combine a relational fragment of first-order logic with probabilistic assessments and judgements of stochastic independence expressed  ... 
doi:10.1016/j.jal.2007.11.002 fatcat:w5357vddprcatkss237jqybtca

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

Felix Weitkämper
2021 arXiv   pre-print
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  ...  the projective families of distributions expressible by probabilistic logic programs.  ...  encapsulates a strong form of domain size independence.  ... 
arXiv:2102.08777v3 fatcat:hfopscohframvfixzzsfdbzhhq

Using Theorem Proving to Verify Expectation and Variance for Discrete Random Variables

Osman Hasan, Sofiène Tahar
2008 Journal of automated reasoning  
Statistical quantities, such as expectation (mean) and variance, play a vital role in the present age probabilistic analysis.  ...  In order to demonstrate the practical effectiveness of the formalization presented in this paper, we also present the probabilistic analysis of the Coupon Collector's problem in HOL.  ...  Lemma 1 sum_two_rv Preserves Strong Function Independence ∀ X Y.  ... 
doi:10.1007/s10817-008-9113-6 fatcat:yxf33czchja4rft7u4gwgfq6mu

Statistical Relational Learning [chapter]

Eric Martin, Samuel Kaski, Fei Zheng, Geoffrey I. Webb, Xiaojin Zhu, Ion Muslea, Kai Ming Ting, Michail Vlachos, Risto Miikkulainen, Alan Fern, Miles Osborne, Luc De Raedt (+13 others)
2011 Encyclopedia of Machine Learning  
Definition Statistical relational learning aka. probabilistic inductive logic programming deals with machine learning and data mining in relational domains where observations may be missing, partially  ...  In doing so, it addresses one of the central questions of artificial intelligence -the integration of probabilistic reasoning with machine learning and first order and relational representationsand deals  ...  Case Study: ProbLog Many formalisms do not explicitly encode a set of conditional independency assumptions, as in Bayesian or Markov networks, but rather extend a (logic) programming language with probabilistic  ... 
doi:10.1007/978-0-387-30164-8_786 fatcat:i6y52kf2rrgfnbocvfyuwu4yoa

Probabilistic logic with independence

Fabio Gagliardi Cozman, Cassio Polpo de Campos, José Carlos Ferreira da Rocha
2008 International Journal of Approximate Reasoning  
This paper investigates probabilistic logics endowed with independence relations. We review propositional probabilistic languages without and with independence.  ...  We then consider graph-theoretic representations for propositional probabilistic logic with independence; complexity is analyzed, algorithms are derived, and examples are discussed.  ...  strong assumptions on independence.  ... 
doi:10.1016/j.ijar.2007.08.002 fatcat:5eyvqx2d5fd3hot6pr2qnwl3gq

Special issue on Combining Probability and Logic

Jon Williamson, Dov Gabbay
2003 Journal of Applied Logic  
The papers in this volume concern either the special focus on the connection between probabilistic logic and probabilistic networks or the more general question of the links between probability and logic  ...  Here we introduce probabilistic logic, probabilistic networks, current and future directions of research and also the themes of the papers that follow.  ...  Next, it discusses independence relations in probabilistic logics with a focus on networks for relational probabilistic logic, and then it explores a possible application.  ... 
doi:10.1016/s1570-8683(03)00009-0 fatcat:ldvbd3jza5axlkp2x4isedswze

Combining Probability and Logic

Fabio Cozman, Rolf Haenni, Jan-Willem Romeijn, Federica Russo, Gregory Wheeler, Jon Williamson
2009 Journal of Applied Logic  
Here we introduce probabilistic logic, probabilistic networks, current and future directions of research and also the themes of the papers that follow. What is probabilistic logic?  ...  In non-probabilistic logics one typically appeals to a  ...  Next, it discusses independence relations in probabilistic logics with a focus on networks for relational probabilistic logic, and then it explores a possible application.  ... 
doi:10.1016/j.jal.2007.12.001 fatcat:uosf3cmdlbbk5b3gxc4uqbxq7m

Special issue: Combining probability and logic

Jürgen Landes, Jon Williamson
2016 Journal of Applied Logic  
The papers in this volume concern either the special focus on the connection between probabilistic logic and probabilistic networks or the more general question of the links between probability and logic  ...  Here we introduce probabilistic logic, probabilistic networks, current and future directions of research and also the themes of the papers that follow.  ...  Next, it discusses independence relations in probabilistic logics with a focus on networks for relational probabilistic logic, and then it explores a possible application.  ... 
doi:10.1016/j.jal.2015.09.009 fatcat:37jxfr4tjrcinlk6vvlontftha
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