Relevant bibliographies by topics / Probabilistic logics

Academic literature on the topic 'Probabilistic logics'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Probabilistic logics"

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Gutierrez-Basulto, Victor, Jean Christoph Jung, Carsten Lutz, and Lutz Schröder. "Probabilistic Description Logics for Subjective Uncertainty." Journal of Artificial Intelligence Research 58 (January 10, 2017): 1–66. http://dx.doi.org/10.1613/jair.5222.

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We propose a family of probabilistic description logics (DLs) that are derived in a principled way from Halpern's probabilistic first-order logic. The resulting probabilistic DLs have a two-dimensional semantics similar to temporal DLs and are well-suited for representing subjective probabilities. We carry out a detailed study of reasoning in the new family of logics, concentrating on probabilistic extensions of the DLs ALC and EL, and showing that the complexity ranges from PTime via ExpTime and 2ExpTime to undecidable.
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Hart, Sergiu, and Micha Sharir. "Probabilistic propositional temporal logics." Information and Control 70, no. 2-3 (August 1986): 97–155. http://dx.doi.org/10.1016/s0019-9958(86)80001-8.

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Ikodinović, Nebojša, Zoran Ognjanović, Aleksandar Perović, and Miodrag Rašković. "Hierarchies of probabilistic logics." International Journal of Approximate Reasoning 55, no. 9 (December 2014): 1830–42. http://dx.doi.org/10.1016/j.ijar.2014.03.006.

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Lukasiewicz, Thomas. "Weak nonmonotonic probabilistic logics." Artificial Intelligence 168, no. 1-2 (October 2005): 119–61. http://dx.doi.org/10.1016/j.artint.2005.05.005.

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Lukasiewicz, Thomas. "Expressive probabilistic description logics." Artificial Intelligence 172, no. 6-7 (April 2008): 852–83. http://dx.doi.org/10.1016/j.artint.2007.10.017.

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Maggi, Fabrizio M., Marco Montali, and Rafael Peñaloza. "Temporal Logics Over Finite Traces with Uncertainty." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 06 (April 3, 2020): 10218–25. http://dx.doi.org/10.1609/aaai.v34i06.6583.

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Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of uncertainty which cannot be handled with classical logics. We thus propose a new probabilistic temporal logic over finite traces using superposition semantics, where all possible evolutions are possible, until observed. We study the properties of the logic and provide automata-based mechanisms for deriving probabilistic inferences from its formulas. We then study a fragment of the logic with better computational properties. Notably, formulas in this fragment can be discovered from event log data using off-the-shelf existing declarative process discovery techniques.
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GORLIN, ANDREY, C. R. RAMAKRISHNAN, and SCOTT A. SMOLKA. "Model checking with probabilistic tabled logic programming." Theory and Practice of Logic Programming 12, no. 4-5 (July 2012): 681–700. http://dx.doi.org/10.1017/s1471068412000245.

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AbstractWe present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of probabilistic models and probabilistic temporal logics. The inference algorithms of existing probabilistic logic-programming systems are well defined only for queries with a finite number of explanations. This restriction prohibits the encoding of probabilistic model checkers, where explanations correspond to executions of the system being model checked. To overcome this restriction, we propose a more general inference algorithm that uses finite generative structures (similar to automata) to represent families of explanations. The inference algorithm computes the probability of a possibly infinite set of explanations directly from the finite generative structure. We have implemented our inference algorithm in XSB Prolog, and use this implementation to encode probabilistic model checkers for a variety of temporal logics, including PCTL and GPL (which subsumes PCTL*). Our experiment results show that, despite the highly declarative nature of their encodings, the model checkers constructed in this manner are competitive with their native implementations.
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De Bona, Glauber, Fabio Gagliardi Cozman, and Marcelo Finger. "Towards classifying propositional probabilistic logics." Journal of Applied Logic 12, no. 3 (September 2014): 349–68. http://dx.doi.org/10.1016/j.jal.2014.01.005.

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Pavičić, M. "Probabilistic forcing in quantum logics." International Journal of Theoretical Physics 32, no. 10 (October 1993): 1965–79. http://dx.doi.org/10.1007/bf00979518.

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Thimm, Matthias. "Inconsistency measures for probabilistic logics." Artificial Intelligence 197 (April 2013): 1–24. http://dx.doi.org/10.1016/j.artint.2013.02.001.

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Dissertations / Theses on the topic "Probabilistic logics"

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Potyka, Nico [Verfasser]. "Solving Reasoning Problems for Probabilistic Conditional Logics with Consistent and Inconsistent Information / Nico Potyka." Hagen : Fernuniversität Hagen, 2016. http://d-nb.info/1082048402/34.

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Weidner, Thomas. "Probabilistic Logic, Probabilistic Regular Expressions, and Constraint Temporal Logic." Doctoral thesis, Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-208732.

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The classic theorems of Büchi and Kleene state the expressive equivalence of finite automata to monadic second order logic and regular expressions, respectively. These fundamental results enjoy applications in nearly every field of theoretical computer science. Around the same time as Büchi and Kleene, Rabin investigated probabilistic finite automata. This equally well established model has applications ranging from natural language processing to probabilistic model checking. Here, we give probabilistic extensions Büchi\\\'s theorem and Kleene\\\'s theorem to the probabilistic setting. We obtain a probabilistic MSO logic by adding an expected second order quantifier. In the scope of this quantifier, membership is determined by a Bernoulli process. This approach turns out to be universal and is applicable for finite and infinite words as well as for finite trees. In order to prove the expressive equivalence of this probabilistic MSO logic to probabilistic automata, we show a Nivat-theorem, which decomposes a recognisable function into a regular language, homomorphisms, and a probability measure. For regular expressions, we build upon existing work to obtain probabilistic regular expressions on finite and infinite words. We show the expressive equivalence between these expressions and probabilistic Muller-automata. To handle Muller-acceptance conditions, we give a new construction from probabilistic regular expressions to Muller-automata. Concerning finite trees, we define probabilistic regular tree expressions using a new iteration operator, called infinity-iteration. Again, we show that these expressions are expressively equivalent to probabilistic tree automata. On a second track of our research we investigate Constraint LTL over multidimensional data words with data values from the infinite tree. Such LTL formulas are evaluated over infinite words, where every position possesses several data values from the infinite tree. Within Constraint LTL on can compare these values from different positions. We show that the model checking problem for this logic is PSPACE-complete via investigating the emptiness problem of Constraint Büchi automata.
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Barbosa, Fábio Daniel Moreira. "Probabilistic propositional logic." Master's thesis, Universidade de Aveiro, 2016. http://hdl.handle.net/10773/22198.

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Mestrado em Matemática e Aplicações
O termo Lógica Probabilística, em geral, designa qualquer lógica que incorpore conceitos probabilísticos num sistema lógico formal. Nesta dissertacção o principal foco de estudo e uma lógica probabilística (designada por Lógica Proposicional Probabilística Exógena), que tem por base a Lógica Proposicional Clássica. São trabalhados sobre essa lógica probabilística a síntaxe, a semântica e um cálculo de Hilbert, provando-se diversos resultados clássicos de Teoria de Probabilidade no contexto da EPPL. São também estudadas duas propriedades muito importantes de um sistema lógico - correcção e completude. Prova-se a correcção da EPPL da forma usual, e a completude fraca recorrendo a um algoritmo de satisfazibilidade de uma fórmula da EPPL. Serão também considerados na EPPL conceitos de outras lógicas probabilísticas (incerteza e probabilidades intervalares) e Teoria de Probabilidades (condicionais e independência).
The term Probabilistic Logic generally refers to any logic that incorporates probabilistic concepts in a formal logic system. In this dissertation, the main focus of study is a probabilistic logic (called Exogenous Probabilistic Propo- sitional Logic), which is based in the Classical Propositional Logic. There will be introduced, for this probabilistic logic, its syntax, semantics and a Hilbert calculus, proving some classical results of Probability Theory in the context of EPPL. Moreover, there will also be studied two important properties of a logic system - soundness and completeness. We prove the EPPL soundness in a standard way, and weak completeness using a satis ability algorithm for a formula of EPPL. It will be considered in EPPL concepts of other probabilistic logics (uncertainty and intervalar probability) and of Probability Theory (independence and conditional).
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Klinov, Pavel. "Practical reasoning in probabilistic description logic." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/practical-reasoning-in-probabilistic-description-logic(6aff2ad0-dc76-44cf-909b-2134f580f29b).html.

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Description Logics (DLs) form a family of languages which correspond to decidable fragments of First-Order Logic (FOL). They have been overwhelmingly successful for constructing ontologies - conceptual structures describing domain knowledge. Ontologies proved to be valuable in a range of areas, most notably, bioinformatics, chemistry, Health Care and Life Sciences, and the Semantic Web.One limitation of DLs, as fragments of FOL, is their restricted ability to cope with various forms of uncertainty. For example, medical knowledge often includes statistical relationships, e.g., findings or results of clinical trials. Currently it is maintained separately, e.g., in Bayesian networks or statistical models. This often hinders knowledge integration and reuse, leads to duplication and, consequently, inconsistencies.One answer to this issue is probabilistic logics which allow for smooth integration of classical, i.e., expressible in standard FOL or its sub-languages, and uncertain knowledge. However, probabilistic logics have long been considered impractical because of discouraging computational properties. Those are mostly due to the lack of simplifying assumptions, e.g., independence assumptions which are central to Bayesian networks.In this thesis we demonstrate that deductive reasoning in a particular probabilistic DL, called P-SROIQ, can be computationally practical. We present a range of novel algorithms, in particular, the probabilistic satisfiability procedure (PSAT) which is, to our knowledge, the first scalable PSAT algorithm for a non-propositional probabilistic logic. We perform an extensive performance and scalability evaluation on different synthetic and natural data sets to justify practicality.In addition, we study theoretical properties of P-SROIQ by formally translating it into a fragment of first-order logic of probability. That allows us to gain a better insight into certain important limitations of P-SROIQ. Finally, we investigate its applicability from the practical perspective, for instance, use it to extract all inconsistencies from a real rule-based medical expert system.We believe the thesis will be of interest to developers of probabilistic reasoners. Some of the algorithms, e.g., PSAT, could also be valuable to the Operations Research community since they are heavily based on mathematical programming. Finally, the theoretical analysis could be helpful for designers of future probabilistic logics.
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Chakrapani, Lakshmi Narasimhan. "Probabilistic boolean logic, arithmetic and architectures." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26706.

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Thesis (Ph.D)--Computing, Georgia Institute of Technology, 2009.
Committee Chair: Palem, Krishna V.; Committee Member: Lim, Sung Kyu; Committee Member: Loh, Gabriel H.; Committee Member: Mudge, Trevor; Committee Member: Yalamanchili, Sudhakar. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Blakely, Scott. "Probabilistic Analysis for Reliable Logic Circuits." PDXScholar, 2014. https://pdxscholar.library.pdx.edu/open_access_etds/1860.

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Continued aggressive scaling of electronic technology poses obstacles for maintaining circuit reliability. To this end, analysis of reliability is of increasing importance. Large scale number of inputs and gates or correlations of failures render such analysis computationally complex. This paper presents an accurate framework for reliability analysis of logic circuits, while inherently handling reconvergent fan-out without additional complexity. Combinational circuits are modeled stochastically as Discrete-Time Markov Chains, where propagation of node logic levels and error probability distributions through circuitry are used to determine error probabilities at nodes in the circuit. Model construction is scalable, as it is done so on a gate-by-gate basis. The stochastic nature of the model lends itself to allow various properties of the circuit to be formally analyzed by means of steady-state properties. Formal verifying the properties against the model can circumvent strenuous simulations while exhaustively checking all possible scenarios for given properties. Small combinational circuits are used to explain model construction, properties are presented for analysis of the system, more example circuits are demonstrated, and the accuracy of the method is verified against an existing simulation method.
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Faria, Francisco Henrique Otte Vieira de. "Learning acyclic probabilistic logic programs from data." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/3/3141/tde-27022018-090821/.

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To learn a probabilistic logic program is to find a set of probabilistic rules that best fits some data, in order to explain how attributes relate to one another and to predict the occurrence of new instantiations of these attributes. In this work, we focus on acyclic programs, because in this case the meaning of the program is quite transparent and easy to grasp. We propose that the learning process for a probabilistic acyclic logic program should be guided by a scoring function imported from the literature on Bayesian network learning. We suggest novel techniques that lead to orders of magnitude improvements in the current state-of-art represented by the ProbLog package. In addition, we present novel techniques for learning the structure of acyclic probabilistic logic programs.
O aprendizado de um programa lógico probabilístico consiste em encontrar um conjunto de regras lógico-probabilísticas que melhor se adequem aos dados, a fim de explicar de que forma estão relacionados os atributos observados e predizer a ocorrência de novas instanciações destes atributos. Neste trabalho focamos em programas acíclicos, cujo significado é bastante claro e fácil de interpretar. Propõe-se que o processo de aprendizado de programas lógicos probabilísticos acíclicos deve ser guiado por funções de avaliação importadas da literatura de aprendizado de redes Bayesianas. Neste trabalho s~ao sugeridas novas técnicas para aprendizado de parâmetros que contribuem para uma melhora significativa na eficiência computacional do estado da arte representado pelo pacote ProbLog. Além disto, apresentamos novas técnicas para aprendizado da estrutura de programas lógicos probabilísticos acíclicos.
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Misino, Eleonora. "Deep Generative Models with Probabilistic Logic Priors." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/24058/.

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Many different extensions of the VAE framework have been introduced in the past. How­ ever, the vast majority of them focused on pure sub­-symbolic approaches that are not sufficient for solving generative tasks that require a form of reasoning. In this thesis, we propose the probabilistic logic VAE (PLVAE), a neuro-­symbolic deep generative model that combines the representational power of VAEs with the reasoning ability of probabilistic ­logic programming. The strength of PLVAE resides in its probabilistic ­logic prior, which provides an interpretable structure to the latent space that can be easily changed in order to apply the model to different scenarios. We provide empirical results of our approach by training PLVAE on a base task and then using the same model to generalize to novel tasks that involve reasoning with the same set of symbols.
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Weidner, Thomas [Verfasser], Manfred [Akademischer Betreuer] Droste, Manfred [Gutachter] Droste, and Benedikt [Gutachter] Bollig. "Probabilistic Logic, Probabilistic Regular Expressions, and Constraint Temporal Logic / Thomas Weidner ; Gutachter: Manfred Droste, Benedikt Bollig ; Betreuer: Manfred Droste." Leipzig : Universitätsbibliothek Leipzig, 2016. http://d-nb.info/1240627777/34.

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Forst, Jan Frederik. "POLIS : a probabilistic summarisation logic for structured documents." Thesis, Queen Mary, University of London, 2009. http://qmro.qmul.ac.uk/xmlui/handle/123456789/467.

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As the availability of structured documents, formatted in markup languages such as SGML, RDF, or XML, increases, retrieval systems increasingly focus on the retrieval of document-elements, rather than entire documents. Additionally, abstraction layers in the form of formalised retrieval logics have allowed developers to include search facilities into numerous applications, without the need of having detailed knowledge of retrieval models. Although automatic document summarisation has been recognised as a useful tool for reducing the workload of information system users, very few such abstraction layers have been developed for the task of automatic document summarisation. This thesis describes the development of an abstraction logic for summarisation, called POLIS, which provides users (such as developers or knowledge engineers) with a high-level access to summarisation facilities. Furthermore, POLIS allows users to exploit the hierarchical information provided by structured documents. The development of POLIS is carried out in a step-by-step way. We start by defining a series of probabilistic summarisation models, which provide weights to document-elements at a user selected level. These summarisation models are those accessible through POLIS. The formal definition of POLIS is performed in three steps. We start by providing a syntax for POLIS, through which users/knowledge engineers interact with the logic. This is followed by a definition of the logics semantics. Finally, we provide details of an implementation of POLIS. The final chapters of this dissertation are concerned with the evaluation of POLIS, which is conducted in two stages. Firstly, we evaluate the performance of the summarisation models by applying POLIS to two test collections, the DUC AQUAINT corpus, and the INEX IEEE corpus. This is followed by application scenarios for POLIS, in which we discuss how POLIS can be used in specific IR tasks.
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Books on the topic "Probabilistic logics"

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Probabilistic logics and probabilistic networks. Dordrecht: Springer, 2011.

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Haenni, Rolf, Jan-Willem Romeijn, Gregory Wheeler, and Jon Williamson. Probabilistic Logics and Probabilistic Networks. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-0008-6.

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Huynh, Van-Nam, Yoshiteru Nakamori, Hiroakira Ono, Jonathan Lawry, Vkladik Kreinovich, and Hung T. Nguyen, eds. Interval / Probabilistic Uncertainty and Non-Classical Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-77664-2.

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Katoen, Joost-Pieter. Formal Methods for Real-Time and Probabilistic Systems: 5th International AMAST Workshop, ARTS99 Bamberg, Germany, May 2628, 1999 Proceedings. Berlin: Springer-Verlag Berlin Heidelberg, 1999.

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Paass, Gerhard. Probabilistic logic. Sankt Augustin: Gesellschaft fur Mathematik und Datenverarbeitung, 1987.

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Goertzel, Ben, Matthew Iklé, Izabela Freire Goertzel, and Ari Heljakka. Probabilistic Logic Networks. Boston, MA: Springer US, 2009. http://dx.doi.org/10.1007/978-0-387-76872-4.

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De Raedt, Luc, Paolo Frasconi, Kristian Kersting, and Stephen Muggleton, eds. Probabilistic Inductive Logic Programming. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78652-8.

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Coletii, Giulianella, and Romano Scozzafava. Probabilistic Logic in a Coherent Setting. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-010-0474-9.

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Fisseler, Jens. Learning and modeling with probabilistic conditional logic. Heidelberg: Ios Press, 2010.

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1964-, Raedt Luc de, ed. Probabilistic inductive logic programming: Theory and applications. Berlin: Springer, 2008.

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Book chapters on the topic "Probabilistic logics"

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Doder, Dragan, and Aleksandar Perović. "Probabilistic Temporal Logics." In Probabilistic Extensions of Various Logical Systems, 71–108. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52954-3_3.

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Gerla, Giangiacomo. "Probabilistic Fuzzy Logics." In Fuzzy Logic, 171–98. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-015-9660-2_9.

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Haenni, Rolf, Jan-Willem Romeijn, Gregory Wheeler, and Jon Williamson. "Introduction." In Probabilistic Logics and Probabilistic Networks, 3–10. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-94-007-0008-6_1.

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Haenni, Rolf, Jan-Willem Romeijn, Gregory Wheeler, and Jon Williamson. "Networks for Probabilistic Argumentation." In Probabilistic Logics and Probabilistic Networks, 107–10. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-94-007-0008-6_10.

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Haenni, Rolf, Jan-Willem Romeijn, Gregory Wheeler, and Jon Williamson. "Networks for Evidential Probability." In Probabilistic Logics and Probabilistic Networks, 111–17. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-94-007-0008-6_11.

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Haenni, Rolf, Jan-Willem Romeijn, Gregory Wheeler, and Jon Williamson. "Networks for Statistical Inference." In Probabilistic Logics and Probabilistic Networks, 119–24. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-94-007-0008-6_12.

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Haenni, Rolf, Jan-Willem Romeijn, Gregory Wheeler, and Jon Williamson. "Networks for Bayesian Statistical Inference." In Probabilistic Logics and Probabilistic Networks, 125–31. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-94-007-0008-6_13.

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Haenni, Rolf, Jan-Willem Romeijn, Gregory Wheeler, and Jon Williamson. "Networks for Objective Bayesianism." In Probabilistic Logics and Probabilistic Networks, 133–37. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-94-007-0008-6_14.

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Haenni, Rolf, Jan-Willem Romeijn, Gregory Wheeler, and Jon Williamson. "Conclusion." In Probabilistic Logics and Probabilistic Networks, 139. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-94-007-0008-6_15.

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Haenni, Rolf, Jan-Willem Romeijn, Gregory Wheeler, and Jon Williamson. "Standard Probabilistic Semantics." In Probabilistic Logics and Probabilistic Networks, 11–20. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-94-007-0008-6_2.

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Conference papers on the topic "Probabilistic logics"

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de Alfaro, Luca, Krishnendu Chatterjee, Marco Faella, and Axel Legay. "Qualitative Logics and Equivalences for Probabilistic Systems." In 2007 4th International Conference on the Quantitative Evaluation of Systems. IEEE, 2007. http://dx.doi.org/10.1109/qest.2007.15.

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Chakraborty, Souymodip, and Joost-Pieter Katoen. "On the Satisfiability of Some Simple Probabilistic Logics." In LICS '16: 31st Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2933575.2934526.

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Ramesh, Yenda, and M. Rao. "Statistical Model Checking for Probabilistic Temporal Epistemic Logics." In 14th International Conference on Agents and Artificial Intelligence. SCITEPRESS - Science and Technology Publications, 2022. http://dx.doi.org/10.5220/0010847900003116.

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Frommholz, Ingo, and Norbert Fuhr. "Probabilistic, object-oriented logics for annotation-based retrieval in digital libraries." In the 6th ACM/IEEE-CS joint conference. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1141753.1141764.

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Kim, Joseph, Christian Muise, Ankit Shah, Shubham Agarwal, and Julie Shah. "Bayesian Inference of Linear Temporal Logic Specifications for Contrastive Explanations." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/776.

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Temporal logics are useful for providing concise descriptions of system behavior, and have been successfully used as a language for goal definitions in task planning. Prior works on inferring temporal logic specifications have focused on "summarizing" the input dataset - i.e., finding specifications that are satisfied by all plan traces belonging to the given set. In this paper, we examine the problem of inferring specifications that describe temporal differences between two sets of plan traces. We formalize the concept of providing such contrastive explanations, then present BayesLTL - a Bayesian probabilistic model for inferring contrastive explanations as linear temporal logic (LTL) specifications. We demonstrate the robustness and scalability of our model for inferring accurate specifications from noisy data and across various benchmark planning domains.
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Aminof, Benjamin, Marta Kwiatkowska, Bastien Maubert, Aniello Murano, and Sasha Rubin. "Probabilistic Strategy Logic." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/5.

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We introduce Probabilistic Strategy Logic, an extension of Strategy Logic for stochastic systems. The logic has probabilistic terms that allow it to express many standard solution concepts, such as Nash equilibria in randomised strategies, as well as constraints on probabilities, such as independence. We study the model-checking problem for agents with perfect- and imperfect-recall. The former is undecidable, while the latter is decidable in space exponential in the system and triple-exponential in the formula. We identify a natural fragment of the logic, in which every temporal operator is immediately preceded by a probabilistic operator, and show that it is decidable in space exponential in the system and the formula, and double-exponential in the nesting depth of the probabilistic terms. Taking a fixed nesting depth, this gives a fragment that still captures many standard solution concepts, and is decidable in exponential space.
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Manhaeve, Robin, Giuseppe Marra, and Luc De Raedt. "Approximate Inference for Neural Probabilistic Logic Programming." In 18th International Conference on Principles of Knowledge Representation and Reasoning {KR-2021}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/kr.2021/45.

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DeepProbLog is a neural-symbolic framework that integrates probabilistic logic programming and neural networks. It is realized by providing an interface between the probabilistic logic and the neural networks. Inference in probabilistic neural symbolic methods is hard, since it combines logical theorem proving with probabilistic inference and neural network evaluation. In this work, we make the inference more efficient by extending an approximate inference algorithm from the field of statistical-relational AI. Instead of considering all possible proofs for a certain query, the system searches for the best proof. However, training a DeepProbLog model using approximate inference introduces additional challenges, as the best proof is unknown at the start of training which can lead to convergence towards a local optimum. To be able to apply DeepProbLog on larger tasks, we propose: 1) a method for approximate inference using an A*-like search, called DPLA* 2) an exploration strategy for proving in a neural-symbolic setting, and 3) a parametric heuristic to guide the proof search. We empirically evaluate the performance and scalability of the new approach, and also compare the resulting approach to other neural-symbolic systems. The experiments show that DPLA* achieves a speed up of up to 2-3 orders of magnitude in some cases.
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Wild, Paul, Lutz Schröder, Dirk Pattinson, and Barbara König. "A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/263.

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The fuzzy modality probably is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt. a suitable notion of behavioural distance. In the present paper, we provide a characterization of the expressive power of this logic based on this observation: We prove a probabilistic analogue of the classical van Benthem theorem, which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic. Specifically, we show that every formula in probabilistic fuzzy first-order logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy description logic.
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Nguyen, Hoang Nga, and Abdur Rakib. "A Probabilistic Logic for Resource-Bounded Multi-Agent Systems." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/74.

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Resource-bounded alternating-time temporal logic (RB-ATL), an extension of Coalition Logic (CL) and Alternating-time Temporal Logic (ATL), allows reasoning about resource requirements of coalitions in concurrent systems. However, many real-world systems are inherently probabilistic as well as resource-bounded, and there is no straightforward way of reasoning about their unpredictable behaviours. In this paper, we propose a logic for reasoning about coalitional power under resource constraints in the probabilistic setting. We extend RB-ATL with probabilistic reasoning and provide a standard algorithm for the model-checking problem of the resulting logic Probabilistic Resource-Bounded ATL (pRB-ATL).
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Leventis, Thomas. "Probabilistic Böhm Trees and Probabilistic Separation." In LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3209108.3209126.

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Reports on the topic "Probabilistic logics"

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Kriegel, Francesco. Learning General Concept Inclusions in Probabilistic Description Logics. Technische Universität Dresden, 2015. http://dx.doi.org/10.25368/2022.220.

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Probabilistic interpretations consist of a set of interpretations with a shared domain and a measure assigning a probability to each interpretation. Such structures can be obtained as results of repeated experiments, e.g., in biology, psychology, medicine, etc. A translation between probabilistic and crisp description logics is introduced and then utilised to reduce the construction of a base of general concept inclusions of a probabilistic interpretation to the crisp case for which a method for the axiomatisation of a base of GCIs is well-known.
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Kriegel, Francesco. Learning description logic axioms from discrete probability distributions over description graphs (Extended Version). Technische Universität Dresden, 2018. http://dx.doi.org/10.25368/2022.247.

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Description logics in their standard setting only allow for representing and reasoning with crisp knowledge without any degree of uncertainty. Of course, this is a serious shortcoming for use cases where it is impossible to perfectly determine the truth of a statement. For resolving this expressivity restriction, probabilistic variants of description logics have been introduced. Their model-theoretic semantics is built upon so-called probabilistic interpretations, that is, families of directed graphs the vertices and edges of which are labeled and for which there exists a probability measure on this graph family. Results of scientific experiments, e.g., in medicine, psychology, or biology, that are repeated several times can induce probabilistic interpretations in a natural way. In this document, we shall develop a suitable axiomatization technique for deducing terminological knowledge from the assertional data given in such probabilistic interpretations. More specifically, we consider a probabilistic variant of the description logic EL⊥, and provide a method for constructing a set of rules, so-called concept inclusions, from probabilistic interpretations in a sound and complete manner.
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Baader, Franz, Patrick Koopmann, and Anni-Yasmin Turhan. Using Ontologies to Query Probabilistic Numerical Data (Extended Version). Technische Universität Dresden, 2017. http://dx.doi.org/10.25368/2022.235.

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We consider ontology-based query answering in a setting where some of the data are numerical and of a probabilistic nature, such as data obtained from uncertain sensor readings. The uncertainty for such numerical values can be more precisely represented by continuous probability distributions than by discrete probabilities for numerical facts concerning exact values. For this reason, we extend existing approaches using discrete probability distributions over facts by continuous probability distributions over numerical values. We determine the exact (data and combined) complexity of query answering in extensions of the well-known description logics EL and ALC with numerical comparison operators in this probabilistic setting.
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Peñaloza, Rafael, and Anni-Yasmin Turhan. Completion-based computation of most specific concepts with limited role-depth for EL and Prob-EL⁰¹. Technische Universität Dresden, 2010. http://dx.doi.org/10.25368/2022.176.

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In Description Logics the reasoning service most specific concept (msc) constructs a concept description that generalizes an ABox individual into a concept description. For the Description Logic EL the msc may not exist, if computed with respect to general EL-TBoxes or cyclic ABoxes. However, it is still possible to find a concept description that is the msc up to a fixed role-depth, i.e. with respect to a maximal nesting of quantifiers. In this report we present a practical approach for computing the roledepth bounded msc, based on the polynomial-time completion algorithm for EL. We extend these methods to Prob-EL⁰¹c , which is a probabilistic variant of EL. Together with the companion report [9] this report devises computation methods for the bottom-up construction of knowledge bases for EL and Prob-EL⁰¹c .
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Kriegel, Francesco. Terminological knowledge aquisition in probalistic description logic. Technische Universität Dresden, 2018. http://dx.doi.org/10.25368/2022.239.

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For a probabilistic extension of the description logic EL⊥, we consider the task of automatic acquisition of terminological knowledge from a given probabilistic interpretation. Basically, such a probabilistic interpretation is a family of directed graphs the vertices and edges of which are labeled, and where a discrete probabilitymeasure on this graph family is present. The goal is to derive so-called concept inclusions which are expressible in the considered probabilistic description logic and which hold true in the given probabilistic interpretation. A procedure for an appropriate axiomatization of such graph families is proposed and its soundness and completeness is justified.
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Blakely, Scott. Probabilistic Analysis for Reliable Logic Circuits. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.1859.

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Kishore, Nand, Radhakrishnan Balu, and Shashi P. Karna. Modeling Genetic Regulatory Networks Using First-Order Probabilistic Logic. Fort Belvoir, VA: Defense Technical Information Center, March 2013. http://dx.doi.org/10.21236/ada582376.

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Dempster, Arthur P. Modelling Probabilistic and Logical Relations with Belief Functions. Fort Belvoir, VA: Defense Technical Information Center, June 1995. http://dx.doi.org/10.21236/ada300015.

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Bamber, D. A Characterization of Probabilistic Entailment in Adams' Logic of Conditionals. Fort Belvoir, VA: Defense Technical Information Center, September 1995. http://dx.doi.org/10.21236/ada301476.

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Gray, III, Syverson James W., and Paul F. A Logical Approach to Multilevel Security of Probabilistic Systems. Fort Belvoir, VA: Defense Technical Information Center, January 1998. http://dx.doi.org/10.21236/ada465040.

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