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Journal articles on the topic 'Probabilistic logics'

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Published: 10 December 2022

Last updated: 28 January 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Aguirre, Alejandro, Gilles Barthe, Marco Gaboardi, Deepak Garg, Shin-ya Katsumata, and Tetsuya Sato. "Higher-order probabilistic adversarial computations: categorical semantics and program logics." Proceedings of the ACM on Programming Languages 5, ICFP (August 22, 2021): 1–30. http://dx.doi.org/10.1145/3473598.

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Adversarial computations are a widely studied class of computations where resource-bounded probabilistic adversaries have access to oracles, i.e., probabilistic procedures with private state. These computations arise routinely in several domains, including security, privacy and machine learning. In this paper, we develop program logics for reasoning about adversarial computations in a higher-order setting. Our logics are built on top of a simply typed λ-calculus extended with a graded monad for probabilities and state. The grading is used to model and restrict the memory footprint and the cost (in terms of oracle calls) of computations. Under this view, an adversary is a higher-order expression that expects as arguments the code of its oracles. We develop unary program logics for reasoning about error probabilities and expected values, and a relational logic for reasoning about coupling-based properties. All logics feature rules for adversarial computations, and yield guarantees that are valid for all adversaries that satisfy a fixed resource policy. We prove the soundness of the logics in the category of quasi-Borel spaces, using a general notion of graded predicate liftings, and we use logical relations over graded predicate liftings to establish the soundness of proof rules for adversaries. We illustrate the working of our logics with simple but illustrative examples.

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12

Doder, Dragan. "A logic with big-stepped probabilities that can model nonmonotonic reasoning of system P." Publications de l'Institut Math?matique (Belgrade) 90, no. 104 (2011): 13–22. http://dx.doi.org/10.2298/pim1104013d.

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We develop a sound and strongly complete axiomatic system for probabilistic logic in which we can model nonmonotonic (or default) reasoning. We discuss the connection between previously developed logics and the two sublogics of the logic presented here.

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13

Morgan, Charles, and Fran�ois Lepage. "Probabilistic Canonical Models for Partial Logics." Notre Dame Journal of Formal Logic 44, no. 3 (July 2003): 125–38. http://dx.doi.org/10.1305/ndjfl/1091030851.

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14

Doder, Dragan, and Zoran Ognjanović. "Probabilistic Logics with Independence and Confirmation." Studia Logica 105, no. 5 (April 9, 2017): 943–69. http://dx.doi.org/10.1007/s11225-017-9718-z.

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15

Du, Wenjie, Yuxin Deng, and Daniel Gebler. "Behavioural Pseudometrics for Nondeterministic Probabilistic Systems." Scientific Annals of Computer Science XXXII, no. 2 (December 7, 2022): 211–54. http://dx.doi.org/10.7561/sacs.2022.2.211.

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For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on Hennessy-Milner logic. The logic for characterising the state-based metric is much simpler than an earlier logic proposed by Desharnais et al. as it uses only two non-expansive operators rather than the general class of non-expansive operators. For the kernels of the two metrics, which correspond to two notions of bisimilarity, we give a comprehensive comparison with some typical distribution-based bisimilarities in the literature.

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16

NOTTELMANN, HENRIK, and NORBERT FUHR. "ADDING PROBABILITIES AND RULES TO OWL LITE SUBSETS BASED ON PROBABILISTIC DATALOG." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 14, no. 01 (February 2006): 17–41. http://dx.doi.org/10.1142/s0218488506003819.

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This paper proposes two probabilistic extensions of variants of the OWL Lite description language, which are essential for advanced applications like information retrieval. The first step follows the axiomatic approach of combining description logics and Horn clauses: Subsets of OWL Lite are mapped in a sound and complete way onto Horn predicate logics (Datalog variants). Compared to earlier approaches, a larger fraction of OWL Lite can be transformed by switching to Datalog with equality in the head; however, some OWL Lite constructs cannot be transformed completely into Datalog. By using probabilistic Datalog, the new probabilistic OWL Lite subsets (both with support for Horn rules) are defined, and the semantics are given by the semantics of the corresponding probabilistic Datalog program. As inference engines for probabilistic Datalog are available, description logics and information retrieval systems can easily be combined.

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17

Kamide, Norihiro, and Daiki Koizumi. "Method for Combining Paraconsistency and Probability in Temporal Reasoning." Journal of Advanced Computational Intelligence and Intelligent Informatics 20, no. 5 (September 20, 2016): 813–27. http://dx.doi.org/10.20965/jaciii.2016.p0813.

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Computation tree logic (CTL) is known to be one of the most useful temporal logics for verifying concurrent systems by model checking technologies. However, CTL is not sufficient for handling inconsistency-tolerant and probabilistic accounts of concurrent systems. In this paper, a paraconsistent (or inconsistency-tolerant) probabilistic computation tree logic (PpCTL) is derived from an existing probabilistic computation tree logic (pCTL) by adding a paraconsistent negation connective. A theorem for embedding PpCTL into pCTL is proven, thereby indicating that we can reuse existing pCTL-based model checking algorithms. A relative decidability theorem for PpCTL, wherein the decidability of pCTL implies that of PpCTL, is proven using this embedding theorem. Some illustrative examples involving the use of PpCTL are also presented.

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18

Ilic-Stepic, Angelina, and Zoran Ognjanovic. "Complex valued probability logics." Publications de l'Institut Math?matique (Belgrade) 95, no. 109 (2014): 73–86. http://dx.doi.org/10.2298/pim1409073i.

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We present two complex valued probabilistic logics, LCOMPB and LCOMPS, which extend classical propositional logic. In LCOMPB one can express formulas of the form Bz,?? meaning that the probability of ? is in the complex ball with the center z and the radius ?, while in LCOMPS one can make statements of the form Sz,?? with the intended meaning - the probability of propositional formula ? is in the complex square with the center z and the side 2?. The corresponding strongly complete axiom systems are provided. Decidability of the logics are proved by reducing the satisfiability problem for LCOMPB (LCOMPS) to the problem of solving systems of quadratic (linear) inequalities.

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19

Peñaloza, Rafael. "A Brief Roadmap into Uncertain Knowledge Representation via Probabilistic Description Logics." Algorithms 14, no. 10 (September 28, 2021): 280. http://dx.doi.org/10.3390/a14100280.

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Logic-based knowledge representation is one of the main building blocks of (logic-based) artificial intelligence. While most successful knowledge representation languages are based on classical logic, realistic intelligent applications need to handle uncertainty in an adequate manner. Over the years, many different languages for representing uncertain knowledge—often extensions of classical knowledge representation languages—have been proposed. We briefly present some of the defining properties of these languages as they pertain to the family of probabilistic description logics. This limited view is intended to help pave the way for the interested researcher to find the most adequate language for their needs, and potentially identify the remaining gaps.

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20

Kupke, Clemens, Dirk Pattinson, and Lutz Schröder. "Coalgebraic Reasoning with Global Assumptions in Arithmetic Modal Logics." ACM Transactions on Computational Logic 23, no. 2 (April 30, 2022): 1–34. http://dx.doi.org/10.1145/3501300.

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We establish a generic upper bound ExpTime for reasoning with global assumptions (also known as TBoxes) in coalgebraic modal logics. Unlike earlier results of this kind, our bound does not require a tractable set of tableau rules for the instance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that potentially avoids building the entire exponential-sized space of candidate states, and thus offers a basis for practical reasoning. This algorithm still involves frequent fixpoint computations; we show how these can be handled efficiently in a concrete algorithm modelled on Liu and Smolka’s linear-time fixpoint algorithm. Finally, we show that the upper complexity bound is preserved under adding nominals to the logic, i.e., in coalgebraic hybrid logic.

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21

Riguzzi, Fabrizio, Elena Bellodi, Evelina Lamma, and Riccardo Zese. "Probabilistic Description Logics under the distribution semantics." Semantic Web 6, no. 5 (August 7, 2015): 477–501. http://dx.doi.org/10.3233/sw-140154.

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22

Thimm, M., and G. Kern-Isberner. "On probabilistic inference in relational conditional logics." Logic Journal of IGPL 20, no. 5 (March 5, 2012): 872–908. http://dx.doi.org/10.1093/jigpal/jzs010.

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23

Tiomkin, M., and J. A. Makowsky. "Decidability of finite probabilistic propositional dynamic logics." Information and Computation 94, no. 2 (October 1991): 180–203. http://dx.doi.org/10.1016/0890-5401(91)90037-3.

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24

Beierle, Christoph, and Gabriele Kern-Isberner. "Semantical investigations into nonmonotonic and probabilistic logics." Annals of Mathematics and Artificial Intelligence 65, no. 2-3 (July 2012): 123–58. http://dx.doi.org/10.1007/s10472-012-9310-1.

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25

Giordano, Laura, Valentina Gliozzi, and Daniele Theseider DuprÉ. "A conditional, a fuzzy and a probabilistic interpretation of self-organizing maps." Journal of Logic and Computation 32, no. 2 (January 17, 2022): 178–205. http://dx.doi.org/10.1093/logcom/exab082.

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Abstract In this paper we establish a link between fuzzy and preferential semantics for description logics and self-organizing maps (SOMs), which have been proposed as possible candidates to explain the psychological mechanisms underlying category generalization. In particular, we show that the input/output behavior of a SOM after training can be described by a fuzzy description logic interpretation as well as by a preferential interpretation, based on a concept-wise multipreference semantics, which takes into account preferences with respect to different concepts and has been recently proposed for ranked and for weighted defeasible description logics. Properties of the network can be proven by model checking on the fuzzy or on the preferential interpretation. Starting from the fuzzy interpretation, we also provide a probabilistic account for this neural network model.

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26

KIMMIG, ANGELIKA, BART DEMOEN, LUC DE RAEDT, VÍTOR SANTOS COSTA, and RICARDO ROCHA. "On the implementation of the probabilistic logic programming language ProbLog." Theory and Practice of Logic Programming 11, no. 2-3 (January 27, 2011): 235–62. http://dx.doi.org/10.1017/s1471068410000566.

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AbstractThe past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension of Prolog motivated by the mining of large biological networks. In ProbLog, facts can be labeled with probabilities. These facts are treated as mutually independent random variables that indicate whether these facts belong to a randomly sampled program. Different kinds of queries can be posed to ProbLog programs. We introduce algorithms that allow the efficient execution of these queries, discuss their implementation on top of the YAP-Prolog system, and evaluate their performance in the context of large networks of biological entities.

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27

Chiara, Maria Luisa Dalla, Roberto Giuntini, Giuseppe Sergioli, and Roberto Leporini. "Abstract quantum computing machines and quantum computational logics." International Journal of Quantum Information 14, no. 04 (June 2016): 1640019. http://dx.doi.org/10.1142/s0219749916400190.

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Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.

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28

Cleaveland, Rance, S. Purushothaman Iyer, and Murali Narasimha. "Probabilistic temporal logics via the modal mu-calculus." Theoretical Computer Science 342, no. 2-3 (September 2005): 316–50. http://dx.doi.org/10.1016/j.tcs.2005.03.048.

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29

Clerc, Florence, Nathanaël Fijalkow, Bartek Klin, and Prakash Panangaden. "Expressiveness of probabilistic modal logics: A gradual approach." Information and Computation 267 (August 2019): 145–63. http://dx.doi.org/10.1016/j.ic.2019.04.002.

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30

Svozil, Karl. "Faithful orthogonal representations of graphs from partition logics." Soft Computing 24, no. 14 (November 4, 2019): 10239–45. http://dx.doi.org/10.1007/s00500-019-04425-1.

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Abstract Partition logics often allow a dual probabilistic interpretation: a classical one for which probabilities lie on the convex hull of the dispersion-free weights and another one, suggested independently from the quantum Born rule, in which probabilities are formed by the (absolute) square of the inner product of state vectors with the faithful orthogonal representations of the respective graph. Two immediate consequences are the demonstration that the logico-empirical structure of observables does not determine the type of probabilities alone and that complementarity does not imply contextuality.

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31

Flaminio, Tommaso, and Franco Montagna. "MV-algebras with internal states and probabilistic fuzzy logics." International Journal of Approximate Reasoning 50, no. 1 (January 2009): 138–52. http://dx.doi.org/10.1016/j.ijar.2008.07.006.

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32

Ognjanović, Zoran. "Discrete Linear-time Probabilistic Logics: Completeness, Decidability and Complexity." Journal of Logic and Computation 16, no. 2 (April 1, 2006): 257–85. http://dx.doi.org/10.1093/logcom/exi077.

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33

Doder, D., J. Grant, and Z. Ognjanovic. "Probabilistic logics for objects located in space and time." Journal of Logic and Computation 23, no. 3 (December 18, 2012): 487–515. http://dx.doi.org/10.1093/logcom/exs054.

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34

ADAMS, ERNEST W. "A note on comparing probabilistic and modal logics of conditionals." Theoria 43, no. 3 (February 11, 2008): 186–94. http://dx.doi.org/10.1111/j.1755-2567.1977.tb00787.x.

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35

Snow, Paul. "Diverse confidence levels in a probabilistic semantics for conditional logics." Artificial Intelligence 113, no. 1-2 (September 1999): 269–79. http://dx.doi.org/10.1016/s0004-3702(99)00054-5.

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36

Konur, Savas, Michael Fisher, and Sven Schewe. "Combined model checking for temporal, probabilistic, and real-time logics." Theoretical Computer Science 503 (September 2013): 61–88. http://dx.doi.org/10.1016/j.tcs.2013.07.012.

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37

Karasev, Vasily, and Ekaterina Karaseva. "LOGICAL AND PROBABILISTIC METHOD FOR RISK MANAGEMENT IN SOCIO-ECONOMIC SYSTEMS." Environment. Technology. Resources. Proceedings of the International Scientific and Practical Conference 2 (June 15, 2017): 58. http://dx.doi.org/10.17770/etr2017vol2.2584.

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In this paper we research the application of logical and probabilistic method to manage risk in socio-economic systems. Logical and probabilistic method is widely used for estimation of reliability and safety in structural complex technical systems. Authors have applied this method to estimate and analyze risk in some practical applications in economics and business. Based on risk scenario as tree of events, logics and probabilistic functions, this approach provides exact quantitative estimation of risk, risk analysis and decision-making procedures. Some promising results were obtained in banking industry and security portfolio management but application of the method has some features.

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38

Konur, Savas. "Towards Light-Weight Probabilistic Model Checking." Journal of Applied Mathematics 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/814159.

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Model checking has been extensively used to verify various systems. However, this usually has been done by experts who have a good understanding of model checking and who are familiar with the syntax of both modelling and property specification languages. Unfortunately, this is not an easy task for nonexperts to learn description languages for modelling and formal logics/languages for property specification. In particular, property specification is very daunting and error-prone for nonexperts. In this paper, we present a methodology to facilitate probabilistic model checking for nonexperts. The methodology helps nonexpert users model their systems and express their requirements without any knowledge of the modelling and property specification languages.

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39

Giang, P. H., D. Dubois, and H. Prade. "A Probabilistic Approach to Ordering Formulas in a Possibilistic Knowledge Base." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 06, no. 03 (June 1998): 241–56. http://dx.doi.org/10.1142/s0218488598000227.

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In this paper, a careful analysis of interval-valued possibilistic knowledge bases indicates that there exists a natural probability distribution over the set of orderings of formulae compatible with the weights given in the knowledge base. We propose a new view, by which a possibilistic knowledge base can be considered in term of such probability distribution. It reveals some interconnections between probabilistic and possibilistic logics. We show that the principle of minimum specificity, widely used in possibilistic logic, is a special case of the principle of maximum likehood (at least, from the standpoint of nonmonotonic reasoning). We propose a formula to calculate probability for a defeasible conclusion. Moreover, the proposed view seems to be useful for other practical purposes. As an example, we apply it to a traditional problem of fusion of possibilistic knowledge from many sources and derive a new solution.

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40

BERNARDO, MARCO, and STEFANIA BOTTA. "A survey of modal logics characterising behavioural equivalences for non-deterministic and stochastic systems." Mathematical Structures in Computer Science 18, no. 1 (February 2008): 29–55. http://dx.doi.org/10.1017/s0960129507006408.

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Behavioural equivalences are a means of establishing whether computing systems possess the same properties. The specific set of properties that are preserved by a specific behavioural equivalence clearly depends on how the system behaviour is observed and can usually be characterised by means of a modal logic. In this paper we consider three different approaches to the definition of behavioural equivalences – bisimulation, testing and trace – applied to three different classes of systems – non-deterministic, probabilistic and Markovian – and we survey the nine resulting modal logic characterisations, each of which stems from the Hennessy–Milner logic. We then compare the nine characterisations with respect to the logical operators, in order to emphasise the differences between the three approaches in the definition of behavioural equivalences and the regularities within each of them. In the probabilistic and Markovian cases we also address the issue of whether the probabilistic and temporal aspects should be treated in a local or global way and consequently whether the modal logic interpretation should be qualitative or quantitative.

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41

Cai, Bibo, Xiao Ding, Bowen Chen, Li Du, and Ting Liu. "Mitigating Reporting Bias in Semi-supervised Temporal Commonsense Inference with Probabilistic Soft Logic." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 10 (June 28, 2022): 10454–62. http://dx.doi.org/10.1609/aaai.v36i10.21288.

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Acquiring high-quality temporal common sense (TCS) knowledge from free-form text is a crucial but challenging problem for event-centric natural language understanding, due to the language reporting bias problem: people rarely report the commonly observed events but highlight the special cases. For example, one may rarely report "I get up from bed in 1 minute", but we can observe "It takes me an hour to get up from bed every morning'' in text. Models directly trained upon such corpus would capture distorted TCS knowledge, which could influence the model performance. Prior work addresses this issue mainly by exploiting the interactions among temporal dimensions (e.g., duration, temporal relation between events) in a multi-task view. However, this line of work suffers the limitation of implicit, inadequate and unexplainable interactions modeling. In this paper, we propose a novel neural-logic based Soft Logic Enhanced Event Temporal Reasoning (SLEER) model for acquiring unbiased TCS knowledge, in which the complementary relationship among dimensions are explicitly represented as logic rules and modeled by t-norm fuzzy logics. SLEER can utilize logic rules to regularize its inference process. Experimental results on four intrinsic evaluation datasets and two extrinsic datasets show the efficiency of our proposed method.

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42

Kokkinis, Ioannis. "The complexity of satisfiability in non-iterated and iterated probabilistic logics." Annals of Mathematics and Artificial Intelligence 83, no. 3-4 (July 6, 2018): 351–82. http://dx.doi.org/10.1007/s10472-018-9593-y.

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43

Grant, John, Francesco Parisi, Austin Parker, and V. S. Subrahmanian. "An AGM-style belief revision mechanism for probabilistic spatio-temporal logics." Artificial Intelligence 174, no. 1 (January 2010): 72–104. http://dx.doi.org/10.1016/j.artint.2009.10.002.

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44

Song, Fu, Yedi Zhang, Taolue Chen, Yu Tang, and Zhiwu Xu. "Probabilistic Alternating-Time µ-Calculus." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 6179–86. http://dx.doi.org/10.1609/aaai.v33i01.33016179.

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Reasoning about strategic abilities is key to an AI system consisting of multiple agents with random behaviors. We propose a probabilistic extension of Alternating µ-Calculus (AMC), named PAMC, for reasoning about strategic abilities of agents in stochastic multi-agent systems. PAMC subsumes existing logics AMC and PµTL. The usefulness of PAMC is exemplified by applications in genetic regulatory networks. We show that, for PAMC, the model checking problem is in UP∩co-UP, and the satisfiability problem is EXPTIME-complete, both of which are the same as those for AMC. Moreover, PAMC admits the small model property. We implement the satisfiability checking procedure in a tool PAMCSolver.

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45

Klinov, Pavel Picado, Bijan Parsia, and David Muiño. "The Consistency of the Medical Expert System CADIAG-2." Journal of Information Technology Research 4, no. 1 (January 2011): 1–20. http://dx.doi.org/10.4018/jitr.2011010101.

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CADIAG-2 is a well known rule-based medical expert system aimed at providing support in medical diagnose in the field of internal medicine. Its knowledge base consists of a large collection of IF-THEN rules that represent uncertain relationships between distinct medical entities. Given this uncertainty and the size of the system, it has been challenging to validate its consistency. Recent attempts to partially formalize CADIAG-2’s knowledge base into decidable Gödel logics have shown that, on formalization, the system is inconsistent. In this paper, the authors use an alternative, more expressive formalization of CADIAG-2’s knowledge base as a set of probabilistic conditional statements and apply their probabilistic logic solver (Pronto) to confirm its inconsistency and compute its conflicting sets of rules under a slightly relaxed interpretation. Once this is achieved, the authors define a measure to evaluate inconsistency and discuss suitable repair strategies for CADIAG-2 and similar systems.

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46

Requeno, José Ignacio, and José Manuel Colom. "Analyzing Phylogenetic Trees with Timed and Probabilistic Model Checking: The Lactose Persistence Case Study." Journal of Integrative Bioinformatics 11, no. 3 (December 1, 2014): 17–31. http://dx.doi.org/10.1515/jib-2014-248.

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Summary Model checking is a generic verification technique that allows the phylogeneticist to focus on models and specifications instead of on implementation issues. Phylogenetic trees are considered as transition systems over which we interrogate phylogenetic questions written as formulas of temporal logic. Nonetheless, standard logics become insufficient for certain practices of phylogenetic analysis since they do not allow the inclusion of explicit time and probabilities. The aim of this paper is to extend the application of model checking techniques beyond qualitative phylogenetic properties and adapt the existing logical extensions and tools to the field of phylogeny. The introduction of time and probabilities in phylogenetic specifications is motivated by the study of a real example: the analysis of the ratio of lactose intolerance in some populations and the date of appearance of this phenotype.

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47

Juba, Brendan. "Polynomial-Time Probabilistic Reasoning with Partial Observations via Implicit Learning in Probability Logics." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 7866–75. http://dx.doi.org/10.1609/aaai.v33i01.33017866.

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Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which efficient algorithms are generally not known. In this work we consider the use of bounded-degree fragments of the “sum-of-squares” logic as a probability logic. Prior work has shown that we can decide refutability for such fragments in polynomial-time. We propose to use such fragments to decide queries about whether a given probability distribution satisfies a given system of constraints and bounds on expected values. We show that in answering such queries, such constraints and bounds can be implicitly learned from partial observations in polynomial-time as well. It is known that this logic is capable of deriving many bounds that are useful in probabilistic analysis. We show here that it furthermore captures key polynomial-time fragments of resolution. Thus, these fragments are also quite expressive.

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48

Ma, Z. M., Fu Zhang, Hailong Wang, and Li Yan. "An overview of fuzzy Description Logics for the Semantic Web." Knowledge Engineering Review 28, no. 1 (October 31, 2012): 1–34. http://dx.doi.org/10.1017/s0269888912000306.

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AbstractInformation imprecision and uncertainty exist in many real world applications, and such information would be retrieved, processed, shared, reused, and aligned in the maximum automatic way possible. As a popular family of formally well-founded and decidable knowledge representation languages, fuzzy Description Logics (fuzzy DLs), which extend DLs with fuzzy logic, are very well suited to cover for representing and reasoning with imprecision and uncertainty. Thus, a requirement naturally arises in many practical applications of knowledge-based systems, in particular the Semantic Web, because DLs are the logical foundation of the Semantic Web. Currently, there have been lots of fuzzy extensions of DLs with Zadeh's fuzzy logic theory papers published, to investigate fuzzy DLs and more importantly serve as identifying the direction of fuzzy DLs study. In this paper, we aim at providing a comprehensive literature overview of fuzzy DLs, and we focus our attention on fuzzy extensions of DLs based on fuzzy set theory. Other relevant formalisms that are based on approaches like probabilistic theory or non-monotonic logics are covered elsewhere. In detail, we first introduce the existing fuzzy DLs (including the syntax, semantics, knowledge base, and reasoning algorithm) from the origin, development (from weaker to stronger in expressive power), some special techniques, and so on. Then, the other important issues on fuzzy DLs, such as reasoning, querying, applications, and directions for future research, are also discussed in detail. Also, we make a comparison and analysis.

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49

Preto, Sandro Márcio da Silva. "Semantics modulo satisfiability with applications: function representation, probabilities and game theory." Bulletin of Symbolic Logic 28, no. 2 (June 2022): 264–65. http://dx.doi.org/10.1017/bsl.2022.2.

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AbstractIn the context of propositional logics, we apply semantics modulo satisfiability—a restricted semantics which comprehends only valuations that satisfy some specific set of formulas—with the aim to efficiently solve some computational tasks. Three possible such applications are developed.We begin by studying the possibility of implicitly representing rational McNaughton functions in Łukasiewicz Infinitely-valued Logic through semantics modulo satisfiability. We theoretically investigate some approaches to such representation concept, called representation modulo satisfiability, and describe a polynomial algorithm that builds representations in the newly introduced system. An implementation of the algorithm, test results and ways to randomly generate rational McNaughton functions for testing are presented. Moreover, we propose an application of such representations to the formal verification of properties of neural networks by means of the reasoning framework of Łukasiewicz Infinitely-valued Logic.Then, we move to the investigation of the satisfiability of joint probabilistic assignments to formulas of Łukasiewicz Infinitely-valued Logic, which is known to be an NP-complete problem. We provide an exact decision algorithm derived from the combination of linear algebraic methods with semantics modulo satisfiability. Also, we provide an implementation for such algorithm for which the phenomenon of phase transition is empirically detected.Lastly, we study the game theory situation of observable games, which are games that are known to reach a Nash equilibrium, however, an external observer does not know what is the exact profile of actions that occur in a specific instance; thus, such observer assigns subjective probabilities to players actions. We study the decision problem of determining if a set of these probabilistic constraints is coherent by reducing it to the problems of satisfiability of probabilistic assignments to logical formulas both in Classical Propositional Logic and Łukasiewicz Infinitely-valued Logic depending on whether only pure equilibria or also mixed equilibria are allowed. Such reductions rely upon the properties of semantics modulo satisfiability. We provide complexity and algorithmic discussion for the coherence problem and, also, for the problem of computing maximal and minimal probabilistic constraints on actions that preserves coherence.Abstract prepared by Sandro Márcio da Silva Preto.E-mail: spreto@ime.usp.brURL:https://doi.org/10.11606/T.45.2021.tde-17062021-163257

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Lukasiewicz, Thomas. "Nonmonotonic probabilistic logics under variable-strength inheritance with overriding: Complexity, algorithms, and implementation." International Journal of Approximate Reasoning 44, no. 3 (March 2007): 301–21. http://dx.doi.org/10.1016/j.ijar.2006.07.015.

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