@article{birkhoffRingsSets1937,
  title = {Rings of Sets},
  author = {Birkhoff, Garrett},
  year = {1937},
  month = sep,
  journal = {Duke Mathematical Journal},
  volume = {3},
  number = {3},
  pages = {443--454},
  issn = {0012-7094},
  doi = {10.1215/S0012-7094-37-00334-X},
  file = {/home/mpwd/Zotero/storage/M4UUX5SM/DPubS.html;/home/mpwd/Zotero/storage/UQ4MRUW9/S0012-7094-37-00334-X.html}
}

@incollection{blackburnSectionCanonicalModels2001,
  title = {Section 4.2 {{Canonical Models}}},
  booktitle = {Modal Logic},
  author = {Blackburn, Patrick and {de Rijke}, Maarten and Venema, Yde},
  year = {2001},
  pages = {196--201},
  abstract = {This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.},
  isbn = {978-1-107-05088-4 978-1-316-09752-6 978-1-316-09907-0},
  langid = {english}
}

@article{bobenriethOriginsUseArgument2010,
  ids = {bobenriethm.OriginsUseArgument2010},
  title = {The {{Origins}} of the {{Use}} of the {{Argument}} of {{Trivialization}} in the {{Twentieth Century}}},
  author = {Bobenrieth, Andrés},
  year = {2010},
  month = may,
  journal = {History and Philosophy of Logic},
  volume = {31},
  number = {2},
  pages = {111--121},
  issn = {0144-5340, 1464-5149},
  doi = {10.1080/01445340903340033},
  langid = {english},
  file = {/home/mpwd/Zotero/storage/IICQTFGA/01445340903340033.html}
}

@incollection{booleChapterXVIIGeneral1853,
  title = {Chapter {{XVII}}. {{General Method In Probabilities}}},
  booktitle = {An {{Investigation}} of the {{Laws}} of {{Thought On}} Which Are Founded the Mathematical Theories of Logic and Probabilities},
  author = {Boole, George},
  year = {1853},
  pages = {253--275},
  langid = {english},
  keywords = {Logic,Logic; Symbolic and mathematical,Probabilities,Symbolic and mathematical,Thought and thinking}
}

@incollection{booleChapterXVITheory1853,
  title = {Chapter {{XVI}}. {{On The Theory Of Probabilities}}},
  booktitle = {An {{Investigation}} of the {{Laws}} of {{Thought On}} Which Are Founded the Mathematical Theories of Logic and Probabilities},
  author = {Boole, George},
  year = {1853},
  pages = {243--252},
  langid = {english},
  keywords = {Logic,Logic; Symbolic and mathematical,Probabilities,Symbolic and mathematical,Thought and thinking}
}

@book{booleInvestigationLawsThought1853,
  title = {An {{Investigation}} of the {{Laws}} of {{Thought On}} Which Are Founded the Mathematical Theories of Logic and Probabilities},
  author = {Boole, George},
  year = {1853},
  copyright = {Public domain in the USA.},
  langid = {english},
  lccn = {EBook-No. 15114},
  keywords = {Logic,Logic; Symbolic and mathematical,Probabilities,Symbolic and mathematical,Thought and thinking}
}

@article{boolosDonEliminateCut1984,
  ids = {boolosDonEliminateCut1984a},
  title = {Don't {{Eliminate Cut}}},
  author = {Boolos, George},
  year = {1984},
  journal = {Journal of Philosophical Logic},
  volume = {13},
  number = {4},
  pages = {373--378},
  publisher = {{Springer}},
  issn = {0022-3611},
  doi = {10.1007/BF00247711},
  langid = {english}
}

@article{broderickBooleanAlgebraProbability1940,
  title = {Boolean {{Algebra}} and {{Probability Theory}}},
  author = {Broderick, T. S. and Schrödinger, E.},
  year = {1940},
  journal = {Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences},
  volume = {46},
  pages = {103--112},
  publisher = {{Royal Irish Academy}},
  issn = {0035-8975}
}

@incollection{daveyChapterRepresentationFinite2002,
  title = {Chapter 5.  {{Representation}}: The Finite Case},
  booktitle = {Introduction to Lattices and Order},
  author = {Davey, B. A. and Priestley, H. A.},
  year = {2002},
  edition = {2nd ed},
  pages = {112--124},
  publisher = {{Cambridge University Press}},
  address = {{Cambridge, UK ; New York, NY}},
  isbn = {978-0-521-78451-1},
  lccn = {QA171.5 .D38 2002},
  keywords = {Lattice theory}
}

@book{daveyIntroductionLatticesOrder2002,
  ids = {daveyIntroductionLatticesOrder2002a},
  title = {Introduction to Lattices and Order},
  author = {Davey, B. A. and Priestley, H. A.},
  year = {2002},
  edition = {2nd ed},
  publisher = {{Cambridge University Press}},
  address = {{Cambridge, UK ; New York, NY}},
  isbn = {978-0-521-78451-1},
  lccn = {QA171.5 .D38 2002},
  keywords = {Lattice theory},
  file = {/Users/mpwd/Documents/Library/Davey and Priestley - 2002 - Introduction to lattices and order.pdf}
}

@article{definettiLogicProbability1995,
  ids = {DeFinettiLogicProbability1995},
  title = {The {{Logic}} of {{Probability}}},
  author = {De Finetti, Bruno and Angell, Brad},
  year = {1995},
  journal = {Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition},
  volume = {77},
  number = {1},
  pages = {181--190},
  issn = {0031-8116}
}

@article{definettiSuiPassaggiLimite1930,
  title = {Sui Passaggi al Limite Nel Calcolo Delle Probabilità},
  author = {De Finetti, B.},
  year = {1930},
  journal = {Reale Istituto Lombardo di Scienze e Lettere},
  volume = {63},
  pages = {1--12}
}

@article{dempsterUpperLowerProbabilities1967,
  title = {Upper and {{Lower Probabilities Induced}} by a {{Multivalued Mapping}}},
  author = {Dempster, A. P.},
  year = {1967},
  journal = {The Annals of Mathematical Statistics},
  volume = {38},
  number = {2},
  pages = {325--339},
  publisher = {{Institute of Mathematical Statistics}},
  issn = {0003-4851},
  abstract = {A multivalued mapping from a space X to a space S carries a probability measure defined over subsets of X into a system of upper and lower probabilities over subsets of S. Some basic properties of such systems are explored in Sections 1 and 2. Other approaches to upper and lower probabilities are possible and some of these are related to the present approach in Section 3. A distinctive feature of the present approach is a rule for conditioning, or more generally, a rule for combining sources of information, as discussed in Sections 4 and 5. Finally, the context in statistical inference from which the present theory arose is sketched briefly in Section 6.}
}

@article{eberlBuffonNeedleProblem2017,
  ids = {Buffons\_Needle-AFP},
  title = {Buffon's Needle Problem},
  author = {Eberl, Manuel},
  year = {2017},
  month = jun,
  journal = {Archive of Formal Proofs},
  issn = {2150-914x},
  abstract = {In the 18th century, Georges-Louis Leclerc, Comte de Buffon posed and later solved the following problem, which is often called the first problem ever solved in geometric probability: Given a floor divided into vertical strips of the same width, what is the probability that a needle thrown onto the floor randomly will cross two strips? This entry formally defines the problem in the case where the needle's position is chosen uniformly at random in a single strip around the origin (which is equivalent to larger arrangements due to symmetry). It then provides proofs of the simple solution in the case where the needle's length is no greater than the width of the strips and the more complicated solution in the opposite case.}
}

@incollection{ellenbergChapter11What2014,
  title = {Chapter 11. {{What}} to {{Expect When You}}'re {{Expecting}} to {{Win}} the {{Lottery}}},
  booktitle = {How {{Not To Be Wrong}}: {{The Power}} of {{Mathematical Thinking}}},
  author = {Ellenberg, Jordan},
  year = {2014},
  publisher = {{The Penguin Press}},
  address = {{New York}},
  abstract = {"In How Not to Be Wrong, Jordan Ellenberg shows us that math isn't confined to abstract incidents that never occur in real life, but rather touches everything we do--the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It's a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does "public opinion" really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician's method of analyzing life and exposing the hard-won insights of the academic community to the layman--minus the jargon. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. "--},
  isbn = {978-1-59420-522-4},
  lccn = {QA99 .E45 2014},
  keywords = {Mathematical analysis,Mathematics,MATHEMATICS / General,Miscellanea}
}

@book{ellenbergHowNotBe2014,
  title = {How Not to Be Wrong: The Power of Mathematical Thinking},
  shorttitle = {How Not to Be Wrong},
  author = {Ellenberg, Jordan},
  year = {2014},
  publisher = {{The Penguin Press}},
  address = {{New York}},
  abstract = {"In How Not to Be Wrong, Jordan Ellenberg shows us that math isn't confined to abstract incidents that never occur in real life, but rather touches everything we do--the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It's a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does "public opinion" really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician's method of analyzing life and exposing the hard-won insights of the academic community to the layman--minus the jargon. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. "--},
  isbn = {978-1-59420-522-4},
  lccn = {QA99 .E45 2014},
  keywords = {Mathematical analysis,Mathematics,MATHEMATICS / General,Miscellanea}
}

@article{gainesFuzzyProbabilityUncertainty1978,
  ids = {gainesFuzzyProbabilityUncertainty},
  title = {Fuzzy and Probability Uncertainty Logics},
  author = {Gaines, Brian R.},
  year = {1978},
  month = aug,
  journal = {Information and Control},
  volume = {38},
  number = {2},
  pages = {154--169},
  issn = {0019-9958},
  doi = {10.1016/S0019-9958(78)90165-1},
  abstract = {Probability theory and fuzzy logic have been presented as quite distinct theoretical foundations for reasoning and decision making in situations of uncertainty. This paper establishes a common basis for both forms of logic of uncertainty in which a basic uncertainty logic is defined in terms of a valuation on a lattice of propositions. The (non-truth-functional) connectives for conjunction, disjunction, equivalence, implication, and negation are defined in terms which closely resemble those of probability theory. Addition of the axiom of the excluded middle to the basic logic gives a standard probability logic. Alternatively, addition of a requirement for strong truth-functionality (truth-value of connective determined by truth-value of constituents) gives a fuzzy logic with connectives, including implication, as in Lukasiewicz' infinitely valued logic. A common semantics for all such variants is given in terms of binary responses from a population. The type of population, e.g., physical events, people, or neurons, determines whether the model is of physical probability, subjective belief, or human decision-making. The formal theory and the semantics together illustrate clearly the precise similarities and differences between fuzzy and probability logics.},
  langid = {english},
  file = {/home/mpwd/Zotero/storage/M6W5EHV6/Gaines - Fuzzy and Probability Uncertainty Logics.pdf}
}

@article{gareySimplifiedNPcompleteGraph1976,
  title = {Some Simplified {{NP-complete}} Graph Problems},
  author = {Garey, M. R. and Johnson, D. S. and Stockmeyer, L.},
  year = {1976},
  month = feb,
  journal = {Theoretical Computer Science},
  volume = {1},
  number = {3},
  pages = {237--267},
  issn = {0304-3975},
  doi = {10.1016/0304-3975(76)90059-1},
  abstract = {It is widely believed that showing a problem to be NP-complete is tantamount to proving its computational intractability. In this paper we show that a number of NP-complete problems remain NP-complete even when their domains are substantially restricted. First we show the completeness of Simple Max Cut (Max Cut with edge weights restricted to value 1), and, as a corollary, the completeness of the Optimal Linear Arrangement problem. We then show that even if the domains of the Node Cover and Directed Hamiltonian Path problems are restricted to planar graphs, the two problems remain NP-complete, and that these and other graph problems remain NP-complete even when their domains are restricted to graphs with low node degrees. For Graph 3-Colorability, Node Cover, and Undirected Hamiltonian Circuit, we determine essentially the lowest possible upper bounds on node degree for which the problems remain NP-complete.},
  langid = {english},
  file = {/home/mpwd/Zotero/storage/N5XBW7LE/Garey et al. - 1976 - Some simplified NP-complete graph problems.pdf;/home/mpwd/Zotero/storage/VTDZI6W9/0304397576900591.html}
}

@article{gentzenUntersuchungenUeberLogische1935,
  title = {{Untersuchungen über das logische Schließen. I}},
  author = {Gentzen, Gerhard},
  year = {1935},
  month = dec,
  journal = {Mathematische Zeitschrift},
  volume = {39},
  number = {1},
  pages = {176--210},
  issn = {1432-1823},
  doi = {10.1007/BF01201353},
  langid = {ngerman}
}

@article{gerlaInferencesProbabilityLogic1994,
  ids = {gerlaInferencesProbabilityLogic1994a},
  title = {Inferences in Probability Logic},
  author = {Gerla, Giangiacomo},
  year = {1994},
  month = oct,
  journal = {Artificial Intelligence},
  volume = {70},
  number = {1-2},
  pages = {33--52},
  issn = {00043702},
  doi = {10.1016/0004-3702(94)90102-3},
  langid = {english},
  file = {/home/mpwd/Zotero/storage/YCGIA5L4/Gerla - 1994 - Inferences in probability logic.pdf}
}

@book{hailperinBooleLogicProbability1986,
  title = {Boole's {{Logic}} and {{Probability}}: {{A Critical Exposition}} from the {{Standpoint}} of {{Contemporary Algebra}}, {{Logic}} and {{Probability Theory}}},
  shorttitle = {Boole's Logic and Probability},
  author = {Hailperin, Theodore},
  year = {1986},
  series = {Studies in Logic and the Foundations of Mathematics},
  edition = {2. ed, rev. and enl},
  number = {85},
  publisher = {{North-Holland}},
  address = {{Amsterdam}},
  isbn = {978-0-444-87952-3},
  annotation = {OCLC: 241617838},
  file = {/home/mpwd/Zotero/storage/ERMQ8GFR/Hailperin - 1986 - Boole's logic and probability a crit. exposition .pdf}
}

@article{hailperinProbabilityLogic1984,
  title = {Probability {{Logic}}},
  author = {Hailperin, Theodore},
  year = {1984},
  month = jul,
  journal = {Notre Dame Journal of Formal Logic},
  volume = {25},
  number = {3},
  pages = {198--212},
  issn = {0029-4527},
  doi = {10.1305/ndjfl/1093870625},
  langid = {english},
  file = {/home/mpwd/Zotero/storage/3QKV65MU/Hailperin - 1984 - Probability logic..pdf}
}

@book{hailperinSententialProbabilityLogic1996,
  title = {Sentential {{Probability Logic}}: {{Origins}}, {{Development}}, {{Current Status}}, and {{Technical Applications}}},
  shorttitle = {Sentential {{Probability Logic}}},
  author = {Hailperin, Theodore},
  year = {1996},
  publisher = {{Lehigh University Press}},
  address = {{Bethlehem : London ; Cranbury, N.J}},
  abstract = {This study presents a logic in which probability values play a semantic role comparable to that of truth values in conventional logic. The difference comes in with the semantic definition of logical consequence. It will be of interest to logicians, both philosophical and mathematical, and to investigators making use of logical inference under uncertainty, such as in operations research, risk analysis, artificial intelligence, and expert systems.},
  googlebooks = {Iu8pSmBMg\_oC},
  isbn = {978-0-934223-45-4},
  langid = {english},
  keywords = {Algebra,Algebraic logic,Boolean,Mathematics / Logic,Probabilities}
}

@article{harrisonMartingalesArbitrageMultiperiod1979,
  title = {Martingales and Arbitrage in Multiperiod Securities Markets},
  author = {Harrison, J.Michael and Kreps, David M},
  year = {1979},
  month = jun,
  journal = {Journal of Economic Theory},
  volume = {20},
  number = {3},
  pages = {381--408},
  issn = {00220531},
  doi = {10.1016/0022-0531(79)90043-7},
  langid = {english}
}

@article{hornMeasuresBooleanAlgebras1948,
  ids = {hornMEASURESBOOLEANALGEBRAS,hornMeasuresBooleanAlgebras1948a},
  title = {Measures in {{Boolean}} Algebras},
  author = {Horn, Alfred and Tarski, Alfred},
  year = {1948},
  month = mar,
  journal = {Transactions of the American Mathematical Society},
  volume = {64},
  number = {3},
  pages = {467--467},
  issn = {0002-9947},
  doi = {10.1090/S0002-9947-1948-0028922-8},
  langid = {english},
  file = {/home/mpwd/Zotero/storage/HZVS3YWL/Horn and Tarski - MEASURES IN BOOLEAN ALGEBRAS.pdf}
}

@article{johanssonMinimalkalkuelReduzierterIntuitionistischer1936,
  ids = {JohanssonMinimal1936},
  title = {{Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus}},
  author = {Johansson, Ingebrigt},
  year = {1936},
  journal = {Compositio Mathematica},
  volume = {4},
  pages = {119--136},
  issn = {0010-437X; 1570-5846/e},
  langid = {german},
  keywords = {Foundations,logic,philosophy}
}

@incollection{kolmogoroffChapterElementareWahrscheinlichkeitsrechnung1933,
  title = {{Chapter 1. Die elementare Wahrscheinlichkeitsrechnung}},
  booktitle = {{Grundbegriffe der Wahrscheinlichkeitsrechnung}},
  author = {Kolmogoroff, A},
  year = {1933},
  series = {{Ergebnisse der Mathematik und Ihrer Grenzgebiete}},
  edition = {First},
  number = {2},
  pages = {1--12},
  publisher = {{Springer-Verlag Berlin Heidelberg}},
  isbn = {978-3-642-49888-6 978-3-642-49596-0},
  langid = {german},
  annotation = {OCLC: 913643439}
}

@article{lehmanConfirmationRationalBetting1955,
  title = {On {{Confirmation}} and {{Rational Betting}}},
  author = {Lehman, R. Sherman},
  year = {1955},
  journal = {The Journal of Symbolic Logic},
  volume = {20},
  number = {3},
  pages = {251--262},
  publisher = {{[Association for Symbolic Logic, Cambridge University Press]}},
  issn = {0022-4812},
  doi = {10.2307/2268221}
}

@article{nilssonProbabilisticLogic1986,
  title = {Probabilistic {{Logic}}},
  author = {Nilsson, Nils J.},
  year = {1986},
  month = feb,
  journal = {Artificial Intelligence},
  volume = {28},
  number = {1},
  pages = {71--87},
  issn = {00043702},
  doi = {10.1016/0004-3702(86)90031-7},
  langid = {english}
}

@incollection{pascucciDiscreteMarketModels2011,
  title = {Discrete Market Models},
  booktitle = {{{PDE}} and {{Martingale Methods}} in {{Option Pricing}}},
  author = {Pascucci, Andrea},
  editor = {Pascucci, Andrea},
  year = {2011},
  series = {Bocconi \& {{Springer Series}}},
  pages = {15--96},
  publisher = {{Springer Milan}},
  address = {{Milano}},
  doi = {10.1007/978-88-470-1781-8_2},
  abstract = {In this chapter we describe market models in discrete time to price and hedge European and American-style derivatives. We present the classical model introduced by Cox, Ross and Rubinstein in [78] and we mention briefly the pricing problem in incomplete markets. General references on topics covered in this chapter are Dana and Jeanblanc [84], Föllmer and Schied [134], Lamberton and Lapeyre [226], Pliska [282], Shreve [310], van der Hoek and Elliott [329]: we also mention Pascucci and Runggaldier [277] where several examples and exercises can be found.},
  isbn = {978-88-470-1781-8},
  langid = {english},
  keywords = {American Option,Call Option,Hedging Strategy,Risky Asset,Underlying Asset}
}

@article{peirceAlgebraLogicContribution1885,
  title = {On the {{Algebra}} of {{Logic}}: {{A Contribution}} to the {{Philosophy}} of {{Notation}}},
  shorttitle = {On the {{Algebra}} of {{Logic}}},
  author = {Peirce, C. S.},
  year = {1885},
  month = jan,
  journal = {American Journal of Mathematics},
  volume = {7},
  number = {2},
  pages = {180--196},
  publisher = {{Johns Hopkins University Press}},
  issn = {0002-9327},
  doi = {10.2307/2369451}
}

@book{poundstoneFortuneFormulaUntold2006,
  title = {Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and {{Wall Street}}},
  shorttitle = {Fortune's Formula},
  editor = {Poundstone, William},
  year = {2006},
  edition = {1. paperback ed},
  publisher = {{Hill and Wang}},
  address = {{New York}},
  isbn = {978-0-8090-4599-0},
  langid = {english}
}

@book{poundstoneFortuneFormulaUntold2006a,
  title = {Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and {{Wall Street}}},
  shorttitle = {Fortune's Formula},
  editor = {Poundstone, William},
  year = {2006},
  edition = {1. paperback ed},
  publisher = {{Hill and Wang}},
  address = {{New York}},
  isbn = {978-0-8090-4599-0},
  langid = {english}
}

@misc{PredictIt,
  title = {{{PredictIt}}},
  howpublished = {https://www.predictit.org/},
  file = {/home/mpwd/Zotero/storage/ULUCIITW/www.predictit.org.html}
}

@incollection{ramseyChapterTruthProbability1931,
  title = {Chapter 3. {{Truth}} and {{Probability}}},
  booktitle = {The Foundations of Mathematics and Other Logical Essays},
  author = {Ramsey, Frank Plumpton},
  editor = {Braithwaite, Joseph Bevan},
  year = {1931},
  series = {The International Library of Philosophy \$ {{Philosophy}} of Logic and Mathematics 32, {{Philosophy}} of Logic and Mathematics : In 8 Volumes},
  number = {5},
  publisher = {{Routledge}},
  address = {{London}},
  isbn = {978-0-415-22546-5},
  langid = {english}
}

@book{rescherManyvaluedLogic1969,
  title = {Many-Valued Logic.},
  author = {Rescher, Nicholas},
  year = {1969},
  month = jan,
  edition = {First},
  publisher = {{McGraw-Hill}},
  address = {{New York}},
  isbn = {978-0-07-051893-3},
  langid = {english},
  annotation = {OCLC: 11761}
}

@article{savageDifficultiesTheoryPersonal1967,
  title = {Difficulties in the {{Theory}} of {{Personal Probability}}},
  author = {Savage, Leonard J.},
  year = {1967},
  journal = {Philosophy of Science},
  volume = {34},
  number = {4},
  pages = {305--310},
  publisher = {{[The University of Chicago Press, Philosophy of Science Association]}},
  issn = {0031-8248}
}

@incollection{suppesProbabilisticInferenceConcept1966,
  ids = {suppesProbabilisticInferenceConcept1966a},
  title = {Probabilistic {{Inference}} and the {{Concept}} of {{Total Evidence}}},
  booktitle = {Studies in {{Logic}} and the {{Foundations}} of {{Mathematics}}},
  author = {Suppes, Patrick},
  editor = {Hintikka, Jaakko and Suppes, Patrick},
  year = {1966},
  month = jan,
  series = {Aspects of {{Inductive Logic}}},
  volume = {43},
  pages = {49--65},
  publisher = {{Elsevier}},
  doi = {10.1016/S0049-237X(08)71662-8},
  abstract = {This chapter examines a cluster of issues centering on the statistical syllogism and the concept of total evidence. A kind of paradox is alleged to arise from the uninhibited use of a statistical syllogism. It is possible to assign probabilities to at least three kinds of entities: sentences, propositions, and events. To avoid going back and forth between the sentence-approach of confirmation theory and the event-approach of standard probability theory, the chapter uses the event-language but standard sentential connectives to form terms denoting complex events. The chapter discusses the rule of detachment and explains that its application in an argument requires no query as to whether the total evidence has been considered; it has exactly the same status as the rule of detachment in deductive logic.},
  isbn = {978-0-444-53408-8},
  langid = {english}
}

@book{troelstraBasicProofTheory2000,
  title = {Basic Proof Theory},
  author = {Troelstra, A. S. and Schwichtenberg, Helmut},
  year = {2000},
  series = {Cambridge Tracts in Theoretical Computer Science},
  edition = {2nd ed},
  number = {43},
  publisher = {{Cambridge University Press}},
  isbn = {978-0-521-77911-1},
  lccn = {QA9.54 .T76 2000},
  keywords = {Proof theory}
}

@article{turnerAnotherAlgorithmBracket1979,
  title = {Another {{Algorithm}} for {{Bracket Abstraction}}},
  author = {Turner, D. A.},
  year = {1979},
  month = jun,
  journal = {Journal of Symbolic Logic},
  volume = {44},
  number = {2},
  pages = {267--270},
  issn = {0022-4812, 1943-5886},
  doi = {10.2307/2273733},
  abstract = {This short article presents an algorithm for bracket abstraction [1] which avoids a combinatorial explosion in the size of the resulting expression when applied repeatedly for abstraction in a series of variables. It differs from a previous solution [2] in introducing only a finite number of additional combinators and in not requiring that all the variables to be abstracted be treated together in a single operation.},
  langid = {english}
}

@article{urquhartImplicationalFormulasIntuitionistic1974,
  title = {Implicational {{Formulas}} in {{Intuitionistic Logic}}},
  author = {Urquhart, Alasdair},
  year = {1974},
  journal = {The Journal of Symbolic Logic},
  volume = {39},
  number = {4},
  pages = {661--664},
  publisher = {{[Association for Symbolic Logic, Cambridge University Press]}},
  issn = {0022-4812},
  doi = {10.2307/2272850},
  langid = {english}
}

@book{vandalenLogicStructure2013,
  ids = {dalenLogicStructure2013,vandalenLogicStructure2013a},
  title = {Logic and {{Structure}}},
  author = {{van Dalen}, Dirk},
  year = {2013},
  series = {Universitext},
  edition = {Fifth},
  publisher = {{Springer-Verlag}},
  address = {{London}},
  doi = {10.1007/978-1-4471-4558-5},
  abstract = {Dirk van Dalen's popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel's famous incompleteness theorem. Propositional and predicate logic are presented in an easy-to-read style using Gentzen's natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness, Skolem-Löwenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, intuitionistic logic and Kripke semantics is carefully explored. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property are also included. The last chapter on Gödel's first incompleteness theorem is self-contained and provides a systematic exposition of the necessary recursion theory. This new edition has been properly revised and contains a new section on ultra-products.},
  isbn = {978-1-4471-4557-8},
  langid = {english},
  lccn = {QA9 .D16 2013},
  keywords = {Logic,Symbolic and mathematical},
  file = {/home/mpwd/Zotero/storage/587FH3RA/9781447145578.html}
}

@misc{wangProjectionProbabilitySimplex2013,
  title = {Projection onto the Probability Simplex: {{An}} Efficient Algorithm with a Simple Proof, and an Application},
  shorttitle = {Projection onto the Probability Simplex},
  author = {Wang, Weiran and {Carreira-Perpiñán}, Miguel Á},
  year = {2013},
  month = sep,
  number = {arXiv:1309.1541},
  eprint = {1309.1541},
  eprinttype = {arxiv},
  primaryclass = {cs, math, stat},
  publisher = {{arXiv}},
  doi = {10.48550/arXiv.1309.1541},
  abstract = {We provide an elementary proof of a simple, efficient algorithm for computing the Euclidean projection of a point onto the probability simplex. We also show an application in Laplacian K-modes clustering.},
  archiveprefix = {arXiv},
  keywords = {Computer Science - Machine Learning,Mathematics - Optimization and Control,Statistics - Machine Learning},
  file = {/home/mpwd/Zotero/storage/AIEY7GNP/Wang and Carreira-Perpiñán - 2013 - Projection onto the probability simplex An effici.pdf;/home/mpwd/Zotero/storage/2K9UZM4V/1309.html}
}

@inbook{wasilewskaChapterHilbertProof2018,
  title = {Chapter 5. {{Hilbert Proof Systems Completeness}} of {{Classical Propositional Logic}}},
  booktitle = {Logics for {{Computer Science}}},
  author = {Wasilewska, Anita},
  year = {2018},
  pages = {179--232},
  publisher = {{Springer International Publishing}},
  address = {{Cham}},
  doi = {10.1007/978-3-319-92591-2_5},
  collaborator = {Wasilewska, Anita},
  isbn = {978-3-319-92590-5 978-3-319-92591-2},
  langid = {english}
}

@article{weathersonClassicalIntuitionisticProbability2003,
  title = {From {{Classical}} to {{Intuitionistic Probability}}},
  author = {Weatherson, Brian},
  year = {2003},
  month = apr,
  journal = {Notre Dame Journal of Formal Logic},
  volume = {44},
  number = {2},
  pages = {111--123},
  issn = {0029-4527},
  doi = {10.1305/ndjfl/1082637807},
  abstract = {We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of  "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of belief are those representable by probability functions from the class appropriate to that logic. Classical Bayesianism, which fixes the logic as classical logic, is only one version of this general approach. Another, which we call Intuitionistic Bayesianism, selects intuitionistic logic as the preferred logic and the associated class of probability functions as the right class of candidate representions of epistemic states (rational allocations of degrees of belief). Various objections to classical Bayesianism are, we argue, best met by passing to intuitionistic Bayesianism—in which the probability functions are taken relative to intuitionistic logic—rather than by adopting a radically non-Kolmogorovian, for example, nonadditive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response among those who have raised these objections. The interest of intuitionistic Bayesianism is further enhanced by the availability of a Dutch Book argument justifying the selection of intuitionistic probability functions as guides to rational betting behavior when due consideration is paid to the fact that bets are settled only when/if the outcome bet on becomes known.},
  langid = {english},
  file = {/home/mpwd/Zotero/storage/KGRF39PS/Disseminate.pdf;/home/mpwd/Zotero/storage/YA26X8Y3/Weatherson - 2003 - From Classical to Intuitionistic Probability.pdf}
}

@incollection{williamsonProbabilityLogic2002,
  title = {Probability Logic},
  booktitle = {Studies in {{Logic}} and {{Practical Reasoning}}},
  author = {Williamson, Jon},
  editor = {Gabbay, Dov M. and Johnson, Ralph H. and Ohlbach, Hans Jürgen and Woods, John},
  year = {2002},
  month = jan,
  series = {Handbook of the {{Logic}} of {{Argument}} and {{Inference}}},
  volume = {1},
  pages = {397--424},
  publisher = {{Elsevier}},
  doi = {10.1016/S1570-2464(02)80011-8},
  abstract = {This chapter discusses probability logic. It highlights probability as a representation of uncertainty, and see how a logic of practical reasoning might involve probability, in order to help agents. The chapter recalls the standard definition of probability, and the standard interpretations of this formal definition. It also recalls the standard definition of probability, and the standard interpretations of this formal definition. The chapter also discusses attempts to incorporate probability into a logic, and go on to investigate a practical question, namely inference. Probability has a rather technical mathematical characterization. Probability has a number of standard interpretations and it presents a brief review of this. The starting point for most theories that integrate probability and logic is to attach probability to logical statements rather than events. The motivation is that logic operates on statements and so it would be natural if a probabilistic logic for practical reasoning has to do the same. A second motivation is that when looking at the application of the mathematical theory of probability, it shows that probabilities are usually posited of a random variable taking a certain value.},
  langid = {english},
  file = {/home/mpwd/Zotero/storage/G246X5AX/S1570246402800118.html}
}

