• README ⤓ .txt 2026-10-22T165042.936 000000000000824
  Logics that integrate probability, uncertainty, and causation into formal reasoning: systems that attach degrees of belief or chance to formulas, combine logic with probabilistic models, or formalize causal and counterfactual inference. Degree here means probability, distinguishing these systems from the truth-degree logics of the many-valued subdivision.
• Adams Probability Logic ⤓ .md 2026-08-20T074559.000 000000000047248
  Ernest W. Adams, The Logic of Conditionals (1975), building on papers from 1965 onward. A logic of the indicative conditional grounded not in truth but in probability: the acceptability of "if A then B" is the conditional probability P(B|A), and validity is the preservation of high probability from premises to conclusion. Founds the probabilistic (suppositional) treatment of conditionals and connects to nonmonotonic reasoning.
• Bayesian Logic ⤓ .md 2026-08-20T072529.000 000000000036392
  Multiple traditions: Bayesian networks (Pearl, 1988), Bayesian logic programs (Kersting, 2000), BLOG (Milch, 2005). Combines first-order logic with Bayesian probability. Uncertain relational domains. Foundation for probabilistic programming and statistical relational learning.
• Causal Inference ⤓ .md 2026-10-22T085053.000 000000000035832
  Pearl (1995, 2000). From association to causation. Structural causal models. Do-calculus. Counterfactual reasoning. Foundation for causal AI.
• Conditional Logic ⤓ .md 2026-08-20T020437.000 000000000042408
  C.I. Lewis introduced strict conditional to fix paradoxes of material implication (1912). Robert Stalnaker (1968) and David Lewis (1973) developed possible worlds semantics for counterfactuals. Conditional logic generalizes: "If A were the case, then B" — not just "A materially implies B." Foundation for counterfactual reasoning and causal analysis.
• Continuous Stochastic Logic ⤓ .md 2026-10-22T085147.000 000000000055400
  Adnan Aziz, Kumud Sanwal, Vigyan Singhal and Robert Brayton, "Verifying continuous time Markov chains" (CAV, 1996; journal version ACM Transactions on Computational Logic, 2000), which defined the logic and proved its model-checking problem decidable. Christel Baier, Boudewijn Haverkort, Holger Hermanns and Joost-Pieter Katoen extended it with interval-bounded until and a steady-state operator and supplied the numerical algorithms that made it practical ("Model-checking algorithms for continuous-time Markov chains", IEEE Transactions on Software Engineering, 2003). CSL is the continuous-time counterpart of PCTL, which does the same job for discrete-time Markov chains.
• Counterfactual Causation ⤓ .md 2026-08-20T075918.000 000000000040264
  David Hume raised the problem of causation; regularity theories proved insufficient. David Lewis (1973) developed the counterfactual analysis: "C causes E" means if C had not occurred, E would not have occurred. Builds on possible worlds semantics for counterfactual conditionals. Refined through debates with preemption, overdetermination, and late preemption cases.
• Dempster-Shafer Theory ⤓ .md 2026-08-20T074206.000 000000000035008
  Dempster (1967), Shafer (1976). Belief functions. Evidence combination. Distinguishes uncertainty from ignorance. Foundation for evidential reasoning.
• Expected Value Logic ⤓ .md 2026-08-20T080721.000 000000000041632
  Fagin and Halpern's logic for reasoning about probability (1994); Halpern, Reasoning About Uncertainty (2003, 2017), which is the standard treatment; expected-utility operators in decision-theoretic logics from the 1990s onward. Various approaches to reasoning about expected utilities. Decision-theoretic logics (Halpern, Pearl). Expected reward temporal logics. Quantitative reasoning beyond probability bounds. Foundation for economic and game-theoretic reasoning.
• Imprecise Probability Logic ⤓ .md 2026-08-20T110258.000 000000000043128
  Walley's work on imprecise probabilities (1991). De Finetti's work on previsions. Dempster-Shafer theory (1960s-70s). Addresses uncertainty where precise probabilities are unknown. Sets of probability measures rather than single measure. Robust reasoning under ambiguity.
• Imprecise Probability ⤓ .md 2026-08-20T105848.000 000000000055408
  Peter Walley, Statistical Reasoning with Imprecise Probabilities (Chapman and Hall, 1991), which unified the field around coherent lower previsions and a behavioural interpretation. The ancestry is long: Boole (1854) computed bounds rather than values where the data underdetermine a probability; Keynes (1921) argued some probabilities are not comparable at all; Smith (1961) and Williams (1975) developed betting-rate accounts with a gap between buying and selling prices; Dempster (1967) and Shafer (1976) gave a special case; Isaac Levi, The Enterprise of Knowledge (1980), argued for convex sets of credal states as the representation of rational belief.
• Information Theory Logic ⤓ .md 2026-08-20T105601.000 000000000039576
  Shannon's information theory (1948). Logical formulations by various authors. Entropy and information as logical measures. Minimum description length. Connections to algorithmic information theory (Kolmogorov complexity).
• Interventionist Causation ⤓ .md 2026-08-20T084005.000 000000000041608
  Judea Pearl's Causality (2000, 2009) developed the interventionist/structural approach, building on his work on Bayesian networks and the do-calculus. James Woodward's Making Things Happen (2003) provided philosophical foundations. Extends work by Sewall Wright (path analysis), Haavelmo (econometric interventions), and Rubin (potential outcomes).
• Markov Logic Networks ⤓ .md 2026-08-20T110004.000 000000000038048
  Richardson and Domingos (2006). Combine first-order logic with probabilistic graphical models. Weighted formulas as soft constraints. Foundation for statistical relational learning.
• Maximum Entropy ⤓ .md 2026-08-20T105717.000 000000000039776
  Jaynes (1957). Least biased distribution given constraints. Information-theoretic foundation. Exponential families emerge naturally. Foundation for statistical mechanics and machine learning.
• Possibility Theory ⤓ .md 2026-08-20T110357.000 000000000045424
  Lotfi Zadeh (1978), developed by Didier Dubois and Henri Prade (1988 onward). A calculus of uncertainty based on possibility and necessity measures rather than additive probability, suited to incomplete or qualitative information and linked to fuzzy sets.
• Probabilistic Argumentation ⤓ .md 2026-10-22T085318.000 000000000055184
  Dung's abstract argumentation frameworks (1995) fix which arguments defeat which and ask which sets survive; the probabilistic extensions add uncertainty to that picture in two incompatible ways. Li, Oren and Norman (TAFA 2011) put a distribution over which arguments and attacks are actually present — the constellations approach. Hunter (2012, 2013) and Thimm (ECAI 2012) instead keep the graph fixed and read a probability on each argument as a degree of belief, constrained by postulates tied to the attack relation — the epistemic approach. Earlier, Haenni, Kohlas and Lehmann's probabilistic argumentation systems (2000) derived degrees of support from Dempster–Shafer theory rather than from a Dung graph.
• Probabilistic Graphical Models ⤓ .md 2026-10-22T165042.936 000000000001008
  Pearl (1988). Graphical structure for probability distributions. Bayesian networks: directed acyclic graphs. Markov networks: undirected graphs. Foundation for probabilistic inference.
• Probabilistic Logic Programming ⤓ .md 2026-10-22T090040.000 000000000054920
  Sato's distribution semantics and PRISM (1995); Poole's independent choice logic (1997), building on his probabilistic Horn abduction (1993); De Raedt, Kimmig and Toivonen's ProbLog (2007). The syntactic variants converged rather than diverged: Vennekens, Verbaeten and Bruynooghe's logic programs with annotated disjunctions (2004) and the causal reading given them by CP-logic (Vennekens, Denecker and Bruynooghe 2009) translate into and out of the others, and Gutmann, Thon, Kimmig, Bruynooghe and De Raedt's distributional clauses (2011) extended the family to continuous variables. The whole group forms the logic-programming half of statistical relational AI, the other half being the weighted-formula approach of Markov logic.
• Probabilistic Logic ⤓ .md 2026-08-20T072025.000 000000000042248
  Nils Nilsson introduced probabilistic logic for AI (1986). Combines first-order logic with probability assignments to formulas. Halpern's work on probabilistic reasoning about knowledge (1990s). Markov Logic Networks (Richardson & Domingos, 2006) combine first-order logic and probabilistic graphical models. Multiple traditions: logical, AI, statistical.
• Probabilistic Programming Logic ⤓ .md 2026-10-22T090047.000 000000000052800
  Two lines meet here. From logic programming: Sato's PRISM (1995), Poole's independent choice logic (1997), De Raedt's ProbLog (2007), where a program denotes a distribution over Herbrand models. From programming-language semantics: Kozen's measure-transformer semantics for probabilistic while-programs (1979, 1981), which gave the first denotational account of a language with random assignment, and its descendants Church (Goodman, Mansinghka, Roy, Bonawitz and Tenenbaum 2008), Anglican and WebPPL, in which any program may be conditioned. Milch et al.'s BLOG (2005) added open universes, where the number of objects is itself unknown.
• Probability Theory ⤓ .md 2026-08-20T071609.000 000000000041032
  Blaise Pascal and Pierre de Fermat's correspondence on gambling (1654) began the mathematical treatment. Jakob Bernoulli's Ars Conjectandi (1713) and Pierre-Simon Laplace's Théorie analytique des probabilités (1812) developed the theory. Andrey Kolmogorov (1933) provided the modern axiomatic foundation using measure theory.
• ProbLog ⤓ .md 2026-10-22T090038.000 000000000053544
  De Raedt, Kimmig and Toivonen, "ProbLog: A Probabilistic Prolog and Its Application in Link Discovery" (IJCAI 2007). The semantics is Sato's distribution semantics, introduced for PRISM in 1995, and shared with Poole's Independent Choice Logic (1997); ProbLog's contribution was to compute with it by knowledge compilation to binary decision diagrams rather than by enumerating proofs. ProbLog2 (Fierens et al., TPLP 2015) recast inference as weighted model counting and extended the language with stratified negation, evidence and annotated disjunctions.
• Ranking Theory ⤓ .md 2026-08-20T105418.000 000000000045296
  Wolfgang Spohn (1988, monograph 2012), originally "ordinal conditional functions." A theory of graded disbelief on an integer scale that combines a qualitative, belief-revision-style structure with a quantitative, probability-like dynamics — bridging AGM revision and Bayesian updating.
• Stochastic Logic ⤓ .md 2026-08-20T110304.000 000000000048496
  Probabilistic model checking emerged 1990s. PCTL (Hansson & Jonsson, 1994) adds probability to CTL. CSL (Aziz et al., 1996) extends to continuous-time. Developed for analyzing randomized algorithms and stochastic systems. PRISM tool (2002) made practical verification possible.
• CRITERIA ⤓ .txt 2026-10-22T180154.561 000000000000840
  Not sufficient: Truth degrees that are not probabilities (Algebraic/Many-Valued). The epistemic modality without probability (Modal/Epistemic). A game-theoretic decision framework (Game).