• README ⤓ .txt 2026-07-17T121634.146 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 2026-07-15T204529.000 000000000031800
  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 2026-07-15T061550.000 000000000019880
  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 2026-07-15T072204.000 000000000015384
  Pearl (1995, 2000). From association to causation. Structural causal models. Do-calculus. Counterfactual reasoning. Foundation for causal AI.
• Conditional Logic ⤓ .md 2026-07-15T054813.000 000000000026728
  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 2026-07-17T120407.600 000000000000984
  Aziz et al. (1996), Baier et al. Continuous-time Markov chains. Probabilistic temporal. Steady-state. Foundation of stochastic model checking.
• Counterfactual Causation ⤓ .md 2026-07-15T052626.000 000000000028144
  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 2026-07-15T073523.000 000000000014248
  Dempster (1967), Shafer (1976). Belief functions. Evidence combination. Distinguishes uncertainty from ignorance. Foundation for evidential reasoning.
• Expected Value Logic ⤓ .md 2026-07-15T235628.000 000000000019584
  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 2026-07-15T060507.000 000000000020384
  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 2026-07-17T120407.600 000000000000936
  Walley (1991), de Finetti, Levi. Sets of probabilities. Lower/upper bounds. Robust Bayesianism. Uncertainty about uncertainty.
• Information Theory Logic ⤓ .md 2026-07-15T063644.000 000000000017240
  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 2026-07-15T052627.000 000000000031376
  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 2026-07-15T071323.000 000000000015136
  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 2026-07-15T065314.000 000000000014872
  Jaynes (1957). Least biased distribution given constraints. Information-theoretic foundation. Exponential families emerge naturally. Foundation for statistical mechanics and machine learning.
• Possibility Theory ⤓ .md 2026-07-17T120407.600 000000000000912
  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 2026-07-17T120407.600 000000000000984
  Li, Oren, Norman (2011), Hunter (2013), various. Extends Dung's abstract argumentation frameworks (see Abstract Argumentation) with probability. Uncertainty in arguments. Probabilistic semantics. Bayesian argumentation.
• Probabilistic Graphical Models ⤓ .md 2026-07-15T065311.000 000000000015040
  Pearl (1988). Graphical structure for probability distributions. Bayesian networks: directed acyclic graphs. Markov networks: undirected graphs. Foundation for probabilistic inference.
• Probabilistic Logic Programming ⤓ .md 2026-07-15T235628.000 000000000015032
  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) and distributional clauses. Distribution semantics. Parameter learning. Foundation of statistical relational AI.
• Probabilistic Logic ⤓ .md 2026-07-15T055421.000 000000000025992
  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 2026-07-17T120407.600 000000000001016
  Sato (PRISM, 1995), Poole, De Raedt. Logic + probability. Probabilistic inference via proof. Relational probabilistic models. Foundation of statistical relational AI.
• Probability Theory ⤓ .md 2026-07-15T052514.000 000000000027664
  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 2026-07-15T071326.000 000000000015104
  De Raedt et al. (2007). Probabilistic logic programming. Facts with probabilities. Distribution semantics. Foundation for probabilistic inference in logic programs.
• Ranking Theory ⤓ .md 2026-07-17T120407.600 000000000000880
  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 2026-07-15T055811.000 000000000022776
  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 2026-07-15T204704.000 000000000008424
  Not sufficient: Truth degrees that are not probabilities (Algebraic/Many-Valued). The epistemic modality without probability (Modal/Epistemic). A game-theoretic decision framework (Game).