README⤓ .txt 2026-10-22T165042.936 000000000000736 Logics of knowledge and belief, in which the operators read "agent i knows that" or "agent i believes that," interpreted over epistemic accessibility relations. Multi-agent settings add group notions—common and distributed knowledge—and the dynamics of how information changes.
Action Model Logic⤓ .md 2026-08-20T013327.000 000000000032512 Baltag, Moss, Solecki (1998). General epistemic actions. Product update. Beyond announcements. Foundation of BMS framework.
AGM Belief Revision⤓ .md 2026-08-20T013155.000 000000000035048 Alchourrón, Gärdenfors, Makinson (1985). Rational belief change. Contraction and revision. Postulates. Foundation of belief dynamics.
Autoepistemic Logic⤓ .md 2026-08-20T013937.000 000000000036328 Robert Moore introduced autoepistemic logic (1985) to formalize reasoning about one's own beliefs. An ideally rational agent reasoning about what they know and don't know. Non-monotonic: "I don't believe P, so P is probably false." Related to default logic but based on belief rather than defaults. Foundation for introspective reasoning in AI.
Awareness Logic⤓ .md 2026-08-20T013025.000 000000000031696 Fagin and Halpern (1988). Agents may be unaware of some propositions. Awareness function: what agent considers. Explicit vs implicit knowledge. Foundation for bounded reasoning.
Belief Logic⤓ .md 2026-10-22T085748.000 000000000031936 Hintikka's epistemic logic extends to belief (1962). KD45 as standard doxastic logic. Weaker than knowledge: belief can be false. Introspection: beliefs about beliefs. Foundation for belief revision and multi-agent reasoning.
Common Knowledge Logic⤓ .md 2026-08-20T012837.000 000000000032008 Lewis (1969), Aumann (1976). Knowledge shared by all and known to be shared. Fixed point: everyone knows everyone knows... Foundation for coordination and convention.
Dynamic Doxastic Logic⤓ .md 2026-08-20T014533.000 000000000042976 Segerberg (1995) proposed putting AGM revision inside the object language as a dynamic modality [*φ] rather than as a conditional, which is what allows the theory to escape Gärdenfors' triviality result for the Ramsey test. Van Benthem (2007) and Baltag and Smets (2008) rebuilt the idea on plausibility models, adding conditional belief, safe belief and a family of upgrade operators, and joining belief revision to the reduction-axiom method of dynamic epistemic logic.
Dynamic Epistemic Logic⤓ .md 2026-08-20T014831.000 000000000035816 Plaza introduced public announcement logic (1989). Baltag, Moss, and Solecki generalized to action models (1998). Van Benthem unified dynamic and epistemic traditions. Combines epistemic logic with dynamic updates. Models how knowledge changes through communication and observation.
Epistemic Logic⤓ .md 2026-08-20T012257.000 000000000040408 Jaakko Hintikka's Knowledge and Belief (1962) established epistemic logic as a formal discipline. Builds on modal logic with knowledge and belief as modalities. Extended to multi-agent systems by Halpern, Moses, and others (1980s-1990s). Common knowledge formalized by David Lewis (1969) and Aumann (1976).
Epistemic Temporal Logic⤓ .md 2026-08-20T015147.000 000000000038760 Combines epistemic and temporal logics (1980s-90s). Also called the temporal logic of knowledge. Halpern, van der Meyden, and Vardi developed foundations. Knowledge changes over time; time reveals information. Security protocols, distributed systems need both. Tools: MCK, MCMAS.
Erotetic Logic⤓ .md 2026-10-22T092948.000 000000000041416 Nuel Belnap and Thomas Steel, The Logic of Questions and Answers (1976), building on Belnap's An Analysis of Questions (1963); Hamblin (1958) and Åqvist's imperative-epistemic reduction (1965) are the other founding lines. Andrzej Wiśniewski's The Posing of Questions (1995) and Questions, Inferences, and Scenarios (2013) give inferential erotetic logic, in which questions stand in consequence relations to each other.
Evidence Logic⤓ .md 2026-10-22T224054.000 000000000076368 Johan van Benthem and Eric Pacuit, "Dynamic Logics of Evidence-Based Beliefs" (Studia Logica 99(1–3), 2011, 61–92), interpreted neighborhood models as records of evidence and derived belief from them. Van Benthem, Fernández-Duque and Pacuit, "Evidence and plausibility in neighborhood structures" (Annals of Pure and Applied Logic 165(1), 2014, 106–133; conference version in Advances in Modal Logic 9, 2011), supplied the static axiomatization the 2011 paper left open. Baltag, Bezhanishvili, Özgün and Smets, "Justified Belief and the Topology of Evidence" (WoLLIC 2016, LNCS 9803, 83–103), with the journal version "Justified belief, knowledge, and the topology of evidence" (Synthese 200, article 512, 2022), made the models topological; Özgün's dissertation Evidence in Epistemic Logic: A Topological Perspective (ILLC Dissertation Series, 2017) develops the program.
Justification Logic⤓ .md 2026-10-22T092208.000 000000000043656 Sergei Artemov introduced the Logic of Proofs (LP) in 1995, solving a long-standing problem about the intended provability semantics of intuitionistic logic. Extended to justification logic more broadly (2000s). Replaces the box □φ with explicit justifications t:φ ("t is a justification for φ"). Makes evidence explicit where modal logic leaves it implicit.
Plausibility Logic⤓ .md 2026-08-20T021101.000 000000000035104 Friedman and Halpern (1995), Baltag and Smets (2008). Graded belief and plausibility. More/less plausible worlds. Dynamic belief revision. Foundation for epistemic plausibility.
Preference Logic⤓ .md 2026-10-22T180154.561 000000000000792 Sören Halldén, On the Logic of "Better" (Library of Theoria 2, Lund: Gleerup, 1957), gave the first complete calculus of the comparative value concepts "better" and "equal in value", and Georg Henrik von Wright, The Logic of Preference (Edinburgh University Press, 1963), grown from his Edinburgh lectures, fixed the field's name, its prohairetic calculus, and its disputes. The modal reconstruction over a betterness ordering is due to Johan van Benthem, Patrick Girard and Olivier Roy, "Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences" (Journal of Philosophical Logic 38(1): 83–125, 2009); the dynamics began with van Benthem and Fenrong Liu, "Dynamic logic of preference upgrade" (Journal of Applied Non-Classical Logics 17(2): 157–182, 2007), and Liu's Reasoning about Preference Dynamics (Synthese Library 354, Springer, 2011) is the systematic treatment.
Probabilistic Epistemic Logic⤓ .md 2026-08-20T021531.000 000000000036424 Fagin and Halpern developed probabilistic epistemic reasoning (1994). Combines probability with knowledge. "Agent i assigns probability ≥ 0.8 to φ." Type spaces (Harsanyi). Foundation for Bayesian games and information economics.
Public Announcement Logic⤓ .md 2026-10-22T180154.561 000000000000880 Plaza introduced PAL (1989). Simplest dynamic epistemic logic. Models truthful public announcements. Announces φ: eliminate worlds where φ false. Foundation for more complex epistemic updates. Extensively studied fragment of DEL.
Topological Epistemology⤓ .md 2026-10-22T085801.000 000000000038320 McKinsey, Tarski (1940s), recent: Baltag, Bezhanishvili. Topology for knowledge. Open sets as evidence. Interior as knowable. Spatial epistemology.
Topological Semantics⤓ .md 2026-10-22T090936.000 000000000037440 Tarski and McKinsey (1944). Modal logic via topology. Interior operator = necessity. Open sets = possible. Foundation for spatial modal logic.
CRITERIA⤓ .txt 2026-07-15T161407.000 000000000007584 Boundary: Belief revision appears here (as doxastic modal logic) and in Applications/Knowledge (as postulate-based KR); the modal logic lives here, the AGM machinery there. Justification logic is cross-listed with Alethic. Probabilistic epistemic logics that foreground probability belong in Applications/Probabilistic. Topological semantics is cross-listed with Metatheory/Model-Theory.