README⤓ .txt 2026-07-17T121634.146 000000000000792 Logics for representing knowledge and drawing inferences from it, especially the defeasible, nonmonotonic, and ontological reasoning that formal knowledge systems require. The concern is representation and inference for artificial reasoning, not the epistemic modality itself.
Abductive Logic⤓ .md 2026-07-15T061335.000 000000000018832 Peirce introduced abduction (late 19th c.). Formalized in AI by Pople, Poole (1970s-80s). Inference to best explanation. Given observation and theory, find hypothesis explaining it. Foundation for diagnosis, planning, theory formation.
Abstract Argumentation⤓ .md 2026-07-15T154335.000 000000000026224 Phan Minh Dung introduced abstract argumentation frameworks (1995). Arguments are abstract entities; the focus is on attack relations and acceptable sets. Unified view subsuming logic programming, default logic, and other non-monotonic systems. Foundation for computational argumentation in AI, law, and multi-agent systems.
Action Languages⤓ .md 2026-07-15T062350.000 000000000017800 Gelfond and Lifschitz introduced action language A (1993). Subsequent: B, C, AL, and others. Formalisms for describing action effects. Connects to situation calculus and event calculus. Foundation for planning and reasoning about change.
Adaptive Logic⤓ .md 2026-07-17T120407.600 000000000000848 Batens (1980s+). Dynamic proof theory. Abnormalities. Paraconsistent dynamics. Foundation of defeasible formal reasoning.
Answer Set Programming⤓ .md 2026-07-15T054028.000 000000000026040 Emerged from logic programming semantics: stable model semantics (Gelfond & Lifschitz, 1988) and well-founded semantics. Answer Set Programming (ASP) as a paradigm crystallized in the 1990s-2000s. Non-monotonic, supports negation as failure, defaults, and constraints. Implemented in efficient solvers: Clingo, DLV, WASP.
ASPIC+⤓ .md 2026-07-17T120407.600 000000000000784 Henry Prakken (2010), generalizing the ASPIC framework of Amgoud et al.; developed with Sanjay Modgil (2013, 2018). A general framework for structured argumentation that builds Dung argumentation frameworks from an underlying logical language, rules, and preferences, with rationality guarantees.
Assumption-Based Argumentation⤓ .md 2026-07-15T072305.000 000000000015176 Bondarenko, Dung, Kowalski, Toni (1997). Structured argumentation. Arguments from assumptions. Rules derive conclusions. Attacks via contraries. Foundation for logic-based argumentation.
Autoepistemic Logic⤓ .md 2026-07-15T054406.000 000000000024488 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.
Belief Revision⤓ .md 2026-07-15T055802.000 000000000021816 Alchourrón, Gärdenfors, and Makinson introduced AGM theory (1985). Formalizes rational belief change. Three operations: expansion (adding belief), contraction (removing belief), revision (adding belief while maintaining consistency). Foundational for AI knowledge base maintenance and epistemology.
Bipolar Argumentation⤓ .md 2026-07-17T120407.600 000000000000904 Cayrol, Lagasquie-Schiex (2005). Support and attack. Two relations. Evidence for. Extends Dung frameworks.
Cardinal Direction Calculi⤓ .md 2026-07-17T121634.146 000000000000944 Frank ("Qualitative spatial reasoning about cardinal directions", 1991) gave the two point-based schemes — cone-based and projection-based — that everything since has been a correction of. Ligozat, "Reasoning about cardinal directions" (Journal of Visual Languages and Computing 9, 1998), supplied the algebraic treatment of the projection-based case. Goyal and Egenhofer (1997; "Cardinal directions between extended spatial objects", IEEE TKDE) replaced points with regions and produced the Cardinal Direction Calculus, the model the field now means by the name. Skiadopoulos and Koubarakis ("Composing cardinal direction relations", Artificial Intelligence 152, 2004) found that Goyal and Egenhofer's composition method fails on some inputs and gave a correct one; Liu, Zhang, Li, and Ying (AIJ 174, 2010) settled the complexity.
Circumscription⤓ .md 2026-07-15T054807.000 000000000026008 John McCarthy introduced circumscription (1980) as a formalization of the closed-world assumption and non-monotonic reasoning. "Minimize the extension of abnormality predicates." A form of default reasoning via model-theoretic minimization. Influential in AI knowledge representation alongside default logic and autoepistemic logic.
Commitment Logic⤓ .md 2026-07-17T120407.600 000000000000864 Walton, Krabbe (1995), Singh, Fornara. Dialogue commitments. Speech acts. Social semantics. Foundation of agent communication.
Datalog⤓ .md 2026-07-15T074917.000 000000000014024 1980s database research. Function-free logic programming. Polynomial evaluation. Bottom-up. Foundation for deductive databases.
Default Logic⤓ .md 2026-07-15T053619.000 000000000027128 Raymond Reiter introduced default logic (1980). A formalization of non-monotonic reasoning: conclusions that hold "by default" and can be retracted when contradicting information arrives. Part of the broader study of non-monotonic logics (circumscription, autoepistemic logic). Models commonsense reasoning where we reason with incomplete information.
Defeasible Logic⤓ .md 2026-07-15T054959.000 000000000025440 Donald Nute developed defeasible logic (1980s-1994). Practical non-monotonic reasoning with explicit rules and priorities. Designed for efficient computation unlike some other non-monotonic logics. Used in legal reasoning, business rules, and agent systems. Related to but distinct from default logic and argumentation.
Description Logic ALC⤓ .md 2026-07-17T120407.600 000000000000848 Schmidt-Schauß and Smolka, "Attributive concept descriptions with complements" (Artificial Intelligence, 1991). Attributive Language with Complements; the basis of OWL (W3C, 2004) and of the SH family of extensions. Core description logic. Basis for OWL. Decidable reasoning about concepts and roles.
Description Logic SROIQ⤓ .md 2026-07-15T071022.000 000000000015752 Horrocks, Kutz, Sattler (2006). Foundation for OWL 2 DL. Extends ALC with: role hierarchies, transitivity, nominals, inverse, qualified cardinality. Most expressive decidable DL in wide use.
Description Logic⤓ .md 2026-07-15T053614.000 000000000029272 Evolved from semantic networks and frame systems (1970s-80s). KL-ONE (Brachman & Schmolze, 1985) was influential. The "description logic" family formalized with attention to computational complexity. Foundation for OWL (Web Ontology Language) and the Semantic Web. Balances expressiveness with decidability.
DL-Lite⤓ .md 2026-07-15T071117.000 000000000013800 Calvanese et al. (2007). Lightweight description logic. Polynomial query answering. Foundation for OWL 2 QL. Designed for databases with ontologies.
Dynamic Epistemic Logic⤓ .md 2026-07-15T055804.000 000000000021864 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.
EL Description Logic⤓ .md 2026-07-17T120407.600 000000000000896 Baader et al. (2005). Tractable description logic. Polynomial reasoning. SNOMED CT. Foundation of efficient ontology.
Epistemic Description Logic⤓ .md 2026-07-15T071657.000 000000000014352 Donini et al. (1992). Combine DL with epistemic operators. Knowledge about ABox: K. Introspection: what is known. Foundation for ontology-based epistemic reasoning.
Epistemic Logic⤓ .md 2026-07-15T052511.000 000000000029664 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).
Equilibrium Logic⤓ .md 2026-07-15T073757.000 000000000014000 Pearce (1996). Logic programming semantics. Here-and-there logic. Answer sets as equilibria. Foundation for answer set programming.
Event Calculus⤓ .md 2026-07-15T060701.000 000000000021008 Kowalski and Sergot introduced Event Calculus (1986). Formalism for reasoning about events and their effects. Alternative to Situation Calculus. Based on time points and fluents. Better handles continuous time and narrative.
Fluent Calculus⤓ .md 2026-07-15T061940.000 000000000017552 Thielscher developed Fluent Calculus (1999). Evolution of Situation Calculus. States as explicit objects containing fluents. Addresses frame problem via state update axioms. Foundation for FLUX agent programming system.
Formal Concept Analysis⤓ .md 2026-07-17T120407.600 000000000000920 Wille (1982). Lattice-based knowledge. Objects and attributes. Concept hierarchies. Foundation of conceptual knowledge.
Frame Logic⤓ .md 2026-07-15T073011.000 000000000014344 Kifer, Lausen, Wu (1995). Object-oriented knowledge representation. Frames with logic. Methods and inheritance. Foundation for F-logic systems.
Fuzzy Logic⤓ .md 2026-07-15T055108.000 000000000026192 Lotfi Zadeh introduced fuzzy sets (1965) and fuzzy logic for reasoning under vagueness. Petr Hájek provided mathematical foundations (Metamathematics of Fuzzy Logic, 1998). Practical applications in control systems, AI, and decision making. Distinct from probability: fuzziness is about vague boundaries, not uncertain events.
Horn Logic⤓ .md 2026-07-17T120407.600 000000000000816 Alfred Horn, "On sentences which are true of direct unions of algebras" (Journal of Symbolic Logic, 1951) — the clauses are named for a preservation theorem, not for a computational property, and the computational property was found twenty years later. Kowalski (1974) read Horn clauses as procedures; Dowling and Gallier (1984) gave the linear-time propositional algorithm.
Judgment Aggregation⤓ .md 2026-07-15T063304.000 000000000019760 List and Pettit developed judgment aggregation (2002). Extends Arrow's social choice to logic. Aggregate individual judgments on propositions. Impossibility results: no perfect aggregation. Foundation for collective reasoning and deliberation.
Logic Programming⤓ .md 2026-07-15T074912.000 000000000012968 Kowalski, Colmerauer (1970s). Computation as deduction. Horn clauses. Prolog. Foundation for declarative programming.
Nonmonotonic Logic⤓ .md 2026-07-17T120407.600 000000000000880 McCarthy introduced circumscription (1980). Reiter developed default logic (1980). McDermott and Doyle on nonmonotonic modal logic (1980). Addresses common-sense reasoning: conclusions may be retracted given more information. Central to AI knowledge representation.
Ontology Languages⤓ .md 2026-07-15T073007.000 000000000013680 KIF (1992), OWL (2004). Formal vocabulary for domains. Description logic basis. Semantic Web standards. Foundation for knowledge representation.
Ontology Logic⤓ .md 2026-07-17T120407.600 000000000000848 Schmidt-Schauß and Smolka, "Attributive concept descriptions with complements" (Artificial Intelligence, 1991). Attributive Language with Complements; the basis of OWL (W3C, 2004) and of the SH family of extensions. Core description logic. Basis for OWL. Decidable reasoning about concepts and roles.
Paraconsistent Logic⤓ .md 2026-07-15T053337.000 000000000026792 Stanisław Jaśkowski (1948) and Newton da Costa (1963) independently developed logics tolerating contradiction. Motivated by: inconsistent but useful theories (early calculus, naive set theory), real-world databases with conflicts, dialethism (some contradictions are true). Graham Priest developed dialetheism and Logic of Paradox (LP).
Preferential Logic⤓ .md 2026-07-17T120407.600 000000000000880 Kraus, Lehmann, Magidor (1990). KLM framework. Ranked models. Non-monotonic consequence. Foundation of defeasible reasoning.
Region Connection Calculus⤓ .md 2026-07-17T120407.600 000000000000928 Randell, Cui, Cohn (1992). Qualitative spatial reasoning. Mereotopology. RCC-8. Foundation of spatial AI.
Rough Set Logic⤓ .md 2026-07-17T120407.600 000000000000856 Pawlak (1982). Indiscernibility. Approximations. Incomplete information. Foundation of approximate reasoning.
Situation Calculus⤓ .md 2026-07-15T053616.000 000000000027984 John McCarthy and Patrick Hayes introduced situation calculus (1969) for reasoning about action and change. The frame problem (what doesn't change?) became central. Ray Reiter's solution (1991) using successor state axioms became standard. Foundation for cognitive robotics, planning, and agent programming (Golog).
Tibetan Collected Topics⤓ .md 2026-07-17T120407.600 000000000000928 Tibetan monastic curriculum, systematized 12th-15th c. Cha-ba Chö-kyi Seng-ge, Sakya Pandita, later dGe-lugs codification. Debate training. Collected topics (bsdus grwa) as primer. Foundation of Tibetan Buddhist logic.
Truth Maintenance⤓ .md 2026-07-15T065025.000 000000000016024 Doyle (1979). Track belief dependencies. Reason maintenance under updates. ATMS: assumption-based (de Kleer 1986). JTMS: justification-based. Foundation for belief revision.
Well-Founded Semantics⤓ .md 2026-07-17T120407.600 000000000000912 Van Gelder, Ross, and Schlipf (1988, 1991). A three-valued, uniquely-defined semantics for normal logic programs with negation-as-failure, giving every program a single intended model and standing as the main alternative to the (multiple, two-valued) stable-model/answer-set semantics.
CRITERIA⤓ .txt 2026-07-15T204700.000 000000000009528 Not sufficient: The epistemic modality of knowledge and belief itself (Modal/Epistemic). Degrees of probability (Probabilistic). Rhetorical or dialectical persuasion (Argumentation and Rhetoric).